■9 ■ h i ■ ■ ■ li .i • ••>* ' t ■ i ■ I m H - ■ I I ■ I ■ ■ ' ■ I <'/-v ■ ■ I ■ ■ J-, < I . v-, ,t . ■ I ftafflji OX LIBRARY 3TGRADUAT£ SCHOOL EHBT.OUJF. 03940 NAVAL POSTGRADUATE SCHOOL Monterey, California THESIS OCEANIC MIXED LAYER RESPONSE TO TIDAL PERIOD INTERNAL WAVE MOTION by Rolf John Burger June 1982 Thesis Advisor: R. W. Garwood, Jr. Approved for public release, distribution unlimited T204555 IJnrlassified ticumrr cl4iif»ic»tion or tmii >»oi (w**> Omm Etewgg U SSSSfSKSi ao^ncy N*m i toomwn «».r-»« *~» i~«~n»»« o»«c* REPORT DOCUMENTATION PAGE Ml^oAf NUMII* 1. OOVT ACCESSION NO • Tl K C •">* Jo»eRHINS ORGANIZATION NAME ANO AOONESS Naval Postgraduate School Monterey, California 93940 Master's Thesis June 1982 s. »t»fo»MiMG o*c. *c»o*t xuMiei S. CONTMACT ON GRAMT NOMKHCtj tO. PROORAM CKMCNT. »NOJECT. TASK AUCA * «0»« UNIT NUHICRS 11 CONTNOLLINO OmCE NAME ANO AOONESS Naval Postgraduate School Monterey, California 93940 12. NIPORT OATE June 1982 II. NUMSEM or PAGES 131 IS. SECURITY CLASS.
    <• tipmrt) Unclassified ISa. OECLASSI'lCATION/OOWNGNAOlNG SCHEDULE it. oisTNia UTION STATEMENT (iliMi *»»»r«) Approved for public release, distribution unlimited. ' ,7 O.STNLUT.ON STATEMENT (., .A. .A."-, —r.- /- •«•«* 30. ,1 -.».,-. K—n) I JuP»L tNCNTANY MOTES i, Scy »onos rasas * as " *—••-* ~ "-"» » "•" "^ , , __. Mixed layer modelling, vertical advection and mixed layer modelling, Tidal period internal waves and mixed layer modelling. 10 A.STNACT fC= - ,» — - •>* " ZZZZ -' >«""» » "««» ~""" The purpose of this research was to investigate the effect of tidal - oeri od internal wave vertical motion on oceanic mixed layer dynamics, and to discern the effect upon the diurnal evolution of thermoclines, as observed during MILE (mixed layer experiment). Vertical advection was d^fo aUone9-dimenslonal bulUdel of the ™ixed layer wi th an^as umed linear in z and sinusoidal in time dependence. The rate of mixed layer deepening was therefore due to the combination of vertical motion and entrapment. The first significant result was the finding that the dd ,: < ■ »m AN 7) 1473 coition or I NOV •• is obsolete S/N 010 J-OI4- »S0I I Unclassified SECURITY CLASSIFICATION Or TNI. -AOE f«» « ••**« Unclassified iKMgM Cl *WtC*TlO« a> Twit »»»«<■»— ggjg ggtgggrf. interaction between vertical mixing and vertical motion depended upon the wave frequency and its phase relation to the diurnal heating cycle. Second, linear and non-linear interactions of the wave induced vertical motion with the cyclical boundary conditions can generate two-dimensional Cx-z) struc- ture in the near-surface temperature field of an initially horizontally homogeneous ocean under the influence of horizontally homogeneous surface boundary conditions. Finally, this advective interaction increases the utility of the mixed layer model in single station forecasting. DD FornQ 1473 Unclassified — Approved for public release; distribution unlimited. Oceanic Mixed Layer Response to Tidal Period Internal Wave Motion by Rolf John Burger Lieutenant, United States Navy B.S., University of North Carolina, 1974 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN METEOROLOGY AND OCEANOGRAPHY from the NAVAL POSTGRADUATE SCHOOL June 1982 t NAV^ L MONTEREY, C ABSTRACT The purpose of this research was to investigate the effect of tidal - period internal wave vertical motion on oceanic mixed layer dynamics, and to discern the effect upon the diurnal evolution of thermoclines, as observed during MILE (mixed layer experiment). Vertical advection was added to a one-dimensional bulk model of the mixed layer with an assumed linear in z and sinusoidal in time dependence. The rate of mixed layer deepening was therefore due to the combination of vertical mction and entrainment. The first significant result was the finding that the interaction between vertical mixing and vertical motion depended upon the wave frequency and its phase relation to the diurnal heating cycle. Second, linear and non-linear interactions of the wave induced vertical motion with the cyclical boundary conditions can generate two-dimensional (x-z) structure in the near-surface temperature field of an initially horizontally homogeneous ocean under the influence of horizontally homogeneous surface boundary conditions. Finally, this advective interaction increases the utility of the mixed layer model in single station forecasting. TABLE OF CONTENTS I. INTRODUCTION - 11 A. BACKGROUND DATA ANALYSIS - 12 B. ADVECTION IN MODELLING 14 C. SCOPE OF THIS STUDY 15 II. MIXED LAYER MODEL AND VERTICAL MOTION THEORY — 17 A. MIXED LAYER MODEL 17 1. Boundary Layer Deepening by Entrainment 20 2. Boundary Layer Shallowing 21 B. VERTICAL MOTION THEORY 22 III. EXPERIMENTS - - 24 A. PRODUCTS - 24 B. STANDARDS 26 1. Standard 1 (SI ) - — 27 2. Standard 2 (S2) — 30 C. EXPERIMENTS - - - 34 1. Case I - 36 a. Constant Downwelling (Case la) 37 b. Constant Downwelling (Case lb) 40 c. Constant Upwelling (Case Ic) 43 d. Constant Upwelling (Case Id) 45 2. Case II - - 48 a. Pulsed Downwelling (Case I la) 48 (1) 180° Out of Phase — 50 (2) Maximum Downwelling Before Heating 50 (3) Coupled Heating and Downwelling 51 b. Pulsed Downwelling (Case lib) 53 (1) 180° Out of Phase With Heating — 53 (2) Maximum Downwelling Before Heating 53 (3) Coupled Heating and Downwelling 54 c. Pulsed Upwelling (Case He) 54 (1) 180° Out of Phase With Heating 55 (2) Maximum Upwelling Before Heating 55 (3) Coupled Heating and Upwelling 56 d. (Pulsed Upwelling (Case lid) 56 (1) 180° Out of Phase With Heating 56 (2) Maximum Upwelling Before Heating 57 (3) Coupled Heating And Upwelling 58 3. Case III 58 a. Shallow Initial Layer (Case Ilia) 60 (1) Peak Upward At Hour 7 60 (2) Peak Upward At Hour 1 61 (3) Peak Upward Motion At Hour 19 62 (4) Peak Upward Motion At Hour 13 62 (5) Two-Dimensional Data 63 b. Deep Initial Layer (Case 1 1 lb) 64 (1) Peak Upward Motion At Hour 7 65 (2) Peak Upward Motion At Hour 1 66 (3) Peak Upward Motion At Hour 19 66 (4) Peak Upward Motion At Hour 13 67 (5) Two-Dimensional Data 68 6 4. Case IV — 70 a. Diurnal Wave (Case IVa) 71 (.1 ) Two- Dimensional Data 71 b. Semi-diurnal Wave (Case IVb) 73 0) Six Hour Shift — 73 (.2) Twelve Hour Shift - 75 (3) Two-Dimensional Data 77 5. Case V (Superimposed Waves } 78 IV. CONCLUSIONS AND RECOMMENDATIONS — 82 FIGURES 11 THROUGH 53 — 84 BIBLIOGRAPHY 127 INITIAL DISTRIBUTION LIST — 129 LIST OF FIGURES Hourly parameters, temperature contours and profiles for Case SI 25 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22, 23, 24, Initial temperature profile for shallow layer condition — 28 Initial temperature profile for deep layer condition 31 Temperature profile variation from t-| to t£ under upwelling conditions Pulsed upwelling form Vertical motion-wave form relationship Diurnal wave relationship to model location Phase relationship of Case IVb [six hour shift) - Phase relationship of Case IVb (.twelve hour shift) Same as Figure 1 for Case S2 As Figure As Figure As Figure As Figure As Figure As Figure As Figure As Figure As Figure As Figure As Figure As Figure As Figure Case Case Case Case Case Case Case Case Case Case Case Case Case la, peak motion at hour 18 la, peak motion at hour 24 la, peak motion at hour 5 lb, peak motion at hour 18 lb, peak motion at hour 24 lb, peak motion at hour 5 Ic, peak motion at hour 24 Ic, peak motion at hour 5 Id, peak motion at hour 24 8 38 49 59 72 74 76 MILE spectral analysis 79 34 85 86 87 88 89 90 91 92 93 94 95 96 97 25. As Figure 1, Case lid, peak motion at hour 5 98 26. Case He and lid, peak motion at hour 18 99 27. As Figure 1, Case Ilia, peaks at hours 7 and 19 100 28. As Figure 1, Case Ilia, peaks at hours 1 and 13 101 29. As Figure 27, reversed direction of the peak motion 102 30. As Figure 28, reversed direction of the peak motion 103 31. Contours for Case Ilia in two dimensional mode 104 32. Profiles for hours 6 and 12 in two dimensional mode, Case Ilia 105 33. Profiles for hours 18 and 24 in two-dimensional mode, Case Ilia 106 34. As Figure 1, Case Illb, peaks at hours 7 and 19 107 35. As Figure 1, Case Illb, peaks at hours 1 and 13 108 36. As Figure 34, reversed direction of the peak motion 109 37. As Figure 35, reversed direction of the peak motion 110 38. As Figure 31, Case Illb Ill 39. As Figure 32, Case Illb - 112 40. As Figure 33, Case Illb - 113 41. Contours of Case IVa with 4 phases of initial wave 114 42. Profiles for Case IVa 115 43. Profiles for Case IVa 116 44. As Figure 31, Case IVa 117 45. As Figure 32, Case IVa - 118 46. As Figure 33, Case IVa — 119 47. As Figure 1, Case IVb, 2 nhase shifts 120 48. As Figure 31, Case IVb - 121 49. As Figure 32, Case IVb — 122 9 50. As Figure 33, Case IVb — 123 51. As Figure 31, Case Va 124 52. As Figure 32, Case Va - 125 53. As Figure 33, Case Vb 126 10 I. INTRODUCTION In recent years much study of internal waves has focused on the linear and non-linear wave interactions. Models for wave prediction have been developed and tested to match the theory. There have been attempts to measure the internal wave fields in situ. Some of the most useful of these have been the observations of temperature and pressure field variations with depth, providing a basis for computa- tions of the vertical motions and interactions involved. These studies and analyses of data demonstrate the importance of the internal wave field in upper ocean and near surface dynamics. Roth et al . (1981) presented clear evidence that internal waves are not as critical in an analysis of the dynamics of mixing at depth because they have little variability. However, near the surface, where they interact with other phenomena such as cyclical heat flux, wind stress, and other boundary conditions, their effect can be considerable when dealing with the budgets of heat and momentum. Holloway (1980) pointed out that internal waves are not weak waves (in the sense of weak resonant interaction theory) and have a high impact on mixed layer dynamics down to and including turbulent scales of motion. Pinkel (1981) showed that the near-surface wave field has a profound effect on the vertical velocity field in the upper ocean. Some mixed layer experiments such as those by Linden (1975) and Kantha et al. (1977) have shown that internal wave radiation may play an important role in controlling the rate of deepening of a turbulent 11 mixed layer in a stratified fluid. Displacements induced by the turbu- lence in the base of the mixed layer served to form internal waves which removed kinetic energy of motion from the mixed layer. Since this energy is also important in the entrainment process, these induced internal waves, of relatively high frequency, serve to retard deepening of a mixed layer. Townsend (1968) has derived an expression for the rate of generation of the internal waves and their energy by a steady disturbance field which is advected relative to a stratified layer at a constant speed. The theory was extended by Bell (1978) to cover general space-time dependence of the disturbance field. These works indicate that internal waves could be a means of retarding the growth of mixed layers, through the removal of the kinetic energy in the layers, Such studies all indicate that the presence of internal waves should be taken into account as a possibly important factor in the mechanical energy budget which controls mixing. It is hypothesized that internal waves which have periods comparable to the dominant time scales of the atmospheric forcing (surface heat flux and wind stress) will be the most likely to result in an interaction with the entrainment mixing process in terms of a positive feedback (increased mixing) effect. A. BACKGROUND DATA ANALYSIS During the period August-September 1977, a mixed layer experiment (MILE) was conducted at Ocean Station P (55° N, 145° M) in the North Pacific. The depth of the mixed layer varied between about five and thirty meters during the period of the experiment. Temperature was continuously observed at fixed depths for a period of three weeks. A spectrum analysis of this data (See Figure 10 in later section) shows some important features. 12 First, a major spectral peak was at about 12.79 t .02 hours, with secondary peaks at 6.62 J .13 and 3.94 * .06 hours. Lower order spectral peaks are at 4.9 hours, and at several frequencies having periods under 3.5 hours. The peak at 12.79 hours is clearly asso- ciated with the semi-diurnal tide (12.45 hrs.), with the other two peaks at 6.62 and 3.94 hours probably being higher harmonics. At all three depths of the analysis it is clear that the semi-diurnal internal tidal wave, with its harmonics, is the dominant cause of vertical motion at the base of the mixed layer. Second, the tidal peaks, including the harmonics, are very coherent vertically throughout the depths analyzed. They are present in all three depths analyzed, below the layer, and in the mixed layer, with very little frequency or phase shift. Finally, the spectral peaks at other than tidal frequencies are not vertically coherent. Also, there is a large variation in non-tidal spectral densities for observations above and below the thirty meter depth— the top of the seasonal thermocline at this time of year. This suggests that something has happened to the higher frequency waves near the surface making the interpretation of their effect on mixed layer dynamics hard to judge from simple theories. However, at the same time it suggests that the effect of tidal internal waves may be quite easily discerned. These results confirm the work of Pinkel (1981) whose studies showed that of the wave fields in the upper ocean, the tide and its harmonics have the greatest vertical coherence. Studies by Simpson and Paulson (1979) demonstrated the variability of the temperature structure in the upper ocean during the POLE experiment. 13 Shook (1980) showed that these variations, were a response to vertical and horizontal advective processes. In a study of Pacific Ocean ship track temperature data, Butler (1981) found definite cyclical varia- tions in the sea surface temperature structure. From these studies of actual data, it is obvious that (1) the tidal period internal waves and their harmonics are an important source of energy in the upper ocean, and (2) surface layer temperature patch- iness exists in the ocean, and may in part be generated by interaction of mixing and internal wave motion. B. A0VECTI0N IN MODELLING To date little has been published concerning the interaction of tidal -period internal waves and entrainment by the mixed layer. De Szoeke (1980) has discussed advection in the mixed layer as a result of horizontal variability of the surface wind stress. He showed that advection, upwelling and downwelling, was an important parameter in mixed layer dynamics, resulting from the boundary forcing of the wind stress. Cushman-Roisin (1981), Garwood et al . (1981), and Price (1981) also demonstrated that advection can play an important role in the dynamics of the mixed layer, but the interaction with internal gravity waves is not treated. De Szoeke and Rhines (1981) discussed coastal upwelling at length, but the advective motion was conceived as a necessary factor to achieve a realistic balance for surface heating, transport, and mixing, in order to produce observed coastal temperature fields. Price et al . (1978) included vertical advection in the test of a mixed layer formulation during storm conditions. They found that the phase dependence between wind stress and mixed layer deepening, and the mixed layer deepening itself were reasonably simulated. 14 Within this discussion of a limited amount of relevant literature on the advective process it has been shown that vertical advection must play an important role in storm response, coastal circulation, and fronts. No one has examined the role of internal wave motion, on the tidal scale, in the open ocean where the geometry and boundary conditions are rather one-dimensional. In possibly the most relevant previous effort, Spigel (1980) looked at the coupling of internal wave motion and entrainment in a two-layer lake model, having a mixed layer which is based upon the one-dimensional turbulent kinetic energy budget. Time scales of internal wave motion, wave decay, and entrainment were widely separated. Using a seiche effect in a basin, he demonstrated that internal waves did in fact play an important role in the entrainment zone. With this background it was believed that the time has come for an investigation of the effects of internal vertical motion in the oceanic mixed layer. The motion is there. Observations show that it dominates Eulerian measurements in the upper thermocline. The importance of this motion to mixed layer evolution needs to be established, C. SCOPE OF THIS STUDY The scope of this initial study shall be confined to a limited number of wave frequencies. There is insufficient time to concentrate on all the types of internal vertical motion, and all of the possible couplings and interactions in this thesis. The purpose of this initial research was to investigate the effect of dominant tidal-period internal 15 wave vertical motion on oceanic mixed layer dynamics, and to discern the effect upon the transient thermocline as observed during the mixed layer experiment. The effects of the vertical motion are explored using a one-dimensional bulk model of the mixed layer originally pro- posed by Garwood (1976,1977) and expanded here to include a prescribed vertical velocity. The first hypothesis to be examined is can alteration of the existing mixed layer model be reasonably done? Can a relatively simple mathematical transformation be applied to include a prescribed vertical motion without altering the basic physics of the entrainment process? The study will show that this in fact can be done, as revealed by a careful examination of the interactions at each step of the alter- ation of the original model. A second hypothesis to be examined is that vertical motion produced by long period internal gravity waves for which the Rossby number is small, through interaction with cyclical boundary conditions (wind stress and heat flux) can produce two-dimensional (x-z) structures in the temperature field of a simple infinite ocean having horizontally homogeneous surface boundary conditions. An objective will be to demonstrate the frequency dependence of the internal vertical motion upon the phases of the cyclical heat fields, and the wind stress. It will be shown that there is a non-linear interaction between super- imposed diurnal and semi-diurnal internal tidal waves. Finally, this study will show the relative strengths of the resultant two-dimensional structures, and relate these to their importance in forming an improved thermodynamic ocean model. 16 II. MIXED LAYER MODEL AND VERTICAL MOTION THEORY A. MIXED LAYER MODEL To study the effects of internal vertical motion on mixed layer evolution, the Garwood (1976*1977) mixed layer model was used in a one- dimensional form. Garwood developed an ocean mixed layer model using the Navier-Stokes equation of motion with the geostrophic component eliminated, the continuity equation for incompressible water, the heat equation from the first law of thermodynamics, the conservation of salt equation, and a linearized equation of state. The entrainment hypothe- sis depends upon the relative distribution of turbulent energy between horizontal and vertical components and is offered as a plausible mechanism for governing both entrainment and layer retreat. Garwood suggested that planetary rotation influences the dissipa- tion of turbulence for deeper mixed layers and enables a cyclical steady state to exist on an annual basis. Furthermore, the rate of entrainment for the stable regime cannot be a simple linear extrapolation of the unstable situations. Unlike the atmospheric boundary case, most of the solar radiation does not penetrate the layer. Therefore, downward turbulent heat flux in the oceanic boundary layer is as important as the upward flux during the course of both diurnal and annual cycles. The non-linearity of the interface entrainment tendency parameter, which is greatest for stable surface boundary conditions, results in a modulation of the long term trend of the mixed layer depth by the diurnal component of surface heat flux. In this model, buoyant pro- duction is somewhat more efficient than shear production as a source 17 of energy for vertical mixing because of its unique effect on the vertical component of the turbulent velocity. The governing heat equation for this model assumes two forms: one for the mixed layer, the other for below the mixed layer. For the mixed layer, the equation has the form .0 a = (w'T'). - (wY) +_aa/,Qdz where < > denotes the mixed layer average and Q is the net heat flux, a product of downward solar radiation, upward turbulent heat flux to the surface, and surface back radiation. Below the mixed layer the heat equation becomes di = -a(wT) + agQ + Kd2T 'p dt dz pC0 dzT (2) where K is the eddy viscosity, and -d(wT)/dz is the term added for the vertical motion. The buoyancy flux at the entrainment zone is modelled according to aq(77).h = -<"77>"2 h t3} which is derived from the local turbulent kinetic energy (TKE) budget where z = -h (3a) In the entrainment zone, the buoyant damping attributed to (w'T' ) is assumed to be balanced by the convergence of TKE flux. This convergence is modeled as a function of the TKE kinetic energy components and the vertical distance over which this energy must be transported. and <£> are the bulk values of the vertical component and the total TKE, 18 respectively. The prognostic equations for these mixed-layer turbu- lence variables are derived using the bulk second-order closure methods of Garwood (1977), and are J_(_h<|>) « muj - ggh(7Tr)_h + aghftw?"). + (77). 1 dt x 2 ' 2R* 2 - (<¥>,/z + fh)<¥> (4) i (h) = aghfd/T"') h + (7t\ ' + JT- 2 — L =h °-J where ( -3)"2 - (l/2+fh) (5) U*- (r/p )V2 with r being the magnitude of the surface wind stress and p is the air density, assumed to be a constant, and aghAT (S? + Av2) R? = aghAT is the bulk Richerdson number. The change in the total TKE, , is a function of wind stress shear production, entrainment shear production, bouyant production/damping, and dissipation. The change in the vertical component, , is a function of bouyant production/damping, pressure redistribution, and dissipation. The quantities AT, Au, and Av are the jump values between the mixed layer (assumed to be vertically uniform), and the underlying stable waters. These bulk TKE equations are solved algebraically assuming quasi-steady state for the TKE budgets 19 and _d_(h) = 0 dt J_(h) = at With this assumption the computed values of and are in phase with the surface boundary conditions— the wind stress, ftu£, and the buoyancy flux, agCw'Dg. Once the entrainment bouyancy flux is known from (3), the downward fluxes of momentum associated with entrainment at the base of the mixed layer, (w'u')_h and (5Tvr) . are given by < '\ * / >*.ii -(wu).h = weAu = -(wT).hJ4u (6) AT -<»7Lh = weA» = -I.tIjI (7) Here the entrainment velocity is < -~>\ AT (3) and the sntrainnent velocity is also defined as wa as dh + w K e TT "h (9) if wa is greater than zero. If w is not greater than zero, equations (10) and (11 ) are applied. 1 . 3oundary Layer Deepening by Entrainment The entrainment heat flux (w'T* ) u is determined algebraically from (3), and the steady-state forms of (4) and (5) in terms of given values of u+, (w*T' ) , h and R. . This heat flux is then applied to the given temperature profile. The new h and new momentum and temperature 20 profiles are unique solutions provided that (i) the mixed layer is homogeneous, (ii) the value of h is just large enough to prevent unstable density profiles (dT/dz greater than zero), and (lit) heat is conserved. 2. Boundary Layer Shallowing Shallowing occurs when there is adequate vertical turbulent energy to transport heat down to the base of the existing mixed layer. The depth at which the vertical heat flux (w'T1) vanishes establishes the new layer boundary, and will be the base of the new mixed layer. In this model, this occurs when (w'w1 ) approaches zero. Then (3) is no longer applicable, and the steady state forms of (4) and (5) reduce to 0 = mu? - (w2+fh) + agh(wf)0 * 2 (10) 0 - <£>** - ('/2 + fh) + agh(wrfr)ft 3 2 (11) Without the planetary rotation term, or if the downward surface buoyancy flux is dominant, h is proportional to the Obukhov length scale L = u*/ag(w'T')0 If, on the other hand, (wT") = 0, h is proportional to u /f. In o general, however, the depth of the shallowing mixed layer is a function of the two non-dimensional parameters, h/L and hf/u*. Heat and momentum are conserved in the profile specifications and, because the mechanical energy budget requires conservation of potential energy on the time scale of the turbulence, a numerical procedure is used that also preserves potential energy. This is 21 intended to ensure that the deepening rate is as correct as possible when the mixed layer deepens to its former position. B, VERTICAL MOTION THEORY 3y following a water particle as it is vertically advected by a prescribed velocity field, w(x,z,t), the distortion of any temperature profile, T(z), after a small, but finite length of time, (At), may be computed by non-linear theory. If we assume is prescribed, then w st - Az COS (cot + Kx) "0 O2) dz = - Azcos(a>t ♦ kx) dt D (13) This may be reformed and integrated •t2 fflz = /-A C08(wt + kx)dt where a water particle starting at time t-j at position z-j is advected to position z2 at time t2. Or following any constant isotherm initially at position z-| , to z2 at t2 gives z, = z, exp{_A_[ sin(ot2 + kx) - sinM, +kx)]} cuD U4j If t = t2 - t] « w"' , then z2 S z, exp{AAt[cos(w(t, + J.) + kx)]} or H 2 z,eR (16) 22 which is the general form approximated by the progression of equations in this study of internal vertical motion. Internal vertical motion is applied to the mixed layer model through equation (10). dh/dt, due to the internal vertical advection, w , , is derived from equation -n (16). For future study, the salinity budget can be handled in a like manner. 23 III. EXPERIMENTS A. PRODUCTS The products used to identify features in the model runs and used for comparison are: 1. Table (Sample Figure la) showing the hourly change in the mixed layer primary variables: H is the mixed layer depth in meters. T is the mixed layer temperature in degrees centigrade. S is the mixed layer salinity in parts per thousand. TAU is the surface wind stress in dynes per square centimeter. QNET is the net heat flux out of the mixed layer in watts per square meter. WDD is the value of the vertical motion parameter affecting the model in centimeters per second. DH is the change in mixed layer depth due to the vertical motion for that time period. 2. Contours of the temperature variation, T(z,t), (Sample Figure 1) between z * 0 and z * -60 meters over the initial 24 hours of the model run. Varying resolution is used to better resolve the evaluation of T(z,t). Temperature contours are in degrees centigrade. 3. Contours of temperature variation similar to 2, in a quasi two- dimensional mode. This is accomplished by running the model 24 times, each time passing the prescribed vertical motion through the 24 hour cycle of the model at a different, progressive phase. The 24 runs are then sorted by hour giving 24 data sets of 24 independent points with a spatial separation of kx from hour one through hour twenty-four. 24 1 Ml I I II I I I I I 1 1 I II I II I I l|l 1 I 6. 3 14. 956 34 000 0. 50 3. s 0. 0 0.0 1 2 7. 3 14. 939 34. 000 0. so -100. 8 0 0 0.0 1 3 S. 0 14 935 n 000 0. 50 -184. 3 0. 0 0.0 1 4 s. S 14 939 34 000 0. SO -248. 4 0 0 0.0 1 5 9 3 14 949 34 000 0. 50 -288. 7 0. 0 0.0 1 o 9 2 14. 9SS 34 000 0. 50 -302. s 0 0 0.0 1 7 9. 5 14 969 34 000 0 SO -288. 9 0 0 0.0 l a 9. a 14. 976 34 000 3 SO -24a 7 0 0 0.0 1 9 .: l 14 978 34 000 0 50 -184 7 0 0 0.0 1 10 10. 4 14 974 34 000 0 50 -101 3 0 0 0.0 1 u 10 7 14 963 34 000 3 50 4 I 0 0 0.0 1 1] 11 1 14 943 34 000 0 50 100 2 0 0 0.0 1 1] 11 4 14 926 34 000 0 50 100 8. 0 0 0.0 1 14 11 a 14 909 34 000 0 50 100 3 0 0 0.0 1 15 12 1 14 393 34 000 3 SO 100 a 0 0 0.0 : 16 12 4 14 377 34 000 3 50 100 8 0 0 0.0 1 17 12' 7 14 362 34 300 0 50 100 8 0 0 0.0 1 19 13 3 14 947 34 000 0 50 100 8 0 0 0.0 1 19 13 3 14 933 34 ooo 3 SO 100 9 0 0 0.0 1 20 13 6 14 919 34 300 3 50 100 8 0 0 0.0 1 21 13 9 14 906 34 000 0 50 100 a 0 0 0.0 1 23 14 1 14 793 34 000 3 50 100 a 0 0 o.o 1 23 14 4 14 781 34 000 0 50 100 a 0 0 0.0 1 24 :4 7 14 767 34 000 3 50 100 3 0 0 0.0 2 I 14 9 14 762 34 000 0 so - 3 5 0 0 0.0 : 2 15 1 14 762 34 000 ) 50 -100 8 0 0 0.0 2 J IS 2 14 768 34 000 0 5 0 -194 3 3 0 0.0 : 4 15 3 14 111 34 300 0 SO -248 4 0 0 0.0 2 5 15 3 14 789 34 300 0 5 0 -288 7 0 0 0.0 ; -> 15 4 14 801 34 000 0 SO -302 S 0 0 0.0 2 7 IS 4 14 314 34 000 0 so -288 9 0 0 0.0 2 3 15 5 14 923 34 000 0 >0 -248 7 0 0 0.0 2 9 IS 6 14 929 34 000 3 50 -184 7 0 0 0.0 2 10 15 7 14 930 34 300 0 50 -101 3 0 0 0.0 2 11 15 9 14 325 34 000 0 50 4 1 0 0 0.0 2 12 16 . 14 314 34 000 3 SO 100 2 0 0 0.0 2 13 .5 3 14 303 34 000 0 50 100 8 0 0 0.0 2 14 IC S 14 793 34 300 0 5 0 100 3 0 0 0.0 2 15 16 6 14 783 34 000 1 5 3 100 a 0 0 0.0 2 16 16 I 14 773 34 .000 0 5 0 100 a 0 0 0.0 2 17 17 0 14 763 34 .uoo 0 50 loo 8 0 0 0.0 2 18 17 2 14 "53 34 .000 0 5 0 ioo a 0 .0 0.0 2 19 17 4 14 743 34 .000 0 50 100 8 0 0 0.0 2 20 17 5 14 734 34 000 0 SO 100 a 0 .0 0.0 2 21 17 7 14 .725 34 300 0 50 100 8 0 .0 0.0 2 22 17 .9 14 .716 34 .000 0 50 100 .8 3 .0 0.0 2 2 J IS . 1 14 . 707 34 .ooo 0 .SO 100 .8 0 .0 3.0 2 24 19 . 2 14 .697 34 . 000 0 50 100 .8 0 .0 0.0 (a) X — 0.301 40 (-;_ soC —14.015- -13.242" -12.408- oO I i I i : I ' i ! I i i J I I I I I I I I I l., TIMETHR) (b) i\ _.. :i.3SS0 ....3390 .4.9340 .1.3330 l». 3*80 14.3S80 : 4 . 9890 14.3750 ..31!-. :..963G 14.1*30 . . i»5 3 :*.30S0 ..?323 I4.877B 14.9620 .3.5: ...9320 14. 9190 14.9050 ». -330 14.7670 S. 2613 '.2940 9.0111 3.4999 9.3230 of hourly values of H is the entrainment ed layer temperature ,yer salinity in o/oo.7 nd stress in dynes/cm", flux in watts/mV WDD n parameter. DH is the d layer depth due to n cm. (bl The contours over a 24 hour period to (c) Successive temperature ie through hour twenty four, true to the temperature Succeeding profiles are 13.00 13.50 -.:0 m.SO 15.00 *E^P. fRELRT [VE TO FIRST) 25 It is assumed that there is a two-dimensional internal wave in x and z passing through this ocean system. Heat flux and wind stress are taken to be the same at all points, with no interaction between any of the points (advection is limited to the vertical). 4. Progressive temperature profiles, T(z), to a depth of 60 meters (Sample Figure lc). Only the first profile matches the horizontal temperature scale which is degrees centigrade. The remaining profiles have been consecutively offset. The accompanying table has the mixed layer temperatures in degrees centigrade, and the mixed layer depth in meters. 5, Progressive temperature profiles as in 4, but in the two- dimensional mode of 3. Profiles are offset from the first, again, to provide an insight to the two-dimensional nature to the data. B. STANDARDS Prior to the examination of the addition of vertical motion to the mixed layer model (MLM), it is beneficial, here, to examine the results of running the mixed layer model in the two modes which will be used as the standards for comparison with the vertical motion modelling experiments. Both standard cases are runs of the mixed layer model from which the effects of evaporation and precipitation have been removed. This has been done to aid in the interpretation of later results by limiting the number of interaction variables to a manageable quantity. The first standard is a run of the MLM in the primarily wind- driven deepening mode. The second standard is for the MLM in a cycli- cal shallowing/deepening response to a strong downward heat flux. 26 1. Standard 1 (SI) This run was initialized with a temperature profile having a surface and mixed layer temperature of 15.0°C. At 5.0 m the initial temperature decreases linearly with the form T(z) = T, - 5.0 X IO"4(Z-H) Where Z is the absolute value of z in centimeters, and H is the mixed layer depth in centimeters. This profile extends to 200m. The result- ing profile is shown in Figure 2. The surface wind stress (TAU) is a constant 0.50 dynes per square centimeter for the entire run. Net heating reaches a maximum of 302.5 watts per square meter at hour six (local noon). Net heat loss after sunset is a constant 100.8 watts per square meter. With no vertical motion the layer deepens continuously over the two-day period of the model run (Figure 1 ) , as expected for pri- marily wind-driven mixing. In examining the first twenty-four hour period it is seen that the mixed layer deepens from an initial depth of 4.5 m to a depth of 14.7 m. The layer cools from 15°C to 14.767°C over the period, with a short period of mixed layer temperature increase of six nours related to that time when the net heat flux is sufficient to overcome the cooling attributed to the entrainment of cooler water into the layer. The salinity in the layer remains constant because there is no precipitation or evaporation allowed which could change the surface salinity, and the below layer salinity is assumed to be a constant 34.00 part per thousand. Therefore, there are no sources of water with a salinity other than 34.00 parts per thousand. 27 Sal. %o 5 Temp. °C io 5- 10- 15-J i i a. Ui Q 190- 95- 200-1 33 T It 20 1 I ' I I 1 I ' ' ' Figure 2. Initial temperature and salinity profiles for Case SI 23 The downward solar radiation, Q , increases from sunrise (hour 1) to noon (hour 6), and then decreases to zero at sunset (hour 12.) A constant is assumed for the net upward turbulent heat flux to the atmos- phere, plus back radiation of 100.3 watts per square meter for the entire day. The one-day response to this cycle can be seen in the contours (Figure lb). The nixed layer deepens continuously over the first 24 hours. Below the layer temperature, at any given depth not penetrated as the layer deepens, remains constant over time. In the layer the temperature is seen to cool slightly initially, then warm to a maximum value at about hour nine (1500 local time), and then cool again for the remainder of the period. In the T(z) graph this sequence is seen again (Figure lc). Here it is seen that all of the slopes of the profiles below the layer are the same from hour one to twenty-four, indicating that with no vertical motion, the characteristics below the layer will not change with time. The included table shows the relationship of the temper- ature, in degrees centigrade, and the layer depth, in meters, and indicates the rate and magnitude of the deepening. The rate of deepening (Table 1) reflects the surface boundary conditions at any given time as well as layer depth and stratification below. As the run begins, the layer deepens quickly in response to the surface wind stress and the short distance over which it must act, as seen in equations (3) and (4). At hour one the layer deepens beginning at a shallow value where the wind flux has a high impact from equation (4), during a period where the heat flux into the layer 29 is a minimum. As the heat flux increases and the layer deepens the wind stress is relatively less effective in deepening, and the entrap- ment now effected by equation (5) slows until hour nine when the solar radiation goes to zero, and the deepening rate increases. This increase is relatively small because of the relatively large temperature jump (AT) in the entrainment zone by this time. After hour eleven (1800 local time) the minor heat loss, small wind stress and increased depth involved all act to slowly decrease the deepening rate. Table 1. Deepening Rate in Meters Per Hour for Case SI Hour Deepening Hour Deepening Rate Rate 1 1.7613 2 1.0227 3 0.7271 4 0.4877 5 0.4242 6 0.3221 7 ' 0.2941 8 0.2964 9 0.2904 10 0.2917 11 0.3291 12 0.3580 Standard 2 (S2) 13 0.3296 14 0.3376 15 0.3287 16 0.3017 17 0.3083 18 0.3115 19 0.2759 20 0.2815 21 0.2872 22 0.2703 23 0.2560 24 0.2607 This run is begun with the same initial layer temperature as for standard 1. Here, however, the initial mixed layer depth is taken to be 49,5 meters. At 50.0 meters, the profile again assumes the linear variability of equation (18), extending to 200.0 meters (Figure 3). All other parameters are the same as those of SI except for the prescribed surface heat flux. The net heat flux has increased to 30 T 45- 50- a. Q 185- 190- 195- 200-1 Sa L.^bo 33 5 TEMR C 10 JL 1 15 t T i 34 L_ I JL r i I 20 L I I I I I X r i i Figure 3. Initial temperature and salinity profiles for Case S2, 31 a maximum of 504.2 watts per square meter by assuming an extremely strong solar heating maximum (Q ) of 600 watts per square meter at local noon. In this case the layer depth remains at 49.5 meters for the first hour (Figure 21a) because the wind stress is not strong enough, coupled with the available heat energy, to cause further entrainment at this depth, and the solar heating is not yet strong enough to cause (w'w1) to go to zero so that equations (10) and (11) are applied. By the second hour the net downward surface heat flux and the surface wind stress are sufficient to cause (w'w* ) to go to zero, and a new h is formulated through the solution of equations (10) and (11), forming a new surface mixed layer with a depth of about 18 m. The layer then continues to shallow until hour 6 (local noon) in response to the increased downward heat flux. Stirring by the wind stress is relatively small as its effect is overcome by the buoyancy flux associated with net surface heat flux. The layer temperature increases as long as there is heating sufficient to overcome the minor cooling due to the entrainment of cooler below layer water which resumes at local noon, but is not strong until hour 10 (1600 local time). At that time the layer cools due to the combined effects of the surface heat loss, and the entrainment of the cooler below layer waters. The salinity, again, remains constant because there is no source of water of a salinity other than 34.00 parts per thousand. As shown by the contours (Figure lib) the original layer of 50 meters shallows to hour 6, not forming a distinct layer, since equations (10) and (11) are applied at each hourly step, until hour 7. The transient thermocline prior to hour 7 is weak. This is seen more 32 clearly, perhaps, on the T(z) profiles (Figure lie). The originally sharp interface at 50 meters becomes diffuse with time due to small (KT = 0.2 cm2/s) be low- layer diffusion. This is clearly seen in the T(z) profiles, and it is the reason for the non-horizontal contours near the 50 m depth. The variability of the temperature structure below the newly formed surface mixed layer is a function of the shal- lowing adjustment by equations (10) and (11) as applied from hour two through six. Again it is evident in the T(z) profiles that the profiles keep the same slope below the layer except for the originally sharp interface at 50 meters where diffusion of the layer occurs with time. This diffusion area is also seen to hold at a relatively constant depth with time. The T(z,t) evolution reflects the turbulent kinetic energy budget for this problem (Table 2). The initial decrease in h from a deep layer to a shallow layer is clearly the result of the surface heating and the surface wind stress acting to form a new, warmer, shallower surface layer. Energy is increased in the surface mixed layer due to excessive solar insolation during the day. The Obukhov length is reduced from hour two through six, and the newly forming Tiixed layer adjusts accordingly. By hour seven the solar insolation begins to reduce. As this happens, the Obukhov length increases, allowing the newly formed layer to deepen. Deepening does not keep up with the Obukhov length because of the damping due to the energy transport which must take place during the mixing process. 3y hour 11 the net heat flux is negligible decreasing to a constant surface 33 loss after sunset. The relative magnitude of the depth increase (dn/dt) with time when compared with that of SI is due to the strength of the temperature jump (AT) at the layer, and the available energy in the layer. In SI a AT of the order of ,4°C was encountered, while in S2, due to the slow formation of the new surface layer, a AT of the order .08°C is the maximum encountered. This allows for more rapid deepening. The rate of deepening increases after hour 16 (2200 local time) because, as seen in the T(z) profiles (Figure lie) the AT at the entrainment zone is decreasing with time due to the net upward surface heat flux. Table 2. Deepening Rate in Meters Per Hour for Case S2. Hour Deepening Hour Deepening Rate Rate 1 0.0152 2 -31.4079 3 -1.9247 4 -3.1646 5 -0.9575 6 -0.2935 7 0.3766 3 0.3445 9 0.4944 10 0.5383 11 0.6793 12 0.8371 13 0.8464 14 0.8317 15 0.8252 16 0.8235 17 0.8278 18 0.8404 19 0.8596 20 0.8879 21 0.9186 22 0.9516 23 0.9870 24 1.0256 C. EXPERIMENTS The addition here to the existing theory of Garwood (1976-77) is approached in a step-by-step procedure, gradually increasing the com- plexity of the problem. A quick reference for this progression can be seen in Table 3. A basic assumption that was made in all of the 34 Table 3. Initial conditions, boundary conditions, and progression of vertical motion inputs for all experiments. For all Cases: 1. Net surface heat loss is constant at 100.8 watts/m2. 2. Surface wind stress is constant at 0.5 dynes/cm2. 3. The initial layer temperature is 15.0°C. 4. The salinity is constant to 200 m at 34.00°/oo. 5. No precipitation or evaporation is allowed during the run. 6. The vertical notion is exponentially decreasing to the surface. Maximum motion is held at 36.0 cm/hr at 10 m, except for Case IVb, where it is 18.0 cm/hr at 10 a. Case B. C. I. C. Vertical Motion Qs max. Temp. MLD (watts/m2) Profile (m) 51 400.00 Fig. 2 4.5 None 52 600.00 Fig. 3 49.5 "None la lb Ic Id B. C. Qs max. (watts/mz) I. C Temp. Profile MLD (■) 400.00 Fig. 2 4.5 600.00 Fig. 3 49.5 SI SI SI 32 S2 S2 SI SI SI S2 S2 S2 SI SI SI S2 S2 S2 SI SI SI S2 S2 S2 SI SI SI S2 S2 S2 S2 S2 S2 Constant downwelling during model run. Constant upwelling during model run. Ila SI SI SI Pulsed downwelling, 12 hour cycle. Phase shifted to peak at hours 5, 18, and 24. lib He SI SI SI Pulsed upwelling, 12 hour cycle. Phase shifted to peak at hours 5, 18, and 24. lid Ilia SI SI SI Single diurnal wave passage. Phase shifted to give maximum downward motion at all hours. 111b S2 S2 S2 Hours 1, 7, 13, and 19 discussed. IVa S2 32 S2 Continuous diurnal wave system passage. Same phase shifts as Case III. Hours 6, 12, 18, and 24 discussed. IVb S2 S2 S2 Continuous semi-diurnal wave system passage. Phase shifted as in Case III. Runs with peak motions at hours 6 and 18, and 12 and 24 are discussed. Va S2 S2 S2 Superimposed diurnal and semi-diurnal continuous wave system passage. Both waves in phase. Input phase shifted as in Case III. Vb S2 S2 S2 As in Case Va, but phases of diurnal and semi- diurnal waves varied relative to one another. 35 work was that the vertical motion moved the water up and down, but did not directly induce turbulence (i.e., mixing). This is a valid assumption if no shear is associated with this motion. The cases of progressively complicated vertical motion examined were: 1. Linearly (in z) varying vertical motion, constant over the entire period. a. Upwelling b. Downwelling 2. Linearly varying vertical motion pulsed in time, a. Short daily upwelling/downwelling events, 3. Linear internal wave motion. a. Passage of a single wave pulse through the experimental point over the 24 hour daily cycle. 4. Non-linear wave variations coupled with diurnal and semi- diurnal boundary conditions (heating, wind). 5. Non-linear response to superimposed waves of different periods. Diurnal and semi-diurnal tidal waves are combined and phase- shifted to determine non-linear interactions. 1 . Case I 3oth upwelling and downwelling are realistically induced with the realization that in a mixed homogeneous layer the vertical dis- placement due to a linear w(z) can be shown to be exponential, going to zero at the surface. Mathematically we know that if ft * WU) (18) w(z) m j*Z_ D where D is a scaling depth, it follows that 36 dz = Az dt 0 or ii = Adt Integration from t, to to yields .*P Z2 = *| (19) which is the equation upon which the following work is based, and which agrees with equation (16) derived earlier. The temperature and salinity profiles must reflect "correct" variation if equations (16) and (19) are correct. Upwelling and/or downwelling will not cause isolines to break the surface or each other. Mixing must be done to induce this. Therefore, above the mixed layer depth Tnew and S must equal T ^ . and S ^ when there is vertical motion without mixing or surface exchange. Below the entrainment depth the profiles must be altered to reflect the type of vertical motion (upward or downward) in accordance with equation (16). Figure 4 shows the expected result from upwelling on a temperature profile. The mixed layer depth has decreased from time one to time two (after upwelling), and the slope of the profile below the mixed layer has been decreased. In all the cases the AT at the entrainment zone has been preserved. a. Constant Downwelling (Case la) (Figure 12) The initial conditions used are the same as those for SI (See Table 3). A constant downward vertical motion is introduced giving the vertical motion parameter, WDD, (WDD = A t/D) a value of .03600, which equates to a value of vertical motion of .01 cm/s or 36 cm/hr at 37 m CVJ 5. Ul »*>. "\ «n. ^^ *— • O 0 *. a: 2 / Time *0. to o +-> -o c o u c 2 a. 3 s- a> -o c 3 CM O c o 4-> o 5- Q. (O S_ cu Q. £ CO CJ s- 3 N 38 ten meters. This is a rather large value, but it demonstrates the inter- actions well. The vertical motion is applied beginning the first hour, and is not applied as the initial condition on the temperature and salinity profiles. The result of this downward motion is, as expected, a more rapid deepening of the surface mixed layer (Figure 12a) when compared to SI. Comparing the depth change due to the mixing in this case (Table 4) to the SI mixing, the same sequence of events as described for SI is seen, and the values are comparable, indicating that the physics of the model nas not been altered by the addition of the vertical motion para- meter in the downwelling mode. It is noted that the effect of the vertical motion quickly becomes greater than the effect of mixing due to the large value of vertical mixing assigned in this run of the model. Table 4. Deepening Rate in Meters Per Hour for the Mixing and Vertical Motion of Case la. .Mixing Vertical Motion Mixing Verticle Motion Hour Deepening Deepening Hour Deepening Deepening Rate Rate Rate Rate 1 1.7613 0.2295 13 0.3201 0.5729 2 0.9705 0,2735 14 0.3169 0.6055 3 0.6606 0.3077 15 0.3134 0.6392 4 0.4759 0.3365 16 0.3102 0.6740 5 0.3535 0.3613 17 0.3068 0.7099 6 0.2945 0.3858 18 0.3034 0.7471 7 0.2444 0.4089 19 0.3017 0.7855 3 0.2282 0.4323 20 0.2983 0.8252 9 0.2394 0.4569 21 0.2949 0.8663 10 0.2513 0.4828 22 0.2914 0.9087 11 0.2793 0.5108 23 0.2881 0.9526 12 0.3219 0.5413 24 0.2094 0.9952 The sequence is vividly displayed in the contours (Figure 12b) where it is seen that the temperature contours deepen as time progresses 39 as one would expect in a downwelling case. The surface heating due to the incoming solar radiation is noted again, followed by cooling as the sun sets and heat is then lost at the surface and colder water is entrained at the bottom of the mixed layer. It is also noted that in only twenty-four hours, the vertical motion added here has deepened the layer to almost twice the value of SI. The T(z) plot (Figure 12c) demonstrates the deepening involved and the effects on the temperature profile below the mixed layer. Note the increased slope (dT/dz) with tine, as warmer near- surface temperatures (water) are carried downward by the downwelling. Also, one can see the effect of the preservation of the AT profile at the entrainment zone from the mixing step through the vertical motion progression in the model where at times there is an apparent discon- tinuity in the profile. This does not appear to cause a problem in the execution of the model, and will be seen in many of the following T(z) plots. One can further see that the vertical motion addition has caused a slight decrease in the jump strength of AT at the layer over that in SI. This can be attributed to the reduced mixing for the larger mixed layer depths. Where, with no downwelling a AT of 1.0°C may have occurred in 18 meters, it now occurs at a greater depth. This effect is transmitted into the entrainment zone as this below layer water is mixed in, causing the AT to be reduced. b. Constant Downwelling (Case lb) (Figure 13) The initial conditions are those of S2 (See Table 3). A constant downward motion is introduced equal to that used in the previous case. 40 The result of the downward motion is again, as expected, a more rapid deepening of the layer after the new surface mixed layer is formed through the surface wind stress and heat flux as applied by equations (10) and (11) (Figure 13a). Comparing the depth change due to the mixing here (Table 5) to the S2 mixing shows that the values are of the same order, which shows that the energy relations of the original model are not impaired by the addition of vertical motion in this mode of the model either. Here it is noted that mixing drives the production of a new surface mixed layer beginning at hour 2 (0800 local) (Figure 13b). The shallowing due to the surface heating is dominant until hour seven (1300 local) when the downwelling becomes the dominant factor until hour nine. From hour nine to hour fifteen the effects of mixing and downwelling are of the same order. After hour Table 5. Deepening rate in meters per hour for the Mixing and Vertical Motion in Case lb. lixing Vertical .lotion Mixing Vertical Motion Hour Deepening Deepening Hour Deepening Deepening Rate Rate Rate Rate 1 0.0152 1.8150 13 0.8093 0.6986 2 -33.4052 0.6571 14 0.7343 0.7511 3 -2.5282 0.5885 15 0.7445 0.8059 4 -3.7245 0.4735 16 0.7131 0.8616 5 -1.4432 0.4392 17 0.7029 0.9190 6 - .7286 0.4286 18 0.6768 0.9775 7 0.1233 0.4489 19 0.6716 1.0379 8 0.3275 0.4773 20 0.6628 1.1002 9 0.4266 0.5104 21 0.6420 1.1641 10 0.5787 0.5504 22 0.6316 1.2299 11 0.6446 0.5942 23 0.6224 1.2978 12 0.8003 0.6986 24 0.6120 1.3678 fifteen the downwelling again, slowly, becomes the dominant factor for layer deepening. 41 It is seen that the layer temperature, again, immediately begins to warm (Figure 13c), and in fact, while the dominant factor is the large amount of surface heating, the layer warms at exactly the same rate as in S2. After hour ten the layer again begins to cool, but because of the deepening of the mixed layer due to downwelling, the mixing of the surface wind stress is reduced. This, along with the fact that a deeper layer has available more mass of water to dilute the effect of the entrained water, results in less cooling over the remaining twelve hours. 3ecause of the downwelling effect on diffusing the temper- ature gradient it is also seen (Figure 13b) that the entrainment zone (layer boundary) remains rather diffuse until hour eight, while in S2 it was sharpened by hour six. This helps explain the magnitude of the deepening effect in the period from hour nine to fifteen, though the depth of the entrainment zone is increasing faster than that in S2 and reaches a difference of five meters from that in S2 by hour fifteen. The AT across the bottom of the layer for the downwelling case is slightly less than that in S2, allowing the mixing to be a more impor- tant factor for deepening in this case. The following decrease in the mixing is then due to the ever increasing depth through which the mix- ing must take place. The wind stress must act over distances that are twice as large as those in S2, and although the AT at the layer depth is not as great, the effect of the depth is quite noticeable. The original deep layer is seen to begin to diffuse, but is quickly carried below the 60 meter level of the graphs. As stated above, the new surface mixed layer begins to show a significant AT 42 at hour eight. Extremely close examination of the T(z) profiles for S2 and the profiles for this run does show a smaller AT at the entrainment zone for this case during the period from hour seven to hour sixteen. After hour 16 there is no discernable difference in the AT in the profiles c. Constant Upwelling (Case Ic) (Figure 14) The initial conditions are those of SI . A constant upward vertical motion is introduced beginning at hour one giving the vertical motion parameter, WDD, a value of .03600, or about 36 cm/hr at ten meters. Again, this is high, but it is done with the realization that later work will be with wave motion where this will not be an unrealistic value, and using it here provides a good benchmark for the effects produced by this motion. Table 5. Deepening Rate in .Meters Per Hour for the Mixing and Vertical motion of Case Ic. Mixing Vertical Motion Hour Mixing Vertical Motion Hour Deepening Deepening Deepening Deepening Rate Rate Rate Rate 1 1.7613 -.2214 13 0.4239 -.3026 2 1.1031 -.2526 14 0.4528 -.3079 3 0.6746 -.2675 15 0.4845 -.3142 4 0.6103 -.2796 16 0.4774 -.3199 5 0.4954 -.2873 17 0.2909 -.3189 6 0.3417 -.2892 18 0.2871 -.3178 7 0.3184 -.2902 19 0.3046 -.3173 8 0,3097 -.2909 20 0.3223 -.3175 9 0.3133 -.2917 21 0.3407 -.3183 10 0.3254 -.2929 22 0.2596 -.3163 11 0.3435 -.2947 23 0.2739 -.3148 12 0.3938 -.2982 24 0.2891 -.3138 The result of the addition of this upward motion is, as anticipated, a slowing of the deepening rate of the mixed layer (Figure 14a) when compared to SI . In fact, due to the size of the vertical 43 motion parameter, an effect is produced which almost holds the mixed layer at a constant depth. This is displayed more dramatically after two model days have been executed, and can be seen to reach a near equilibrium condition after four to five days. Comparing the deepening rates due to the effect of the mixing in the model and the vertical motion in this case (Table 5) to the SI mixing it can be seen quite clearly that the effects described for the mixed layer model standard, SI, are still present. From equations (1) and (3) the slightly increased magnitude of the cooling of the mixed layer by entrainment and the subsequent heating are attributed to the reduced depth over which the wind stress and heat flux must be distributed. Again, it can be seen, that the model TKE balance, equations (3-5), is not violated by the addition of this upwelling motion. The layer temperature initially falls (Figure 14a), then rises until 1400 local time. It then falls again in response to the mixing and the surface heating cycle, as in SI. The heating of the layer is not as great here as in the downwelling case (Figure 13), because the entrainment is sufficiently enlarged due to the smaller h, and because cooler water becomes available for entrainment more quickly due to the upwelling. This is more clearly seen in comparing the contoured fields, T(z,t), (Figure 14b) of this case with those of the downwelling case (Figure 13b). By the end of the twenty- four hour period this has resulted in a very strong temperature jump, AT, at the entrainment zone, as is seen best in the T(z) profiles (Figure 14c). It is seen that AT grows with time. The strengthening of the jump, and the lifting of the cooler water is demonstrated clearly by the contours, and it is 44 clearly evident the contours not only lift, but also merge in time, indicating the AT grows with time. This effect is seen in the T(z) profiles by the increased gradient of the profiles with time. Equilibrium is reached in this case as the jump gets too large for the mixing to have an effect greater than the effect of the vertical motion. Equation (8) shows that dh/dt vanishes as we approaches w_n, d. Constant Upwelling (Case Id) (Figure 15) The initial conditions applied are identical to those of S2. A constant upward vertical motion is introduced at hour one of about 36 cm/hr at ten meters, as before. The net result of the vertical motion after 24 hours is a reduced layer depth in comparison to the case having no vertical motion (S2). The total reduction in depth of six meters, however, is not as great as the previous case (Ic). After two days it is seen that the mixed layer is approaching an equilibrium depth of near eleven meters (Figure 15a). The deepening rates (Table 6), when compared to those of S2, demonstrate that the basic model is still preserved in this run. From hours two through five the model is in the shallowing mode, and the new layer depth is established by equations (10) and (11), while there is a massive influx of solar radiation to the sea surface. The increased deepening rate due to the mixing seen from hour twelve through twenty-three is attributed to the effect of equations (1), (4) and (5). The mixed layer is maintained at a shallow level by the upward vertical motion, therefore, the mixing takes place over a much smaller distance than in S2. 45 Table 6. Deepening Rate in Meters Per Hour for the Mixing and Vertical Motion of Case Id. Mixing Vertical Motion Hour Mixing Vertical Motion Hour Deepening Deepening Deepening Deepening Rate Rate Rate Rate 1 0.0152 -1.7509 13 0.9465 -.4751 2 -29.4675 -0.6470 14 0.9470 -.4917 3 -1.3404 -0.5767 15 1.0159 -.5103 4 -2.6147 -0.4639 16 1.0611 -.5298 5 -0.5166 -0.4292 17 1.1449 -.5515 6 0.1312 -0.4186 18 1.2301 -.5755 7 0.3085 -0.4148 19 1.3043 -.6013 8 0.4578 -0.4163 20 1.4087 -.6298 9 0.5885 -0.4224 21 1.5577 -.6626 10 0.6775 -0.4314 22 1.6638 -.6980 11 0.7113 -0.4413 23 1.3743 -.7219 12 0.9078 -0.4578 24 0.6909 -.7208 Further, there is a concentration of energy in this shallower layer. The great variance in the last hour is a direct result of the magnitude of the upwelling, which, by hour four, has set up a large gradient in the temperature (Figure 15b). By hour twenty-four a gradient has been set up with such a large slope that mixing is becoming very difficult. Continued upward motion of this magnitude, without shallow- ing as is seen on the second day, would quickly make it extremely difficult to entrain much water into the mixed layer. The progression in the change of the mixed layer temperature (Figure 15a) shows that as the model is shallowing, governed by equation (10) and (11), the same adjustment takes place as is seen in S2. The temperatures produced are exactly those seen in S2. This is another indication that the model is performing as before. Since we is zero, the upwelling has no effect on the setup of the new layer. If the H values had been listed immediately after the mixing phase of the compu- tation, this could be seen more clearly. After the layer again begins 46 to mix downward, however, the upwelling begins to have some effect on T and h due to the upward transport of the entrainment zone. Though the layer is one to two meters shallower than in S2, the temperature of the layer is the same as that in the deeper standard to hour ten. At hour ten the heat flux of equation (1) has been reduced sufficiently so that wind mixing again becomes the dominant deepening force. At this point the upwelling has moved water cooler than that in S2 at the same time to the entrainment zone. The change in entrainment rate due to the upwelling, the entrainment of cooler waters, and the net surface heat loss after hour eleven combine to produce a cooling of .147°C from the maximum warm temperature, as compared to .109°C for S2. For the mass of water involved, and the relatively short time involved, this is a significant difference. The effect of the upward vertical motion is perhaps best shown in the T^z) diagram (Figure 15c), where it is seen that the model initially adjusts, through equations (10) and (11), to a new surface layer which slowly strengthens, in terms of the jump, AT, as it en- trains. As the process continues the profiles below the layer rise by upwelling and the initial deep interface is smoothed by diffusion until it disappears. By hour twenty-four a sufficiently stable pro- file has been set up to make deepening of the layer more difficult. This indeed is the case in the second day of the run (Figure 15a) as the layer reaches a temporary equilibrium. It is temporary, in that once the profile has been reached which makes deepening sufficiently difficult through equations (4) and (5), the dominant force becomes the upwelling, w_h of equation (9). 47 The contours (Figure 15b) further demonstrate the effect of the upward lifting of the cooler water, as the contours tend to converge with time. The initial interface is quickly lost, as the model smooths this into its uplifted profile. 2. Case II The next step of this progressive series of tests is to explore the effects of a simple pulsed motion varying in time. This is accom- plished by varying the input motion in a sinusoidal pattern. By using the equation w (t) s AA sin ( 2irt + kx) o 4A 24 , • (20) as the particular form of equation (12) applied for this case, where AA is the velocity scale factor such that AA s Az/D is scaled for an appropriate motion at 100 meters, and limiting the value of wQ(t) to only values in one direction (+ or -), and zero, a pattern of motion can be produced such as that seen in Figure 5. A pulse of vertical motion of twelve hour duration is produced, followed by a twelve hour period of no motion. To determine the relationship of this motion with the cyclical boundary conditions one need only shift the phase of the pulse relation. This will cause the motion to peak at varying selected times during any twenty-four hour period run. a. Pulsed Downwelling (Case Ha) (Figure 16, 17 and 13) The initial conditions are the same as those of SI. Three different phase relationships of the downwelling to the cyclical boundary conditions are presented. In the first (Figure 16) the maximum of the downwelling occurs 180° out of phase with the heating 48 z. > -a 3 O UJ 2 s aanindnv 3. S 4-> c o a. -t-> (O C/) i- E T3 O O c o fO at E s- o c 3 "O to 3 Q_ tO 3 O ■M 4-> O 0) > a) •!« s- 4-» to rO to 0) a> S- T 3 ^— * ■*-> OJ •r» c r^ • 1— a. l_ E -a a; — • to (Q s- ■a .c *— * e 4-> o •P— 0) 4-> E O •r— E 4-> f~ +-> «s (T3 o •r- ^— N 4-> X J- ^_— a» > c • • o a. a. •r" .£= c to 0) c > o •n* •*■• o> -t-> C o a; CD •r— > c +J re •r» «o ■>• to 3 T to O" c to OJ o c "P» <3J +J ^^ o; o CJ on - c r— r— a (O 4J O T3 3 H"* ■r— r™" +j i— o s- o to ai to J3 > *— ■ » to U3 dJ J- 3 CD 59 The initial conditions used were those of cases SI and S2. The vertical motion was introduced at hour one, and the amplitude was varied as t varied in equation (21), to give a wave induced vertical motion. This was then run twenty-four times, each time starting at a different phase of the wave, to test the interrelation of the wave input with the cyclical heat flux. For simplicity, only four major phase relation- ships are discussed here, as they will demonstrate the primary effects. Also, here, the two-dimensional field will be discussed for the first time. The wave form of the desired vertical motion does appear in all four of the displayed runs. The difference in each run is the phase of the vertical motion in relation to the heat flux (daily solar heating cycle). a. Shallow Initial Layer (Case Ilia) (Figures 27-33) In all four phase relationships presented, maximum downward motion at hours 1, 7, 13, and 19, the initial conditions are those of SI. The magnitude of the peak upward and downward motions is 36 cm/hr at ten feet, as before. The wave is introduced at hour one, and pro- gresses through the system through hour twenty-four. (1) Peak Upward at Hour 7 (Figure 27). In this case the initial upward motion, hours one through twelve, the heating and the surface wind stress combine to give a slowly deepening layer, which, due to the upward advection of the layer and of cooler, below layer water, is almost .1°C cooler at its maximum temperature than SI. At the end of the upward cycle the layer has deepened about two meters less than SI at the same time, and has set up a slightly larger AT at 60 the entrainment zone. As a result, the following downward cycle pro- duces a smaller effect in combination with the wind stress in deepen- ing than that seen previously. Because of the initial upward motion effects on the temperature profile, the combined effect of wind stress mixing, surface cooling, and the downward motion produce a layer that, after twenty-four hours, is only two meters deeper than SI. Addition- ally, the downward effect of the motion on the temperature gradient is sufficient only to make up about 60 percent of the deviation in temperatures caused by the upwelling motion, as to that of SI. The maximum 8T for this case is .245°C. It, also, produced the deepest layer of the four runs discussed here, over the twenty-four hour period. (2) Peak Upward at Hour 1 (Figure 28). In this case the upward motion was present during the first six hours of the heating cycle only. The downward motion cycle tjjen progressed for twelve hours, followed by six hours of upward motion to complete the twenty-four hour sequence. During the first six hours the layer deepened to within less than one meter of the depth reached by hour six in SI, but the layer temperature is seen to be about .01°C cooler. The reversal of the motion was too late in the heating cycle to overcome that trend, and by hour nine, the time of the maximum surface temperature for SI, this experiment produced a surface temperature that is ,013°C cooler. The layer depth reached here is within half a meter of the SI depth for the same time. The difference is attributed to the initial lift- ing of the entrainment zone. 61 As the downward motion continues, along with the sur- face cooling, the layer deepens more quickly while the cooling of the layer slows as the effect of mixing is reduced. A maximum depth is reacned two hours after the downward motion has stopped, when the upward motion is of sufficient magnitude to overcome the wind stress mixing. The layer becomes shallower from its extreme depth of 15.56 meters to 14.94 meters by hour twenty-four, with associated layer cooling due to surface heat loss, and increased entrainment due to the increased effect of the wind stress mixing. The maximum 8T for this run is ,189°C. The final layer depth is within .3 meters of SI for hour twenty-four. The variations of depth and temperature during the run are obviously much greater than for SI . (3) Peak Upward Motion at Hour 19 (Figure 29). The fact that the downwelling and the heating cycle are in phase, as in Case I la, produces, by hour nine, a layer that is two meters deeper and .006°C warmer than SI for this same time. The following upward motion is sufficient to halt layer deepening at hour sixteen in opposition to the mixing, but is not sufficient to cool the layer as much as for SI. The final layer temperature is .035°C warmer than that in SI, while the final layer depth is about one meter less, though at hour sixteen a depth of 14.2 meters was reached. The maximum 8T for tne mixed layer in this case was ,181°C. (4) Peak Upward Motion at Hour 13 (Figure 30). This case produced the warmest layer temperature at hour nine, though the downward motion was only present during the first six hours of the 62 surface heating cycle. The initial downward motion deepened the layer, and thereby reduced mixing in this period, over the SI case, allowing the surface layer to be heated to 14.988°C, an increase of .01°C over that in SI. The following upward motion was sufficient, hours eleven through fourteen, to hold the mixed layer at a relatively constant depth. This allowed a relatively constant, and strong wind stress entrainment to combine with surface cooling to rapidly cool the layer. The result after twenty-four hours is to produce a layer of about the same depth as that of SI, but one that is slightly cooler. The 8T here was ,237°C, a very noticeable difference from SI, though the final product did not vary much in layer temperature or layer depth. ( 5 ) Two Dimensional Data (Figure 31, 32 and 33) . The two dimensional oceanic field was produced as previously discussed. The data covered here is that of the evolution of the ocean system at hours 6, 12, 18, and 24. By hour six the wave has progressed into the oceanic field, and its effect below the layer is dramatic, (Figure 31a). It has produced a mixed layer that has a mean depth of about 9 meters (initial h was 4.5 meters) with a mean temperature of 14.957°C. A temperature structure, as could be measured at the surface in x, is being formed. The present maximum difference in surface temperatures (in x) is ,016°C. 8y nour twelve (Figure 31b) the effect of the wave is at its maximum, as seen in the amplitude of the contours below the layer. The layer is generally deeper than at hour six with a mean depth of about 11.5 meters. The deviation from the mean is much 63 greater for this time, however. The mean of the layer temperature has gone to 14,950°C, a slight decrease from hour six, but more significant is the deviation of the surface temperatures in the x direction. There is now a very definite variation in x of .951°C. The layer has deepened to a mean depth of about 13 meters by hour eighteen (Figure 31c), with the effect of the wave beginning to be reduced in the system. The mean layer temperature has dropped to 14.846°C, a cooling of almost .05°C in the six hours between illustrations. The surface temperature deviation has reached .091 °C. .Jarm and cold temperature bands are becoming defined in x. The single wave has passed through the ocean by hour twenty-four, and only the remnant of its passage is seen (Figure 31a). In an ocean that is defined by SI conditions everywhere, the twenty- four hour product would be an ocean with a mixed layer depth constant at 14.65 meters, and mixed layer temperature of 14.767°C. With the introduction of a single diurnal wave cycle, a variable condition ocean has been produced. The mean depth of this ocean is 15.012 meters, with local variations of up to +1.73 meters and -1.32 meters, with depths at small x being somewhat greater than depths at large x. The mean layer temperature is 14.764°C, but more importantly, the surface temperature variation is now ,095°C, in a clearly defined pattern. The pattern that exists is that of a narrow zone of rela- tively cool water centered near kx ■ 5, with a wider zone of relatively warmer water centered near kx = 18. Below the layer the isotherms are found to be parallel after the passage of this single wave cycle. b. Deep Initial Layer (Case I lib) (Figures 34-40) The initial conditions for these runs were the same as 64 for S2. The wave cycle passed through the system as in the previous runs (Ilia). The wave form is harder to discern in these runs, but looking at the contours below the original layer (Figures 34-37) the same forms as the previous run are apparent. ( 1 ) Peak Upward Motion at Hour 7 (Figure 34) . As i n the previous deep initial layer cases, the shallowing due to the surface heating drives the model in the first six hours. The coincident up- ward motion during this time combines with the shallowing and mixing to produce a layer that is about 1.5 meters shallower, but at the same temperature as in S2, by hour ten. Two noticeable effects during this period of upward motion are (i) a slight shallowing of the newly formed surface layer, and (ii) the upward transport of cooler below layer water, setting up a larger AT at the entrainment zone for this case over that of the standard. The downward motion then contributes to the deepening of the layer as does the mixing which must initially act over a relatively shallow depth. This entrains cool water, form- ing a quickly deepening and cooling surface mixed layer. As the down- ward motion decreases the cooling slows, and the increase in the depth of the layer is seen to be caused mostly by the vertical motion. Of all the phases examined this produced the deepest layer (30.34m) and has the second coolest layer at the end of the period (15.059°C) in relation to the other three cases discussed. The 8T for this case is .115°C. This is about half that for the shallow layer case discussed previously. The original deep interface can be followed on the contours (Figure 34b) over the twenty-four hour period. During the downward motion it, again, is 65 diffusing, while during the upward case there is a slight reinforce- ment of the interface. (2) Peak Upward Motion at Hour 1 (Figure 35). Again it is seen that the shallowing mode of the mixed layer model, equations (10) and (11), controls the layer development to hour ten. The layer depth reached through the shallowing, upward, and downward motion combination by hour ten has reached a depth that is about .5 meters deeper than that in S2 for the same time. The temperature is the same as S2. Also, the downward motion makes entrainment of water into the mixed layer due to mixing more difficult, such that cooling after hour ten progresses much more slowly than in that of the previous case, and that of S2. The net result in the layer depth of this run is a layer that is about as deep as that of S2 after the twenty- four hour period. The model did not deepen more than S2 due to the dominant upward motion during the last six hours. The mixed layer temperature was slightly wanner than that of S2 at the end of the run (.071°C). Also, it can been seen that the below layer water is somewhat warmer than in S2 for the end of the period, due to the combined effects of the heating and downward vertical motion timing. The 8T for this case is .092°C. This is less signi- ficant than in the previous run. (3) Peak Upward Motion at Hour 19 (Figure 36). Again, the shallowing mode of the model controls the initial ten hour layer temperature adjustment. The downward vertical motion, however, drives the layer two meters deeper during this time causing reduced mixing due to the surface wind stress. The upward motion keeps the layer 66 from deepening as quickly as before after hour twelve. Because of the below layer temperature adjustment by the downward motion and the initial deepening of the layer, the layer, also, does not cool as quickly. This case produced the shallowest final layer depth, and the second warmest layer at the end of the period, relative to the other three runs. The 8T for this case is .103°C, which is about the same as the first case which was 180° out of phase with this run. (4) Peak Upward Motion at Hour 13 (Figure 37). The coincident shallowing, wind stress mixing, heat flux, and cycled vertical motion over the first ten hours produce a surface mixed layer that has the same temperature as S2, and almost the same layer depth (to within less than .5 meters). Below the layer, however, the upward motion has made relatively cooler water available by hour ten (in comparison with S2), and the layer, though not rapidly deep- ening due to the continued upward motion, cools quickly as large quantities of water are entrained over a relatively shallow depth, a trend which continues to the end of the period. The net result is a mixed layer that is 1.5 meters deeper than that of S2, but is also the coolest layer of the four runs. Because of the below layer temp- erature profiles which are set up by the upward motion for the mid- twelve hours, the continued run of this model over a second day gives continued rapid cooling of the layer due to increased entrainment of cooler, upward advected water, and to increased effects of mixing. A noticeable deepening does take place at the end of the period due to the downward motion, which accounts for the fact that this run ended deeper than S2. 67 The 8T for this run is .125°C. This is the largest of the four runs, but it is still only half of the maximum 8T seen for the shallow initial layer case. (5) Two-Dimensional Data (Figure 38, 39 and 40). The two- dimensional oceanic field is produced, here, as previously discussed, for the single wave cycle. The data covered is for hours 6, 12, 18, and 24, A common feature is the varying below layer temperature struc- ture set up because of the introduction of the initial deep layer. Because of this, the changes in the thermocline below the initial deep interface best show the effect of the wave progression through the system. As in the shallow case, by hour six, the wave has progressed into the oceanic system producing some horizontal sea sur- face temperature structure. However, the effect on the surface temperature is almost negligible, in that the variability of the surface temperature in x is only .001 °C. This is due to the shallow- ing mode response of the model over the first six hours. Even with this, however, the depth structure has varied (Figure 38a) so that there has been a change from the constant structure that would be seen in S2 of 11.767 meters for the layer depth, to a layer of mean depth of 11.769 meters . .35 meters, indicating that an adjustment due to the wave is taking place. By hour twelve much more temperature and layer (h(x)) variation is beginning to take shape. At hour twelve the case without the vertical motion has a layer depth of 15.037 meters, and a layer temperature of 15.159°C everywhere. In this case, where the maximum effect of the wave has been reached, the layer depth has a mean of 68 15.231 meters with a deviation of t 2.5 meters. The variability in the surface temperature in x has reached .01 °C. Though the variabil- ity in the surface temperature is not very large, a pattern is again beginning to emerge in the x direction. At small x cooler water is forming, while at large x a band of warmer water is emerging. The layer has continued to deepen to hour eighteen. The layer depth has increased to a mean of 19.46 m, t 3.4 m, and the variation in the surface temperature structure in x has reached .03°C. The warm-cold pattern seen at hour six is repeated and strengthened. Though the temperature difference between warm and cool water is not as great as in the shallow case, the banding of the patches is much more distinct here (Figure 38, Figure 31). At the end of the period the wave has, again, been removed from the system, and only the remnant of its passage is seen. The final layer depth is deeper than in the previous hours, and much deeper than in the shallow case. The variability of h in x is also much greater here than in the shallow case. The surface temperature patchiness is well-defined, but the variability of the temperature in x is only ,035°C. Comparing the two cases, shallow and deep initial layers, it is seen that for the same amplitude wave the model produces two distinct ocean types. For the shallow case an ocean is formed that has a relatively shallow layer with a large temperature varia- tion in the x direction, but with that temperature variation primarily in wide bands. For the deep case a deep surface layer is formed with smaller variability in the surface temperature. However, the temp-, erature structure in x is much better defined. Also in the deep case, 69 the patches of warm and cold water are much closer to each other (in x). This could suggest a mechanism for generating or sharpening SST fronts through surface heating, and internal solitary wave passage. 4. Case IV It was noted in Case III that after twenty-four hours the wave form had passed through the ocean system, and had left behind only the residue of its effect on the system, over and above the standard effects. This can be compared to a solitary wave passing through an ocean system. While this has theoretical advantages, it is not a very realistic prob- lem, in that wave forms seldom take on this sort of motion. One pos- sible exception may be soli tons generated at extreme tidal stages (Apel, 1982). The next progression, therefore is to look at a continuous wave system that passes through the ocean with constant form, until the run is terminated. This is done by simply modifying the mathematics of the previous case to include initialization of the temperature and salinity profiles with the wave form according to the following. We know that w(x,z,t) = AAz cos(cut + kx) and or therefore dt 8h = -/wdt 8h = -AAz 8ln(oit ♦ kx) 70 For initial displacement 8h(x,z,0) - 8h0 therefore 8h0 m -AAz sin(kx) u>D (22) Applying equation (22) to form the initialized layer depth, and com- bining this with equation (16) to initialize the temperature profile, a continuous wave field can now be passed through the model ocean (Figure 7). From this point on the discussion will be confined to the deep initial layer case, S2 standard, and variations thereof. This is done because all the primary effects discussed to this point appear in both the shallow and deep cases, as do the effects to be discussed in vary- ing degrees, and it is not necessary to continuously reiterate this discussion. a. Diurnal Wave (Case IVa) (Figures 41, 42 and 43) Because of the overriding effect of the shallowing mode of the model in the first six hours of the runs, the results produced here were exactly the same as those discussed in Case Illb, for the phase relationships. This was of course expected from the theory. (1) Two-Dimensional Data (Figure 44, 45 and 46). Again, Decause of the dominance of the shallowing mode, the hour 6, 12, 18, and 24 two-dimensional fields produced here are the same as those of Case 1 1 lb for the area of the entrainment zone, and the mixed layer. Below the layer, however, the wave form is now seen to progress through the system in a continuous mode. This is best seen in the contours 71 c o a o 3<3nindnv 0) o E i- o <♦- 0) > 2 c i- 3 to 3 O 3 C O u o 10 c •p» • ■(-> > A3 2 a; -o r— 3 C '!- $- r- 3 Q. ••"■ s OT 72 in which the amplitude of the system remains a constant, but the v/ave form is shifted with time. It can be seen that the patch of warmer waters forms (Figure 44) and takes a phase that barely leads the peak of the wave system. The entrainment zone ( h(x) ) now takes the form of the passing wave system, as would be expected, and yet was not obvious in the previous case. The divergence and convergence of below layer fields is also obvious here, where previously it was not particularly obvious. b. Semi-diurnal Wave (Case IVb) (Figures 47-50) A dominant internal wave system of the temperate oceans is the semi-diurnal tidal cycle. South of 30° N there is also a strong diurnal tidal cycle. A semi-diurnal tidal field can be pro- duced for testing in this model by simply adjusting the frequency of the prescribed w for equation (21), and setting the initial profiles with the appropriate frequency of equation (22) and (17). The amplitude of the motion remains the same as the diurnal cycle case. 3ecause the cycle of wave mixing interactions repeats itself after a 2ir phase shift, which occurs after 12 hours in this case, only the cases of six and twelve hour phase shifts will be discussed. The 18 and 24 hour phase shifts are merely repeats. (1) Six Hour Shift (Figure 47a and b). Figure 8 shows the relationship of the heating cycle to the wave motion in this case. The vertical motion is seen to immediately combine with the shallowing mode of the model through the initialization to give a somewhat shallower initial layer. The shallowing mode of the model holds the layer temperature the same as in S2 to hour six, while the vertical 73 $ \ .00 aanindhv TJ C S_ 3 •r— -a o 4-> s • '- r— o (T3 <4- C •^ 3 i_ o r— a. "3 o c s- s_ a. 3 •r— 4-> •a o i c • r™ fj5 a ai s_ (/) "3 <+- c/1 o OJ ■o *— ** 3 4-) ■M <+- •j— •f- r— -C Q. l/> E < S_ 3 O • .c *^*» i/i X i- •r™ -C V) "— - 0) -Q £ > •^ •— • 4-> OJ i- (/) OJ 03 > CJ o <♦- ai O r-» u CL >> •r— u JZ en c c o •r* • ^ -(-> ■M *J (TJ a r— j3 OJ S- 0) a ai «3 l/l *+- (H 1_ _^ 3 a. to CO $_ 3 74 motion varies the layer depth, and alters the below layer temperature structure. By hour six a half-cycle of the wave has passed through the model point, and a layer has been produced that is almost one meter deeper than S2 at this time, but which has the same layer temp- erature. Continued but decreasing downward motion combines with the downward heat flux until hour nine to slowly deepen the layer, but the layer continues to warm. This process continues through hour ten, though upward motion has begun because the heating and entrainment of relatively warm water are greater than the effect of the resistance to deepening due to the surface heat flux, and the small upward motion. By hour eleven the upward motion dominates, and the layer shallows while it cools slightly due to the increased entrainment. At hour twelve the layer is as shallow as it will ever get, and the first wave has passed. Now decreased upward motion followed by downward motion, combined with surface cooling and mixing through a progressively cooler surface mixed layer quickly increases the layer depth to a maximum of 26.7 meters at hour twenty-one. This is deeper than S2 gets in the entire twenty-four hour period. Yet, the layer is not as cool as in the S2 case. 3y hour twenty-one the upward motion is again dominant and the layer shallows. (2) Twelve Hour Shift (Figure 47c and d). Figure 9 shows the relationship of the heating cycle with the wave in this case. The initialization combines with the vertical motion and shallowing mode to produce an initial layer that is deeper than that in S2, but soon becomes shallower, as the new surface layer is established. By hour six a layer of the same temperature as S2, but .72 meters shallower 75 . ** Ul I • »-^ ^ ^ / 1 5***s % M N X s \ • # ■ % • * 1 eu, \ V. X «x «**» / aanindhv i- O a> to to c o •r— »o o s o CM • ro CD Ln T3 <3- o c o •r"» +-> fO > 4-> to •f- to >> r— ■: 21.7797 5.0830 22.5983 :s.0770 13.6499 24.6369 IS.tSSC 25.5625 (c) Figure 11. Sa for case 52. as figure (1) , except 13.50 rEMP. 14.00 14.50 15.00 [RELATIVE TG -IRST) 5.50 16.00 15.50 34 :av hr a T s ran JNET JOO OH I 1 6 .5 14 .956 34 .000 0 . 50 - 3 .5 0 .03600 22.951 1 2 7 . 7 14 .940 34 .000 0 .50 -100 .8 0 .03600 27.350 1 3 S . 7 14 . 938 34 .000 0 . >0 -184 .3 0 . 03600 30. 774 1 4 9 . 5 14 .944 34 .000 0 .50 -248 .4 0 .03600 33.646 1 5 10 .2 14 .954 34 .000 0 50 -288 . 7 0 .03600 36. 175 1 6 10 .9 14 . 96S 34 .000 0 50 -302 .5 3 .03600 38. 580 : 11 .6 14 .977 34 .000 0 50 -288 .9 0 .03600 40.390 i a 12 .2 14 . 986 34 000 0 50 -248 .7 0 .03600 43. 226 1 9 12 .9 14 .991 34 000 0 .so -184 7 0 .03600 4S.688 i ;o 13 7 14 .990 34 000 0 50 -101 3 0 03600 48. 284 l n 14 4 14 984 14 000 0 30 4 1 0 03600 51.078 1 12 IS 3 14 971 34 000 0 50 100 2 0 03600 54. 130 1 13 it 2 14 960 34 000 0 so 100 8 0 03600 57.287 1 14 17 1 14 9S0 34 000 0 50 100 8 0 03600 60.549 1 IS 18 J. 14 940 34 000 0 50 100 a 0 03600 63.917 1 it 19 1 14 932 34 000 0 so 100 s 0 03600 67. 397 1 17 U 1 14 924 34 000 3 50 100 a 0 03600 70.992 1 IS 21 1 14 915 34 000 0 5 0 100 8 0 03600 74. 707 1 19 22 2 It 908 34 000 0 50 100 8 0 03600 78.551 1 20 23 3 14 901 34 000 0 50 100 8 0 03600 32. S24 1 21 2 4 5 14 395 34 000 0 so 100 8 0 03600 96.630 1 22 25 7 14 899 34 000 0 so 100 8 0 03600 90.873 1 23 26 9 14 884 34 ooo 0 50 100 8 0 03600 9S. 260 1 24 :i 1 14 879 34 000 0 50 100 8 0 03600 99. 519 2 1 :) 1 14 877 34 000 : 50 - 3 5 0 J3600 103.63} 2 2 13 4 14 880 34 000 3 50 -100 a 0 03600 107.626 2 ] .'1 2 14 386 34 000 0 so -L34 3 0 036OO 95. 396 : 4 20 0 14 396 34 000 0 50 -248 4 0 03600 70.654 2 5 -3 S 14 908 34 000 0 50 -238 7 3 03600 65. 386 : fi 18 1 14 921 34 000 0 50 -302 5 0 03600 64.099 2 7 -> 1 14 933 34 000 0 5 0 -288 9 0 03600 67.431 2 3 3 14 942 14 000 0 50 -248 7 3 036OO 71. 745 2 9 21 a 14 948 34 JOO 0 SO -184 7 0 03600 77.107 2 10 2 ) 4 14 950 34 000 0 50 -101 3 0 03600 92.804 2 11 23 3 14 948 34 000 0 50 1 1 0 03600 89.514 2 12 27. S 14 943 34 000 0. SO 100 2 0 03600 97.279 2 13 :* 7 14 939 M 000 0 50 100 a 0 03600 105. 191 2 14 12 1 24 934 34. 000 3 50 100. 8 0 03600 113.353 2 IS 14. S 14 330 :■( 000 0. 50 100. 8 0. 03600 121.334 2 16 37. 0 24 926 34. 000 0. 50 100. 8 0 03600 130.806 2 17 IS 6 14 923 34. 000 0. 5 0 100. 8 0. 03600 140.034 2 18 ;: 3 14 920 34. 000 0. 50 100. 8 0. 03600 149.572 2 19 19 1 14. 917 34. 000 0. 50 100. 8 0. 03600 159.512 2 20 H 0 14 915 34. 300 0. 50 100. * 3. 33600 169. 789 2 21 92 0 14. 912 34. 000 0. 50 100. a 0. 03600 180. 441 2 22 - < 2 14. 910 34. 000 0. 50 100. 8 0. 0 3600 191.488 . : ) S7. 4 14. 908 34. 000 0. SO 100. a 0. 03600 202.906 2 24 M . 7 14. 906 14. 000 3. 50 100. a 0. 03600 214. 586 TIME THR) (b) 13.50 ,.:o 4.50 15.00 fEMP. RELATIVE TO -;RST) 85 II |N I |l|l| II I l| !|l_ 1 I 51. 3 15. 001 34. ooo 0. 50 - 55 7 0. 03600 181. 500 1 2 13. 6 15. 009 ■4 000 0. so -201. S 0. 03600 65. 70S 1 3 16. 6 15. 024 34. ooo 0. 50 -326. 8 0. 03600 58. 846 1 4 '.3 4 15. 048 34. 000 0. so -423. 0 0. 03600 47. 351 1 5 12. 4 15. 076 34. 000 0. 50 -483 s 0. 036OO 43. 922 1 6 12. 1 15. 10S 34. 000 0. so -S04 2 0 03600 42. 362 1 1 12. 7 15 133 34. 000 0 50 -483. 7 0. 03600 44 385 1 8 13 5 15 1SS 34. 000 0. 50 -423 5 0 03600 47 730 1 9 14 4 15 170 34 000 0 50 -327 5 0 03600 51 043 1 10 IS 6 15 176 34 000 0 so -202 4 0. 03600 5S. 035 1 n 16 a 15 175 34 000 0 so - 56 6 0 03600 59 415 1 12 IS 2 15 16S 34 000 0 50 99 9 0 03600 64 527 1 13 19 a 15 157 34 000 0 50 100 S 0 03600 69 859 1 14 21 2 15 149 34 300 0 so 100 a 0 03600 75 111 1 IS 22 a 15 142 34 000 0 50 100 8 0 03600 80 S93 1 16 24 4 15 136 34 000 0 50 100 a 0 03600 36 161 1 17 26 3 15 130 34 000 0 so 100 a 0 03600 91 896 i 18 27 6 15 125 34 300 0 50 100 3 0 03600 97 745 1 19 29 4 IS 120 34 300 0 50 100 a 0 03600 103 790 1 20 31 1 15 116 34 300 0 50 100 8 0 03600 110 024 1 21 .•: 9 15 112 34 000 0 so 100 a 0 03600 116 410 1 22 34 S 15 108 34 000 0 50 100 8 0 03600 122 992 1 23 jo 7 15 104 34 000 0 so 100 3 0 03600 129 782 1 24 38 7 IS 101 34 000 0 so 100 8 0 03600 136 782 2 1 40 } 15 102 34 000 0 50 - 55 7 0 03600 142 466 2 2 19 9 IS 110 34 000 0 50 -201 5 0 03600 70 411 2 3 LS 2 15 125 34 000 0 so -326 3 0 03600 57 316 2 4 13 4 IS 148 34 000 0 50 -423 0 0 03600 47 469 2 5 12 4 15 176 34 000 0 50 -483 5 0 03600 43 665 2 6 12 1 15 206 34 ooo 0 5 0 -504 2 0 03600 42 702 2 7 12 6 15 234 34 000 0 50 -483 7 0 03600 44 704 2 9 13 5 15 256 34 000 0 50 -423 5 0 03600 47 553 2 9 14 S 15 270 34 000 0 50 -327 5 0 03600 SI 119 2 10 15 6 15 277 34 000 0 50 -202 4 0 03600 SS 287 2 11 16 9 15 275 34 000 0 50 - 56 6 0 03600 59 629 2 12 IS 3 15 266 34 000 0 5 0 99 9 0 03600 64 707 2 13 19 a 15 258 34 .000 0 50 100 a 0 03600 69 993 2 14 21 2 IS .250 34 000 0 50 100 a 0 03600 75 21S 2 15 22 a 15 .243 34 .000 0 50 100 8 0 03600 ao 664 2 16 24 4 15 .237 14 .000 0 SO 100 a 0 03600 96 134 2 17 26 a 15 .231 34 .000 0 .50 100 a 0 036OO 91 323 2 13 27 .6 15 .226 34 .000 0 .SO 100 .8 0 03600 97 623 2 19 . 9 3 IS .221 34 .000 0 5 0 100 .3 0 03600 103 616 2 20 31 .0 15 .217 34 .000 0 5 0 100 .3 0 03600 109 738 2 21 ;: .9 15 .213 34 .000 0 50 100 .8 0 03600 116 216 2 22 34 . 7 IS .209 34 .000 0 50 100 .8 0 03600 122 785 2 23 it .6 15 .205 34 .000 3 .50 100 .8 0 .03600 129 540 2 24 39 .6 15 .202 34 .000 3 .50 100 .8 0 0 3600 136 504 H3 — O UJ<*V (a) '.ore* 'I". 5. goon '.5.3240 15.0070 •5.0750 :S. 1050 IS. 1320 - IS. 1090 :s..'SO ■.s..'xo .s. :sso IS. ISM 5. ..90 5. '.429 5. ;3S0 IS. 1300 15.1250 15.1200 IS. 1 ISO IS. .110 IS. 070 IS.'.OIO is. :ooo )■" JEPTH 51.3302 19.5821 :S. 542-4 '.3.3919 12.9211 12. 1211 12.5933 ;3..995 14.9356 15.5546 :->.3733 19.2489 19.7568 21.2422 22.7325 25.3892 27.6434 29.3529 32.9220 '4. '335 36.7037 33.6835 (c) Figure 13. 3a«ie as figure <1), except for Case lb. :3.S0 m.oo m.so ;5.oo [RELATIVE ~0 FIRST) 6.00 15.50 86 1 rr DAT HA H T 5 TAU JNET HDD 08 1 1 6.0 14. 956 34.000 O.SO - 3.5 -.03600 . 22 140 1 2 6.9 14. 937 34.000 o.so -100.8 -.03600 - :s 258 1 ] 7. 3 14 931 34.000 0.50 -184. 3 -.03600 - 26. 750 1 4 7.6 14 934 34. 000 o.so -248.4 -.03600 - 27 962 1 S 7.8 14 941 34.000 0.50 -288. 7 -.03600 - 28. 72S 1 6 7.9 14 949 34.000 0.50 -302.5 -.03600 - 28 917 1 7 7.9 14 957 34.000 0.50 -288.9 -.03600 - 29 021 1 3 7.9 14 961 34.000 0.50 -248. 7 -.03600 - 29 089 1 9 8.0 14 959 34.000 o.so -184.7 -.03600 - 29 169 . 8.0 14 949 34.000 o.so -101.3 -.03600 - 29 288 1 11 3.0 14 930 34.000 o.so - 4.1 -.03600 - 29 467 1 12 3.1 14 398 34.000 o.so 100.2 -.03600 - 29 817 1 13 3.3 14 369 34.000 o.so 100.3 -.03600 - 10 262 1 14 3.4 14 342 34.000 0. so 100.3 -.03600 - 30 793 1 15 3.6 14 31S 34.000 0.50 100.3 -.03600 - 31 417 1 16 3.7 14 789 34.000 3. 50 100.8 -.03600 - 31 994 1 17 3.7 14 763 34.000 0. SO 100.8 -.03600 - 31 392 i ia 3.7 14 735 34.000 o.so 100.3 -.03600 - 31 779 1 19 3. 7 14 709 34.000 3. 50 100.8 -.03600 - 31 733 ~* 1 20 8. 1 14 683 34.000 3. 50 100.8 -.03600 - 31 7S0 z 1 21 3.7 14 657 34.000 O.SO 100.8 -.03600 - 31 332 1 22 3.6 14 631 34.000 O.SO 100.3 -.03600 - 31 625 X 1 23 3.6 14 60S 34.000 0.50 100.8 -. 03600 - 31 47S 1 24 8.6 14 573 34.000 0.50 100.8 -. J36O0 " 31 384 Q_ 2 1 a. 5 14 556 34. 000 O.SO - 3.5 -.03600 . 31 297 Ill 2 2 3. 5 14 547 34.000 3.50 -100.3 -.0 3600 - 31 1S5 o . 3. 4 14 S46 34.000 O.SO -184.3 -.03600 - 30 956 2 4 3. 4 14 551 34.000 o.so -248. 4 -.03600 - 30 709 2 5 3. 1 14 559 34.000 0. 50 -298. 7 -.03600 - JO 435 2 6 9.2 14 554 34. 000 O.SO -302. 5 -.33600 - 30 162 2 7 3.2 14 S62 34.000 3. 50 -288.9 -.03600 - 29 951 2 3 8.1 14 567 34.000 O.SO -248. 7 -.03600 - 29 80 2 2 3 9. 1 14 S65 34.000 3.50 -184. 7 -.03600 - 29 74S 2 10 8. 1 14 555 34.000 O.SO -101. 3 -.03600 - 29 308 2 11 3.2 14 535 34.000 0.50 - 4. 1 -.03600 - 30 018 2 12 3. 3 14 477 34.000 O.SO 100.2 -.03600 - 30 407 2 13 a. s 14 449 34.000 o.so 100.3 -. 03600 - 31 019 2 14 3.7 14 422 34.000 o.so 100.8 -.03600 - 31 729 2 IS 3.7 14 396 34.000 O.SO IOC. 8 -.03600 - 31 972 2 16 3.5 14 369 34. 300 o.so 100.8 -.03600 - 31 2S6 2 17 a. 3 14 341 34.000 0. 50 100.8 -.03600 - 30 533 2 19 3.2 14 304 34. 000 O.SO 100.8 -.03600 - 29 953 2 19 a.o 14 274 34. 300 3. 50 100.8 -.03600 - 29 370 2 20 7.9 14 243 34.000 J. 50 100.8 -.03600 - 28 828 2 21 7.7 14 212 34. 000 J. 50 100.8 -.03600 - 28 323 2 22 7.6 14 .179 34.000 O.SO 100.8 -.03600 - 27 792 2 23 '.4 14 146 34.000 0.50 100.8 -.03600 - 27 302 2 24 7. 3 14 .095 34.000 o.so 100.3 -.03600 - 26 352 (a: TIME THR) (b) rrn •;»» _OTE» DEPTH :«.3Sso 6.3399 1».93'0 S.9904 '.4.9910 \29>S 14.9330 7.5282 14.3410 .3361 .1.9480 7.3889 14.95 70 7.9170 14.9810 * 9359 :4.9S90 V9S'4 .4. 9490 -?999 ■4.3J90 9.3387 14.3970 9. 1343 14.8690 9.2S56 14.8410 9.1005 14.8140 9.5709 14.1980 9. 1283 4.7630 9.7009 :-..'3S0 9.5696 14. -090 9.6569 14.5830 5.5617 14.65'0 9. 594 1 ..-.313 9.6274 ...505: '.=365 14.57J0 9.5619 Figure 14. Same as figure (1), except for Case Ic. :2.oo :2.so 30 '.3.50 m.00 '.4.50 '.5.00 15.50 15.00 16.50 rEMP. RELATIVE ~Z -IRST) 87 1 1 47 a IS 001 4 000 1 2 17 6 15 009 4 000 1 3 LS IS 024 4 000 1 4 12 IS 047 4 000 1 5 11 IS 075 4 000 1 6 11 IS 104 14 000 1 | 11 IS 131 4 000 1 9 11 15 154 14 000 I 9 11 15 168 14 ooo 1 10 11 8 IS 174 4 000 I 11 12 0 IS 169 4 000 1 12 12 5 15 154 14 000 1 13 1 3 0 IS 139 4 000 1 14 .3 4 IS 126 4 000 1 15 13 9 15 113 4 000 1 16 14 5 IS 101 14 000 I 17 IS 0 IS 090 4 000 1 IS 15 7 15 079 4 ooo 1 1» 16 4 15 069 4 000 1 20 17 2 15 060 ■1 000 1 21 -3 1 15 051 4 000 1 22 19 0 IS 043 4 000 1 23 19 7 IS 035 14 000 1 24 19 7 IS 026 4 000 2 1 19 3 15 026 14 000 : : IS 7 15 033 14 000 : 3 15 4 15 048 4 ooo 2 4 12 7 15 071 14 000 : 5 11 7 15 099 14 000 2 6 11 4 IS 128 4 000 2 7 11 3 IS 155 14 000 2 a 11 4 15 178 14 000 : 3 .1 5 IS 192 4 000 2 10 11 a 15 198 4 000 2 11 11 9 15 193 14 000 2 12 11 9 IS 174 4 000 2 13 11 9 15 159 14 000 2 14 11 a IS 141 4 000 2 15 11 7 IS 126 4 000 2 16 11 5 15 110 4 000 2 17 11 4 15 093 4 000 2 16 11 3 IS 067 4 000 2 19 11 2 15 oso 4 000 2 20 11 2 IS 013 4 000 2 21 11 1 15 01S 4 ooo 2 22 11 1 14 998 4 000 2 23 11 2 14 980 4 000 2 24 -: 2 14 J3S 4 000 -1 55 7 - 03600 ^5 0 86 201 s - 03600 - 64 697 326 a - 03600 - 57 669 423 0 - 03600 - JB 385 483 s - 03600 - 42 918 504 2 - 03600 - 41 364 483 7 - 03600 - 41 475 423 5 - 03600 - 41 627 327 5 - 03600 - 42 236 202 4 - 03600 - 43 138 56 s - 03600 - 44 127 99 9 - 03600 - 45 777 100 8 - 03600 - 47 505 100 8 - 03600 - 49 174 100 8 - 03600 - SI 027 100 8 - 03600 - 52 975 100 a - 03600 - 55 150 100 a - 03600 - 57 549 100 a - 03600 - iO 126 100 a - 03600 - 62 981 100 a - 03600 - 66 262 100 a - 0 3600 - 69 803 100 8 - 0 3600 - 72 194 100 I " 03600 - 72 084 55 7 - 03600 . 70 858 201 5 - 03600 - 68 722 326 a - 03600 - 56 584 423 0 - 03600 - 4o 598 483 7 - 03600 - 42 853 504 2 - 03600 - 41 356 483 7 - 33600 - 41 494 423 5 - 03600 - 41 671 327 5 - 0 3600 - 42 303 202 4 - 03600 - 43 077 56 6 - 03600 - 43 472 99 9 - 03600 - 43 770 100 8 - 03600 - 43 658 100 a - 03600 - 43 310 100 8 - 03600 - 42 348 100 a - 03600 - 42 310 100 8 - 0 3600 - 41 34S 100 a - 0 3600 - 41 4S5 100 a - 03600 - 41 171 100 a - 03600 - 40 969 100 8 - 03600 - 40 350 100 8 - 03600 - 40 319 .30 8 - 03600 - 40 881 100 8 - 03600 - 41 042 (a) re* LB7ER OEP 5.0000 4'. -S43 5.0090 ;'.S497 :5.o»o 5. '>2S :5.:«'0 -.2.554: -.5.0740 11.7083 iS.IOtO 1.4209 15.1310 : 1.3146 1 1 . 156 1 S -.680 11.5222 :s. U30 . 1. '533 1 M 12.0393 :5.i530 .i.983 S. 1390 12.9S91 5 250 .1.4:50 :5.:l30 13.9206 5.1310 .5.0690 S.34S3 IS.»7»e 15.9999 5 53: 1 E . 4029 1 KM 17.1918 -.5.0510 .1. -!59 S.0420 19.0427 S.C350 19.5951 .5.3250 19.6652 TIME (HR> (b) Figure 15. Same as figure (1), except for Case Id. m.oo . 4. sa is.ao RTIVE TO FIRST) 88 1 Ml I I II I ! ! I II I I I I I I I II I 1 1 6 3 I 4 9S6 14 000 0 so 3 5 0 0 0 0 1 2 7 3 ] 4 939 34 000 0 50 -100 8 0 0 0. 0 1 3 a 0 ] 4 935 34 000 0 50 -134 3 0 0 0 0 1 4 a S ] 4 939 34 000 0 so -248 4 0 0 0 0 1 5 a 9 ] 4 949 34 000 0 50 -288 7 0 0 0 0 1 6 9 2 4 958 34 000 0 50 -302 s 0 0 0 0 1 7 9 5 ] 4 969 34 000 0 so -288 9 0 0 0 0 1 9 9 8 ] 4 976 34 000 0 so -248 7 0 0 0 0 1 9 U 1 4 978 34 000 0 30 -184 7 0 0 0 0 1 10 10 4 ] 4 974 34 000 0 so -101 3 0 0 0 0 1 11 10 7 J 4 963 34 000 0 so 4 1 0 0 0 0 1 12 11 1 ] 4 943 34 300 0 so 100 2 0 0 0 0 1 1) 11 S 1 4 926 34 000 0 so 100 a 0 00932 10 704 1 14 13 1 4 909 34 000 0 so 100 8 0 01800 21 570 1 15 12 7 1 4 893 34 000 0 50 100 a 0 02S46 32 045 1 16 .:• S 4 879 34 000 0 50 100 a 0 03118 41 401 1 17 14 3 4 866 34 000 0 50 100 a 0 03477 43 730 1 18 IS 1 4 352 34 300 0 so 100 a 0 03600 53 293 1 19 IS 9 1 4 341 34 000 0 50 100 8 0 03477 54 315 1 20 16 7 4 831 34 000 0 50 100 a 0 03118 51 153 1 21 17 3 1 4 821 14 ooo 0 50 100 8 0 02S46 43 605 1 22 17 9 ] 4 811 34 JOO 0 50 100 a 0 01800 31 960 1 23 ia 3 4 303 34 ooo 0 so 100 3 0 00932 15 987 1 24 13 S 4 793 34 000 0 50 100 3 0 0 0 0 2 1 13 7 4 790 34 000 0 5 0 3 S 0 0 0 0 : : 13 9 .4 792 34 000 0 50 -100 8 0 0 0 0 2 1 la 9 4 798 34 000 0 50 -134 3 0 0 0 0 2 4 19 0 4 807 34 000 0 50 -248 4 0 0 0 0 2 5 .5 2 4 819 34 ooo 0 50 -288 7 0 0 0 0 2 4 17 6 L4 832 34 000 0 50 -302 5 0 0 0 0 2 7 18 0 .4 344 14 000 0 50 -288 9 0 0 0 0 2 a LI 2 L4 353 34 000 0 50 -248 7 0 0 0 0 2 9 18 4 L4 359 34 000 0 5 0 -184 7 0 0 0 0 2 10 18 a 4 861 34 ooo 0 50 -101 4 0 0 0 0 2 11 19 l L4 957 34 000 0 5 0 4 1 0 0 0 0 2 12 '. * 3 L4 348 14 000 0 50 100 2 0 0 0 0 2 13 .3 7 .4 340 14 000 0 50 100 8 0 00932 18 275 2 14 20 3 L4 332 34 ooo 0 50 100 8 0 01800 36 187 2 IS 21 3 L4 824 34 000 0 SO 100 8 3 02546 52 365 2 16 21 9 L4 317 14 000 0 50 100 8 0 03113 67 292 2 17 22 9 L4 811 34 000 0 SO 100 3 0 03477 78 276 2 IS 23 9 L4 303 34 000 0 50 100 8 0 03600 84 62S 2 19 2S 0 .4 797 34 000 0 SO 100 a 0 03477 95 298 2 20 25 9 .4 792 34 000 0 50 100 a 0 03118 79 561 2 21 26 a .4 7 86 34 000 0 50 100 a 0 02546 67 239 2 22 27 4 14 781 34 000 0 5 0 100 8 0 01300 48 873 2 23 27 a L4 7 76 34 .000 0 50 100 8 0 .00932 25 790 2 24 28 .0 14 .771 14 .000 0 SO 100 8 0 0 0 0 =2 4.3560 4.9380 4.3340 4.9390 4 . 3480 4.3580 4 . 3680 . . 5'bO 4.9780 4.3'40 .-9630 4.9430 4.9250 4.9090 4.9930 4.8790 ■..35s: ,.3520 •..5410 4.9300 4.92O0 4.8110 4.9020 4.7930 (a) _dTER OEPTM 5.2613 ' ir40 9.0111 3.4989 9.9230 9.2451 3.5392 3.3356 10. :260 10. '4S8 11.1 048 : 1.5415 ;2.09IS :2. "495 .3.4876 :».259' 15.3720 15.8928 16.6645 1 7. 3499 17.9153 16.3160 .8.5398 TIME (HR) (b) Figure 16. Same as figure (1), except for Case Ha with peak motion at hour 18. .3.50 m.00 U.SO 15.00 'F»p. RELATIVE TO FIRST) 39 1 CTT-T TAO JNET 1 I 6.S 1 4 956 14.000 3. 50 3.5 0.03477 22. 1S6 7.7 J, 4 940 34.000 0. 50 -100.3 0.03118 2). 607 a. 6 i 4 938 34.000 0.50 -184.3 0.02S46 21.546 9.2 1 4 943 34.000 0.50 -243.4 0.01800 16.469 9.7 1 10.0 ! 4 4 9S4 964 34.000 34.000 0.50 0.50 -238. 7 -302. 5 0.00932 0.0 8.979 0.0 10 10. J j 4 976 34.000 O.SO -288. 7 0.0 0.0 10.5 1 4 984 14.000 0.50 -248. 7 0.0 0.0 10. S 1 4 987 34.000 0.50 -184. 7 0.0 0.0 1 10 11.1 1 4 984 34.000 O.SO -101. 3 0.0 0.0 11.4 4 974 34.000 O.SO - 4.1 0.0 0.0 11.9 4 956 34.000 0.50 100.2 0.0 0.0 12.2 4 940 34.000 0. 50 100.8 0.0 0.0 12. S J 4 924 34.000 0.50 100.8 0.0 0.0 1-2.9 1 4 909 34.000 0.50 loo. a 0.0 0.0 1 16 13.1 ] 4 895 34.000 0.50 100.8 0.0 0.0 :o 1 17 13.4 4 381 34. 000 0.50 ICO. 8 0.0 0.0 I 18 13. 9 4 367 34.000 O.SO 100.8 0.0 0.0 1 19 14. 2 4 354 34.000 0.50 100.8 0.00932 13.167 1 20 14.7 4 341 34.000 0.50 100.3 0.01800 26.290 _» 1 21 IS. 4 4 330 34. 000 O.SO '00.9 0.02S46 33. 712 2 1 22 16.2 4 819 34. 300 3. 50 100.3 0.03118 49.581 1 2] 1 24 17. 3 17.9 4 4 908 798 34.000 14.000 0.50 3. 50 100.8 100.8 0. 03477 3.03600 58.047 63.1)2 X Ul Q 18.7 19. 4 20.0 4 4 4 795 796 902 34.000 34.000 )4. 000 O.SO O.SO O.SO i.5 -100. 3 -134. 3 0.03477 0.03118 3.02546 53.342 59. 563 50.219 20.4 4 312 34.000 O.SO -248.4 0.01900 36. 313 18.0 4 324 34. OOO o.so -288. 7 0.00932 16.670 17.7 .4 837 34.000 0.50 -302.5 0.0 0.0 18.2 L4 348 34.000 o.so -28a. 9 0.0 0.0 18.8 L4 358 34.000 :.50 -248. 7 0.0 0.0 19.3 4 864 34. 300 o.so -184. 7 0.0 0.0 19.9 4 865 34.000 o.so -101. 3 0.0 0.0 10 20.2 L4 363 14.000 o.so - 4. 1 0.0 0.0 20.5 14 353 14.000 o.so 100.2 0.0 0.0 20.8 L4 846 34.000 o.so 100. 8 0.0 9.0 21.1 L4 839 34.000 o.so 100.8 0.0 0.0 21. 3 L4 8)1 34.000 o.so 10O.8 0.0 0.0 21. 5 14 324 34.000 o.so 100.8 0.0 0.0 21.7 4 318 34.000 o.so 100.8 o.o 0.0 21.9 L4 809 34.000 o.so 100.8 0.0 0.0 22.3 L4 30 2 34.000 o.so 100.3 0.00932 20. 705 so 22.9 L4 796 34.000 o.so 100.8 0.01600 40.866 23.7 L4 790 34. 300 3. 50 100.8 0.02S46 59.S00 24-6 L4 783 34.000 0.50 100.8 0.03118 75. 477 25.6 14 778 34.000 3. 50 100.8 0.0)477 37.570 2 24 26.7 L4 772 34.000 o.so 100. 3 0.0)600 94.494 14.9560 14. 9400 .4.33'Q :i.9»x> «. 95)0 ■ - : 4. 9830 IH.9 7HO 14.9550 . -.>9'- .4.3240 :4.9090 . 19,: 14.1 I -iss; .4.9530 :4.84I0 . -n. 4.9180 14.9090 ■..'990 a-« (a) 1.0'Efl OEP'h 5.4829 '.6907 9.SJ22 9.2324 9.6916 9. 991' 10.2800 10.52'S 10.9156 .1.1180 11.4941 . I . '985 12.1500 12.480* 12.919' 13. 1420 1 3 . 4460 13. -561 .4. .359 14.')'5 15.4019 .5.1524 16.9949 l'.8S43 TIME (HR) (b) Figure 17. Same as figure (1), except for Case Ila with peak at hour 24. .3.50 rEMP. IH.OO 14.50 15.00 3r^PTIVE TO FIRST) •.5.50 16.00 15.50 90 Eo — o -•- _ - _ a 17 . i 6 4 4 956 4 000 0 50 3 s 0 01300 11 372 7 6 14 940 14 000 0 50 -100 8 0 02S46 13 996 3 5 4 937 4 000 0 50 -184 3 0 03118 26 072 » 3 4 942 4 000 0 50 -248 4 0 03477 !1 792 10 1 4 951 4 JOO 0 50 -288 7 0 03600 35 360 10 8 4 963 4 000 0 50 -302 5 0 03477 36 754 11 4 4 974 4 000 0 50 -288 9 0 03113 34 961 11 9 4 9S3 4 000 0 50 -248 7 0 02546 29 977 12 4 4 988 4 000 0 50 -184 7 0 01300 22 093 12 a 4 986 4 000 0 so -101 3 0 00932 11 837 13 l 4 979 4 000 0 50 - 4 1 0 0 0 0 13 4 ] 4 964 4 000 0 50 100 2 0 0 0 0 13 7 4 951 4 000 0 5 0 100 a 0 0 0 0 14 0 1 4 938 4 000 0 so 100 3 0 0 0 0 14 1 4 924 4 000 0 so 100 8 0 0 0 0 14 6 4 913 4 000 0 50 100 3 0 0 0 0 .5 0 4 902 4 000 0 50 100 a 0 0 0 0 IS 2 4 889 4 000 0 SI 100 8 0 0 0 0 .5 5 4 878 14 000 0 5 0 100 a 0 0 0 0 15 3 4 867 4 000 J 5 0 100 a 0 0 0 0 16 1 4 857 14 000 0 so 100 a 0 0 0 0 lo 3 4 84 7 4 300 0 50 100 8 0 0 0 0 le 6 4 837 4 000 0 50 100 8 0 0 0 0 17 0 ] 4 826- 4 000 0 50 100 8 c 00932 15 904 17 6 1 4 322 4 000 0 50 3 s 0 01800 31 3S5 LI 2 4 823 4 000 J 50 -uo 6 0 02S46 4S 744 IS 3 4 829 1 000 0 50 -184 5 J 03113 r.i 962 .=> 6 4 838 4 000 0 50 -248 4 0 03477 66 9SS LI 7 4 351 4 000 0 50 -288 7 0 03600 65 962 L3 1 4 864 4 000 0 5 0 -302 5 0 03477 61 8S1 . < 0 4 876 14 000 0 50 -2 88 9 0 03118 58 420 : > 1 4 88S 4 000 0 50 -248 7 0 02546 50 426 21 2 4 891 4 000 0 50 -134 7 0 01600 37 889 El 3 1 4 893 14 JOO 0 50 -101 3 0 00932 20 646 22 5 4 391 14 000 J 50 4 1 0 0 0 J :: 9 4 383 4 000 0 50 100 2 0 0 0 0 -j 2 4 876 4 ooo 0 50 100 8 0 0 0 0 : j 4 4 870 4 000 0 50 100 3 0 0 0 0 : J 7 4 864 14 000 0 so 100 8 0 0 0 c :j 9 4 358 4 000 0 50 100 3 0 0 0 0 II 2 4 352 .4 000 0 50 100 a 0 0 0 0 . 4 1 4 84 5 14 000 0 50 100 8 0 0 0 0 24 5 4 840 4 000 0 50 100 8 0 0 0 0 24 7 4 834 4 000 0 5C 100 8 0 0 0 0 21 9 4 328 1 000 0 so 100 3 0 0 0 0 :s 1 4 82 2 14 JOO 0 50 100 a 0 0 0 0 :s 3 4 817 4 000 0 50 100 8 0 0 0 0 25 7 4 811 4 000 0 50 100 a 0 0 0 0 (a) as figure (1) , except peak at hour 5. 13.50 r e m p . pe_-t : .,: :i.30 :5.oo TO rIRST) 91 .4 5 15. 001 34. 000 0. 50 - 55. 7 0. 0 0. C la. 1 15. 009 34. 000 0. 50 -201. 5 0. 0 0. 0 16. 2 IS. 024 34. 000 0. SO -326. 8 0. 0 3. 0 U 3 15. 047 34. 000 0. SO -423. 0 0. 0 0. 0 12. 1 15. 075 34. 000 0. 50 -483. 5 0. 0 0. 0 11. a 15 105 34. 300 0. SO -504. 2 0. 0 0. 0 12. l 15. 132 34. 000 0. 50 -483. 7 0. 3 0. 0 12. 5 IS 154 34. 300 0. 50 -423. 5 0. 3 3. 0 13 0 15 168 34. JOO 0 50 -327 5 0. 0 0. 0 13 s 15 175 34 30 0 0 SO -202. 4 0 3 3. 0 14 2 15 172 34. 000 0. 50 - 56 6 0. 0 0. 0 15. 0 15 160 •1 000 0 SO 99 9 3 0 0. 0 16 0 15 149 34 000 0 50 100 8 0 00932 14 869 17 2 IS 139 34 000 0 50 100 8 0 01800 30 739 '.3 6 15 130 34 coo 0 50 100 8 0 32546 46 756 10 0 15 122 34 000 0 SO 100 8 0 33118 61 334 21 5 15 :i4 34 000 0 50 100 8 0 33477 73 399 >3 1 IS 107 34 300 3 SO 100 a 0 33600 31 S28 24 7 IS 101 34 300 3 50 100 a 0 03477 34 247 26 2 15 096 34 300 3 50 100 a 3 03118 80 442 27 7 15 390 34 300 3 50 100 8 0 02S46 69 511 .3 9 15 386 34 300 C 50 100 3 0 01800 51 613 JO 0 IS 081 34 OOC 0 SO 100 a 0 3C932 27 799 M a 15 377 34 300 0 SO 100 a 0 0 3 0 31 i 15 077 34 300 0 5 3 - 5S 7 0 3 0 0 21 0 IS J85 34 000 0 50 -201 S 3 3 0 0 15 4 IS 101 34 000 0 50 -326 a 0 3 0 0 13 1 15 123 14 000 0 50 -423 0 0 0 0 0 :. 0 15 152 34 000 0 53 -483 5 G 3 0 0 n 7 15 lei 34 000 0 SO -534 2 0 0 0 3 12 0 15 208 >4 000 0 50 -483 7 0 0 0 3 12 4 15 231 14 300 0 50 -423 5 0 0 0 0 12 9 15 245 34 000 0 50 -327 S 0 3 3 0 . ; 4 15 251 34 3CC 0 50 -202 4 0 0 0 0 14 1 15 248 34 000 0 50 - 56 6 3 0 0 0 14 9 IS 236 34 000 0 SO 99 9 0 3 0 0 15 9 15 22S 34 000 0 so 100 a 0 .00932 14 752 17 0 IS 215 34 000 c .50 IOC 8 0 01800 30 358 IS 3 15 206 34 300 3 .50 100 .8 0 32546 46 032 19 a 15 .198 34 ooo 3 .50 100 a 0 .33118 60 690 21 3 15 . 190 34 .000 0 .SO 100 .8 0 .33477 72 794 332 9 15 .183 34 .000 0 . 53 100 .8 0 .33600 31 054 24 .6 15 .177 34 . 300 0 .50 ICO .8 0 . 03477 83 323 M .2 15 .172 34 .000 0 .50 100 .8 0 .03118 SO 282 27 .6 IS .166 34 .000 0 . 50 100 .3 0 .02546 69 .477 28 .9 15 .162 34 .300 0 . 50 100 .8 0 .31300 51 .644 J : .0 15 .157 34 .000 0 .50 130 .8 0 .30932 27 .333 )0 .8 IS .153 34 .000 0 .SO 100 .8 0 .0 3 .3 (a) UTEB ■ = " .orcn :£PtH IS. 0000 49.5152 .5.3090 15.0240 16.1826 IS. OHIO •3.3:60 15.0750 :?.060S IS. 1040 11.7670 :i. :4i6 IS. ,530 .2.4881 15. ;sso 12.3925 S. . HO 13.5208 14.2001 15.1590 15.33'? 1 5 . : .80 16.0323 :5. :380 17.2318 15.1290 18.5022 15.1210 19.9813 ■ 23.3571 24.5510 : 5 . 3950 36.2363 : 5. 3 330 27.55S8 38.331. IS. 3313 '9.3--" :S.0'60 30.7565 (c) Figure 19. Sim as figure 1), except for Case lib with peak at hour 18. !3.30 fEMP. U.00 14.50 [RELATIVE TC 92 : i SI 3 IS 301 14 000 0 50 - 55 7 0 03477 17S 207 1 2 la S IS 009 34 000 0 50 -201 5 3 03118 S6 784 i ) U s IS 024 34 000 0 so -326 8 0 32546 41 448 1 4 1] 2 i 04a 34 000 0 so -423. 0 0 31600 22 522 I 5 12 1 15 076 34 300 0 3 0 -483 s 0 00932 11 257 o 11 3 15 10S 34 ooo 0 50 -504 2 0 0 0 0 1 7 12 1 IS 132 34 000 0 50 -481 7 0 0 0 0 1 3 12 5 15 154 34 000 0 so -423 5 c 0 0 0 1 9 13 0 15 169 34 300 0 50 -327 5 0 0 0 0 1 10 1} 6 IS 175 34 300 3 50 -202 4 0 0 0 0 1 11 14 2 IS 172 14 000 0 so - 56 6 0 0 0 0 1 12 IS 1 IS 160 34 000 0 so 98 9 0 0 0 0 1 U 15 ) IS 149 34 000 0 50 100 S 0 0 0 0 1 14 16 a IS 138 34 000 0 so 100 8 0 0 0 0 1 15 17 6 15 130 )4 oco 0 50 100 8 0 0 3 a 1 16 ia 5 IS 121 34 000 0 50 100 8 0 0 0 0 1 17 18 3 15 113 34 000 0 50 100 8 0 0 0 0 1 18 20 2 15 10S 34 ooc 0 50 100 8 0 3 0 0 1 19 21 3 15 38e 34 000 0 5 0 ICO a 3 00932 19 714 1 20 22 5 IS 081 34 000 0 50 100 8 0 oiaoo 40 182 1 21 24 0 15 385 34 000 0 50 IOC a c 02546 60 364 1 22 25 7 15 078 34 000 0 50 100 a 0 03118 78 928 1 21 27 6 IS 374 14 000 0 SO 100 a 0 03477 94 207 1 24 28 5 15 069 34 000 0 so 100 a 0 33600 104 3 86 1 1 31 0 IS 070 34 300 0 5 0 - 55 ? 0 03477 106 ooa : : :i 7 15 077 34 GOO 0 50 -201 5 0 03118 66 710 2 3 15 6 IS 393 34 300 0 50 -326 8 0 02546 39 216 : 4 11 3 IS 116 34 000 a 50 -42 3 0 0 oiaoo 23 782 2 5 12 1 IS 144 34 000 0 50 -481 s 0 00932 11 192 2 6 :i T IS 173 34 000 : 50 -504 2 0 0 0 C 2 7 12 0 15 201 34 000 0 50 -481 7 0 0 0 0 2 8 12 4 15 223 34 000 0 SO -421 s 0 0 0 0 2 9 12 8 IS 236 M 000 0 so -327 5 0 0 0 0 2 10 11 5 IS 244 34 ooo 0 St -202 4 0 0 0 0 2 11 14 2 IS 241 :•< 000 0 50 - 56 6 0 0 0 0 : ;; )S 0 15 229 34 coo 0 50 99 9 0 0 c 0 2 12 IS a 15 21S 14 ooc 0 50 100 8 0 0 0 0 2 14 16 7 IS 20a 34 300 0 so 100 a 0 0 0 0 : is 17 5 15 198 14 ceo 0 5 0 100 a 0 0 0 0 : 16 ia 3 15 199 34 300 0 iO ICO 4 0 0 0 0 : 17 u 2 15 181 34 300 0 50 100 a c 0 0 3 2 ia 20 1 IS 173 34 300 0 50 100 a 0 0 0 0 2 19 21 2 15 166 34 coo 0 SO IOC 0 c 009 3 2 19 677 a 20 22 5 15 159 34 300 0 53 ICO a 0 01800 40 216 2 21 24 1 IS 153 34 000 0 50 100 a 0 02546 60 511 2 22 25 I IS 147 34 000 0 SO 100 a 0 33118 79 246 ; 1 27 7 15 142 34 ooo 0 50 100 4 1 03477 94 597 : 24 28 «. .5 13" 34 300 3 sc 100 a 0 03600 104 817 (a) 5 BOO :5.3C9C : 5.02»0 IS.34'0 :s.07S0 ;S. :3»0 5. me :s. .5*0 15. 1630 :5.: ".0 5 . : 'JO :5. :soo :5.H90 ■ 15. .290 :S.;2I0 :5. ::20 .5. .350 ■ :s. 39:0 :5.33»0 IS. 3790 IS.07M 5.3680 51.2673 .8.1991 IS. 490' 13. .960 2. 1380 ll.'SIO .2. 139) .2. 1952 .3.5514 1.51.3 .5. cans 15.9397 ■8. 13)17 ■ • .386 19.3379 20. 1931 21.2566 22.5307 29.5162 25.7130 27.565k 29. 52 IS (c) F.jure 20. iime as figure 1), except tor Case lib with put at hour 24. TIME (HR) I III!! (b) ;2.so 13.50 HI. 00 1H. 50 15.00 "EMP. iRELRTIVE TO FIRST) 93 50. 4 18.5 16.6 11. 4 12.4 12. 1 12.6 13. 3 14.1 14.9 15.6 16.5 17.3 18.1 18.9 19.7 20.5 21.4 12.2 23.0 2 3. J 24. 7 2S.6 26. 7 27.6 17. .a. 21.1 22.3 22.8 23. 7 24.0 25.5 26. 7 . ; ■ s.cooa 5.2210 s.:-53 S.132S ■ 5. ISM 5.: '50 S. I'M 5.:sjo 5 . : 4«0 5.1360 5.. 280 S.IM • 5. mm 1S.077Q 15.001 15.009 15.024 IS. 348 15.076 15. 105 15.133 15.155 15.169 15.176 15.174 IS. 163 15. 1S4 15.145 15.136 IS. 128 15.121 15.114 15.107 15.100 15.394 15. 089 15.083 15. :"3 IS. 078 15.085 15. 101 15.124 IS. 152 IS. 182 15.210 15.232 15.247 15.253 15.251 15.241 15.231 15.222 15.213 .3.205 15. 197 15. 190 15.183 15.177 15.171 15. 165 15. 159 15.154 34.000 34.000 34.000 34.000 34.000 34.000 34.000 3 4.000 34.000 34.000 3 4.000 34.000 34.000 34.000 34. 300 34.000 34.000 34.000 34.000 34.000 34.000 34.000 34.000 34.*CC 34.000 34.000 34. 300 34.000 34.000 34. 000 34.000 34.000 34. 000 3 4.000 34.000 34.000 34.000 34.0OO 34.000 14. 000 34.000 34.000 34.000 34.000 34. 000 34.000 34.000 14.000 0.50 0.5C 50.4145 8. 4 797 :S.5906 : 3. 3868 .2.»2J7 :2.:0«7 .2.6361 13.3217 .-•.0968 14.9357 5.S2S9 .6. 4616 :.2-9l ■ .9.9090 19.7210 21.3563 22. 1925 23.3234 23.8532 £4.6944 25.5522 ?5.6784 0.50 - 55.7 0.50 -201.5 -326.8 -423.0 -483.5 -504.2 -483. 7 -423.5 -327.5 -202.4 - 56.6 99.9 100.8 100.8 100.8 100.8 100.8 100.8 100.8 100.3 100.8 100.8 100.8 100.3 -55.7 -201.5 -126.8 -423.0 -483. 5 -504.2 -483.7 -423.5 -327. S -202.4 - 56.6 99.9 100.3 100.8 100.3 100.8 100.8 100.3 100.3 100.8 100.8 100.3 100.8 100.8 0.50 3. 50 0.50 O.SC 3. 50 (a) (c) Figure 21. Ssae is figure (1), except for Csse lib with pes* at hour 5. rE*P. 1.00 U.SO :S.30 'RELATIVE TO FIRST) 94 1 |_! ' I ! 1 II ! I I 111 I II ! I] I I II I I l[_ 6.00 16.50 95 1 i I M I I i I I [ III ! 1 I I Mil I !| I I I 1 6. 1 14. 956 34. 000 0. 50 3. 5 -. 01800 -11. 170 1 2 7. 0 14. 938 34. 000 0. 50 -100. 8 - 02546 -18. 121 1 3 7 . 5 14. 933 34. 000 0. so -184. 3 - 01118 -23. 828 1 4 7. a 14. 936 34 000 0. so -248. 4 - 01477 -27. 771 1 5 8. 0 14. 944 34. 000 0. 50 -288. 7 - 03600 -29. 128 1 6 8. 0 14. 952 34. 000 0. so -302. 5 - 03477 -28. 357 I 7 8 l 14. 960 34 000 0. so -288. 9 - 03118 -25. 656 1 9 8 2 14. 96S 34. 000 0. 5 0 -248 7 - 02546 -21 259 1 9 8. S 14 964 14 000 0. so -184 7 - 01800 -15 187 1 10 8. 8 14. 956 34 000 0. 50 -101 2 - 00932 - 8 241 I 11 9 2 1.4 940 34 000 0 50 4 1 0 0 0 0 1 12 9 5 14 914 34 000 0. so 100 2 0 0 0 0 1 13 9 9 14 892 34 000 0 50 100 a 0 0 0 0 1 14 10 2 14 871 )4 000 0 so 100 a 0 0 0 0 1 15 M S 14 351 34 000 0 so 100 8 0 0 0 0 1 16 10 a 14 831 34 000 0 so 100 8 0 0 0 0 1 17 11. i 14 S13 34 000 0 50 100 8 0 0 0 0 1 18 11 4 14 793 34 000 0 50 100 a 0 0 0 0 1 19 11 7 14 776 14 000 0 50 100 a 0 0 0 0 1 20 .1 9 14 760 14 000 0 50 100 a 0 0 0 0 1 21 -. 2 14 744 34 000 0 so 100 a 0 0 0 0 1 22 12 4 14 728 34 000 0 so 100 8 0 0 0 0 1 13 12 7 14 711 34 000 0 5 0 100 a 0 0 0 0 1 24 12 a 14 696 14 000 0 50 100 8 - 00932 -12 025 : l 12 8 14 689 34 000 0 so - 3 5 - 01800 -23 311 2 2 12 7 14 ,38 34 000 0 50 -100 a - 02546 -32 680 ; j 12 4 14 693 14 000 0 5 0 -184 3 - 03118 -39 327 2 4 l: 1 14 702 34 000 0 50 -248 4 - 03477 -42 847 2 S .. 9 14 714 34 000 0 50 -288 7 - 03600 -43 202 2 6 11 5 14 725 34 000 0 5 0 -302 S - 03477 -40 6S1 2 7 -* 3 14 737 14 000 0 50 -288 9 - 03118 -35 629 2 a .. 1 14 74S 14 000 0 so -248 7 - 02546 -28 620 2 9 11 1 14 749 34 000 1 5 0 -184 7 - 01800 -20 084 2 10 11 1 14 746 34 000 0 so -101 1 - 00932 -10 427 2 11 11 4 14 736 34 000 a 50 4 1 0 0 0 0 2 12 11 6 14 :13 34 000 a 50 100 2 0 0 0 0 2 13 n a 14 696 34 000 0 50 100 a 0 0 0 0 2 14 U i 14 680 14 000 0 5 0 100 a 0 0 0 0 2 15 12 3 14 664 34 000 0 so 100 a 0 .0 0 0 2 16 12 4 14 648 34 000 0 50 100 8 0 .0 0 0 2 17 12 6 14 633 34 .100 0 = 0 100 8 0 .0 0 0 2 19 L2 8 14 615 34 000 0 = 0 100 .8 0 .0 0 .0 2 19 LI 0 14 600 34 000 0 50 100 .8 0 .0 0 0 2 20 .3 2 14 5 86 34 .000 0 .50 ioo .8 0 .0 0 .0 2 21 1) 3 14 572 34 ooo 0 .50 100 6 0 .0 0 .0 2 22 : ) 5 14 .558 34 .100 0 5 1 100 .8 0 .0 0 0 ] 23 -i . 7 14 .544 34 .100 0 .50 100 .8 0 .0 0 . 0 2 24 13 .7 14 .528 34 .000 0 50 100 .8 - . 00932 -12 .831 TIME CHR) (b) gure ( 1) , except at hour S. '.3.50 U.00 m.SO 15.00 ■EMP. iRELPTIVE "3 FIRST) 96 TAD JMET 1 1 47. a 15 001 14 000 0. 50 - ss. 7 - 03477 -169 223 1 2 17. 7 IS 009 34. 000 0 50 -201. 5 - 03118 - 56 143 1 1 IS. 9 IS 024 34. 000 0 sg -326. a - 02546 - 40 938 1 « 12. 9 IS 047 34. 000 0. >0 -423 0 - 01800 - 23 344 1 5 .. 0 15 0 7S 34 000 0 50 -483 5 - 00932 - 11 218 1 6 11 a IS 104 ;< OOO 0 so -504 2 - 00000 0 000 1 7 12. 1 IS 121 34 000 0 50 -483 7 0 0 0 0 i a 12 s IS 1S3 34 000 0 50 -423 s 0 0 0 0 i 9 12 9 IS 168 34 000 0 50 -327 s 0 0 0 0 1 10 13 S IS 174 34 000 0 so -202 4 0 0 0 0 i 11 14 1 15 171 34 000 0 so - 56 6 0 0 0 0 1 12 IS 0 15 1S9 34 000 0 50 99 9 0 0 0 0 1 1] 15 s IS 148 34 000 0 50 100 8 0 0 0 0 1 14 16 6 IS 128 34 000 0 50 100 8 0 0 0 0 1 IS 17 4 15 128 34 000 0 50 100 8 0 0 0 0 1 16 IS 2 15 119 34 000 0 50 100 8 0 0 0 0 1 17 19 0 IS 111 34 000 0 50 100 8 0 0 0 0 1 IS 19 9 IS 103 34 000 0 50 100 a 0 0 0 0 1 19 20 6 15 09S 34 000 0 50 100 3 - 00932 - 19 256 1 20 21 1 IS 088 34 000 0 50 100 8 - 01800 - 38 331 1 21 21 5 IS 082 34 000 0 50 100 s - 02546 - 55 477 1 22 21 a 15 075 34 000 0 50 100 3 - 03118 - 69 136 1 2} 22 l IS 068 34 ooo 0 50 100 3 - 03477 - 78 296 1 24 22 s IS 062 34 000 0 50 100 8 - 03600 - 82 402 2 1 22 4 15 062 34 000 0 so - 55 7 . 03477 - ^9 400 2 2 21 9 15 069 34 000 0 so -201 5 - 03118 - 69 231 2 3 14 S 15 085 34 000 0 50 -326 3 - 02546 - 38 163 2 4 :s 0 IS 108 34 000 0 50 -423 0 - 01800 - 23 637 2 5 n J 15 136 34 000 3 50 -493 5 - 00932 - 11 136 2 6 11 a 15 165 34 000 0 50 -504 2 - OOOOO 0 000 2 7 .. l IS 192 34 000 0 so -483 7 0 0 0 0 2 3 12 4 IS 214 34 000 0 so -423 7 0 0 0 0 2 3 12 9 IS 229 34 ooo 0 50 -327 S 0 0 0 0 2 10 1) 4 15 235 34 000 0 53 -202 4 0 0 0 0 2 11 14 1 15 232 !4 000 0 50 - 56 6 0 0 0 0 2 12 14 9 15 220 !4 JOO 0 SO 99 9 0 0 0 0 2 1) :s 7 15 209 34 000 0 50 100 3 0 0 0 0 2 14 16 S IS 199 34 000 0 50 100 8 0 .0 0 0 2 IS 17 3 IS 189 34 000 0 50 100 8 0 0 0 0 2 16 LI 2 IS 180 34 000 0 50 100 a 0 .0 0 0 2 17 19 0 IS .172 34 000 0 50 100 a 0 .0 0 0 2 It 19 a IS 163 34 000 0 50 100 a 0 0 0 0 2 19 i« 4 IS 156 34 000 0 50 100 3 - 00932 - 19 065 2 20 :: 7 15 .149 34 000 0 5 0 100 3 - 01800 - 37 614 2 21 M s 15 142 34 000 0 5 0 100 a - .02546 - S3 606 2 22 IS 8 15 . 134 34 000 0 50 100 a - .03118 - 63 729 2 2} 20 7 15 . 127 34 ooo 0 50 100 a - .03477 - 73 101 2 24 20 o IS . 120 34 .000 0 50 100 a - .03600 - ''S 372 (a) .an* -£•<» n aepTN 41.9239 : 5 . 2 390 !".'29' .5. 22-10 5.8771 •5.24'; : 2. 9521 IS.O'SO 11. 9834 .5. :o«o :l.'927 is. una .2.1353 :5. .530 2. ,61 < 5. '.680 2.3355 5.1N0 .3. 4 M .5..-19 . 4 . : 4 32 :s. 1590 4.3'59 is. -»o IS. '99' ,5.:3-2 IS.59'2 15.1290 • • - 19. 0460 :s. :020 19.8926 5 2153 20.SJ3' •■ 21. .240 - 21.5173 ,5.07»0 21.8317 :s :68C >2. IJ7I .5.. 620 22.4800 (c) Figure 14. :-*me as figure il), except for C»se lid »ith peak it hour 24. TIME (HR) (b) B 13.50 "EMp. 111.00 IU.50 15.00 RELATIVE TO rIRST! 97 . » I 11 a T S TAO QNBI WDD DH 1 1 48 6 15 001 34 000 0. 50 - 55.7 -.01800 -38 332 1 2 17 7 IS 009 34 000 0.50 -201.5 -.02546 -4S 748 1 3 15 a IS 324 34 000 0.50 -326. a -.03118 -49 982 1 4 12 7 15 047 34 000 0.5O -423.0 -.03477 -44 793 1 5 11 7 15 075 34 000 0.50 -483. 5 -.03600 -42 914 1 6 11 4 15 104 34 000 0.50 -504.2 -.03477 -40 46 3 1 7 11 4 15 131 34 000 3. 50 -483.7 -. 03118 -36 036 1 3 11 5 15 1S4 14 000 0. 50 -423. 5 -.02546 -29 723 1 9 11 3 IS 163 34 000 0. 50 -327.5 -. 01800 -21 547 1 10 12 3 15 174 34 000 0.50 -202.4 -.00932 -11 53a 1 11 1} 0 15 170 34 000 o.so - 56.6 0.0 0 0 1 12 13 9 15 1S6 14 000 o.so 99.9 0.0 0 0 1 1} 14 7 15 144 34 000 0.50 100.3 0.0 0 0 1 14 15 5 IS 133 34 000 0.50 100.3 0.0 0 0 1 15 16 4 15 122 34 000 o.so 100.3 0.0 0 0 1 16 17 3 15 113 34 000 0.50 100.3 0.0 0 0 : 1 17 18 2 15 104 34 000 0.50 100.8 0.0 0 0 1 18 19 1 IS 09S 34 300 0.50 100.3 o.o 0 0 1 19 ;.- 1 IS 087 34 000 o.so 100.3 0.0 0 0 i 20 21 1 IS 080 34 000 o.so 100.8 0.0 0 0 1 21 22 1 15 073 34 000 o.so 100.8 0.0 0 0 2 1 23 : 1 2 15 067 34 000 0. 50 100. 3 0.0 0 0 1 23 24 3 IS 061 34 000 0. 50 100.3 0.0 0 0 1 14 :s ; IS 355 34 000 0. 50 100.3 -.00932 -23 635 I 2 1 25 5 IS 356 34 000 0. 50 - 55.7 -.01800 -46 285 S"3 2 2 22 1 15 063 34 000 0.50 -201. 5 -.02546 -57 014 Id Q : ) .4 7 15 079 34 000 0.50 -326.3 -. J3118 -46 435 2 4 12 9 IS 101 14 000 0.50 -423.0 -.03477 -45 491 : 5 11 6 IS 129 34 000 O.SO -483. 5 -. 33600 -42 599 2 3 11 2 15 159 34 000 0.50 -504.2 -.03477 -39 717 2 7 11 3 IS 186 14 000 o.so -483. 7 -.03118 -35 651 2 a 11 5 IS 209 34 000 o.so -423. 5 -.02546 -29 523 2 3 11 8 15 223 34 000 0.50 -327. 5 -. 31800 -21 473 2 10 12 3 15 229 34 000 o.so -202.4 -.00932 -11 486 4 2 11 13 0 15 225 34 000 o.so - 56.6 0.0 0 0 2 12 13 a 15 211 34 000 o.so 99.9 O.O 0 0 2 U 14 6 IS 199 34 000 o.so 100.3 0.0 0 0 2 14 -i s IS 187 34 000 o.so 100.8 0.0 0 0 : is -o 4 15 177 34 000 o.so 100.8 0.0 0 0 2 16 17 3 15 167 34 000 o.so 100.8 0.0 0 0 2 17 13 2 15 158 34 000 o.so 100.8 0.0 0 0 2 19 19 a 15 150 34 000 3.50 100.8 0.0 0 0 2 19 19 7 15 142 14 000 o.so 100.3 0.0 0 0 2 20 20 5 IS 114 34 000 o.so 100.8 0.0 0 0 S 2 21 21 1 IS 127 34 000 0. so 100.8 0.0 0 0 2 22 .. a IS 120 14 000 0.50 100.8 0.0 0 0 2 2) 22 s 15 113 34 000 0.50 100.8 0.0 0 0 2 24 :: 9 15 107 34 000 o.so ioo. a -.00932 -21 475 (a) TIME fHR) y^ ,aiE« '•"«". LATER 1EPTH .8.3319 s.:03o • -35 '.5.:jio 5. 932 ■ 12.5537 ■ ■ ■ i . . sso .3 '92 ■s.:533 - 5. 1530 1 . 8629 .2.3248 3 5.. 690 :3..<95 IS. .560 '.1*683 T> - .5. =407 S- 1220 16.3963 5 21 P.2'29 19. :>52 1 S . 0950 ?. ioes 20.0899 3 - 2 ! . 26W .'2. .043 3E .5.2560 ■'1. .331 14 24.3091 35.2192 ~=> _ = --. (c) Figure 25. Sa»e as figure (1). except for Ca.se lid with peak at hour S. 13.50 'EMP. '4.30 |i|. SO IS. 00 (RELATIVE T0 PIBST 5.00 16.50 98 OAT as. a T s TAD O.NET HDD OH 1 1 6. 3 14. 9S6 34. 000 0. 50 - 3. s 0. 0 0. 0 1 2 7. 3 14. 939 34. 000 0. 50 -100. 8 0 0 0. 0 1 3 3. 0 14. 335 34. 000 0. 50 -184. 3 0. 0 0. 0 1 4 3. S 14. 339 34. 000 3. 50 -248. 4 0. 0 0 0 1 S 8. 3 14. 949 34 000 0. 50 -288. 7 0. 0 0 0 1 6 3. 2 14. 958 34 000 3 50 -302. S 0. 0 0 0 1 7 9 5 14. 969 34 ooo 0. so -288. 9 0 0 0 0 1 8 I 3 14 976 34 000 0. 50 -248. 7 0 0 0 0 1 9 10. 1 14. 978 34 ooo 0 50 -184. 7 0 0 0. 0 1 10 10 « 14 974 34 000 0. 50 -101. 3 0. 0 0 0 I 11 10 7 14 363 34 000 0. 50 , 4. 1 0 0 0 0 1 12 11 1 14 343 34 000 0 50 100. 2 0 0 0 0 1 13 11 3 14 926 34 000 0 50 100. 8 - 30932 -10 604 1 14 11 5 14 909 34 000 0 so 100 8 - oieoo -20 316 1 IS 11 5 14 392 34 000 0 50 100. 8 - 02546 -29 699 1 16 11 5 14 375 34 ooo 0 50 100. a - 03118 -36 504 1 IT 11 5 14 3S8 34 000 0 50 100. 8 - 03477 -40 743 1 13 11 5 14 837 34 000 0 50 100 8 - 03600 -42 198 1 19 11 6 14 820 34 000 0 50 100 8 - 03477 -40 904 1 20 11 7 14 304 34 000 0 50 100 a - 03118 -36 911 1 11 11 6 14 787 34 000 0 50 100 8 - 02546 -29 966 I 32 11 7 14 770 34 ooo 0 50 100 8 - 01800 -21 230 1 23 11 9 14 754 34 ooo 0 50 100 8 - 00932 -11 ioa i ;« 12 1 14 737 34 000 0 50 100 8 0 0 3 3 2 1 12 4 14 728 34 000 0 50 3 S 0 0 0 0 2 2 12 5 14 727 34 ooo 0 50 -100 8 0 0 0 0 2 3 .; 7 14 731 34 000 0 so -134 3 3 0 0 0 2 4 12 8 14 741 34 000 0 50 -248 4 0 0 0 0 2 5 12 9 14 753 34 000 0 50 -288 7 0 0 0 0 2 6 13 0 14 765 34 000 0 so -302 5 0 0 0 0 > 7 13 1 14 777 34 000 0 so -288 9 0 0 0 0 2 3 13 2 14 786 34 000 0 so -248 7 0 0 0 0 2 3 1} 3 14 731 34 300 0 so -134 7 0 0 0 0 2 13 13 4 14 790 34 000 0 so -101 3 0 0 0 0 2 11 13 6 14 784 34 000 0 50 - 4 1 0 0 0 0 2 12 13 8 14 769 34 000 0 so 100 2 0 .0 0 0 2 13 13 9 14 755 34 000 0 so ioo B - 00932 -12 .973 2 14 13 .8 14 742 34 .000 0 so loo 8 - 01800 -25 .062 2 15 13 .6 14 729 34 .000 0 .50 100 8 - 02546 -35 .120 2 16 13 4 14 716 34 .000 0 .so 100 a - . 03113 -42 . 369 2 17 13 .1 14 702 34 .000 0 .50 100 .8 - . 03477 -46 .369 2 18 12 .3 14 686 34 .000 0 .so 100 3 - . 03600 -47 . 334 2 13 12 .6 14 .671 34 .000 3 . 50 100 3 - .03477 -44 .S47 2 20 .: .4 14 .656 34 .000 0 .50 100 .8 - .03118 -39 .233 2 21 12 . 3 14 .641 34 .000 0 .so 100 .8 - .02546 -31 .643 2 22 12 . 3 14 .625 34 .000 0 .so 100 .8 - .01300 -22 .265 2 23 12 .4 14 .610 34 .000 0 .50 100 i - .00932 -11 . 568 2 :< 12 .6 14 .590 34 .000 0 .50 100 .8 0 .0 0 .0 (a) 1 49.5 15. 001 34.000 0. SO - 55. 7 0. 0 0.0 2 18.1 15. 009 34.000 0.50 -201.5 0. 0 0.0 1 16.2 15. J24 34.000 3.50 -126.8 0. 0 0.0 4 13.0 IS. 047 34.000 O.SO -423.0 0. 0 0.0 s 12. 1 15. 075 34.000 o.so -483.5 0. 0 0.0 6 11. a IS. 105 3 4.000 O.SO -504.2 0. 0 0.0 7 12.1 15. 132 34.000 O.SO -483. 7 0. 0 0.0 a 12.5 IS. 154 34.000 o.so -423. 5 0. 0 0.0 9 11.0 15. 168 34.0OO o.so -327.5 0. 0 0.0 LI 13.5 IS. 175 34.000 O.SO -202.4 0. 0 0.0 11 14.2 IS. 172 34.000 o.so - 56.6 0 0 0.0 12 15.0 15. 160 34.000 0.50 99.9 0. 0 0.0 ' ) 15.7 IS. 149 34.000 0.50 100.8 - 00932 -14.731 14 16. 3 15. 138 34.000 o.so 100.8 - 31800 -29.577 i 16. 1 15. 129 34. 300 0. so 100.3 - 02546 -43.104 16 17.0 15 119 34.000 o.so ioo. a - 03118 -53. 910 1 7 17.3 15. 110 34. 300 o.so ioo. a - 03477 -61. 301 18 17.6 15 101 34.000 o.so ioo. a - 03600 -64.690 19 13.0 15 092 34.000 o.so ioo. a - 03477 -63.643 20 18.4 15 084 34.000 o.so 100.8 - 03118 -58.407 21 19. 1 IS 076 34.000 3.50 100.8 - 02546 -49. 130 22 19.9 15 36a 34.000 o.so 100. 3 - 01800 -36. 125 :i 20.9 15 16 1 34.000 o.so 100.3 - 00932 -19.604 24 22. 3 15 0S4 34.000 0.50 100.8 - 00000 -00.001 1 23. 1 15 054 34.000 0.50 - 55.7 0 0 0.0 2 23.1 15 061 34.000 3. 50 -201. 5 0 0 0.0 1 14. ) 15 077 34.000 3. 50 -326.9 0 0 0.0 4 13. 3 15 100 34.000 0. 50 -423. 0 g 0 0.0 5 12.0 IS 128 34.000 0.50 -483. 5 0 .0 0.0 6 11.7 IS 157 34.000 o.so -504.2 0 .0 0.0 7 12. 1 IS 134 34.000 0.50 -483. 5 0 .0 0.0 a 12.4 15 206 34.000 0.50 -423.5 0 .0 0.0 < 12.9 15 ;2i 34.000 o.so -327.5 0 .0 3.0 10 13.5 15 .227 34.000 0. 50 -202.4 0 .0 0.0 11 14.2 IS .224 34.000 o.so - 56. i 0 .0 0.0 12 15.0 15 .212 34.000 0.50 99.9 0 .0 0.0 1 15.6 15 .201 34.000 o.so 100.3 - .00932 -14.641 14 16.2 IS . 131 34.000 0. 50 100.9 - .01800 -29. 359 1 5 16.6 15 .181 34. 000 0. 50 100.3 - .02546 -42. 771 16 16. 1 15 .172 3 4.000 0.50 ioo. a - .03113 -53.606 17 17.2 15 .162 34.000 0.50 100.8 - .03477 -61.038 18 17.6 15 .153 34.000 0.50 100.8 - .03600 -o4. 530 ; 3 17. > 15 .144 14.000 3.5 0 100.8 - .03477 -63.417 20 13. 2 15 . 136 34.000 3. 50 100.8 - . 03118 -57. 717 21 18.7 15 . 128 34.000 0.50 100.8 - .02546 -48.092 22 19.1 15 .119 34.000 0. SO 100.3 - .01600 -34.610 ?1 19. : 15 .112 34.000 o.so ioo. a - .00932 -ia. 398 24 20.4 15 .104 34.000 0.50 ioo. a - .00000 -00.001 TIME (HR) (b) 1 -i"1 rtfWI1 'I (c) Figure 16. i) and (b) same as figure (1), except for :ase ilc with peak at hour 18. (e) and (d) same as (a) ind bl, except for Case lid. TIME '(HR) 99 6. i 14. 9S6 34. 000 3. 50 3. s 0. 0 3. 3 7. 2 14. 939 34. 000 0. so -100. 8 -. 00932 - 6. 758 7. a 14. 935 34. 000 0. 5 0 -184. 3 -. 01800 -14. 212 S. l 14. 939 34. 000 0. so -248. 4 -. 02546 -20. 986 9. 3 14. 947 34. 000 0. 5 0 -288. 7 -. 03118 -26. 310 a 4 14. 954 34. 000 0. 50 -302. 5 - 03477 -29. 781 a. S 14. 963 34. 000 3. 50 -288. 9 - 03600 -31. 198 a 6 14. 969 34. 000 0 so -248. 7 - 03477 -30 526 a a 14. 969 34. 000 0 5 0 -184. 7 - 03118 -27 771 9 a 14 962 34 000 0 5 0 -101. 3 - 02546 -22. 787 9 D 14 946 34 000 0 53 - 4. 1 - 01800 -16. 328 9 2 14. 920 34 000 0. 5 0 ♦100 2 - 30912 - 3. 652 i 6 14 996 34 000 3 50 100 a 0 0 0 0 10 0 14 874 34. 000 3 50 100 a 0 00932 9 319 10 6 14 353 34 000 0 50 100 a 0 01900 18 919 11 1 14 835 34 000 0 50 100 a 0 02S46 2a 302 12 0 14 817 34 000 0 5 0 100 8 3 03113 36 338 12 9 14 797 34 000 0 50 100 3 0 03477 43 781 13 6 14 783 34 000 0 50 100 3 0 03600 48 172 14 4 14 770 34 000 0 50 100 3 0 03477 49 208 IS 1 14 758 34 000 0 5 0 100 3 0 03113 46 482 15 a 14 747 34 000 0 50 100 8 0 02546 39 755 L< 4 14 736 34 000 0 50 100 8 0 01800 29 195 .6 7 14 725 34 000 0 SO 100 8 0 00932 15 526 u 9 14 720 34 000 0 50 - 1 5 0 0 0 3 16 9 14 722 34 000 0 50 -100 a - 00932 -15 818 It ] 14 728 34 000 0 50 -184 i - 01800 -30 300 .5 1 14 737 34 000 3 SO -248 4 - 02S46 -42 078 .5 9 14 749 34 000 3 50 -288 7 - 03113 -50 223 L3 4 14 761 34 000 3 50 -302 s - 03477 -54 338 14 9 14 773 34 000 0 SO -238 9 - 03600 -54 494 14 4 14 783 34 000 3 50 -248 7 - 03477 -51 381 14 1 14 788 34 000 0 50 -184 7 - 03118 -44 649 :i 9 14 788 34 000 3 50 -101 3 - 02S46 -35 799 13 8 14 782 34 000 3 50 4 1 - 01800 -25 074 13 9 14 768 34 300 0 50 100 2 - 00932 -12 981 14 1 14 75S 34 000 0 50 100 a 0 .0 3 3 14 4 14 742 34 000 0 50 100 a 0 30932 13 323 .i 3 14 7 30 34 000 0 30 100 3 0 01300 26 414 -5 4 14 718 34 000 0 SO 100 .8 0 .02546 38 631 16 .0 14 70 7 34 000 0 5 0 100 .8 0 .03113 49 224 Li -a 14 695 34 000 0 ;0 100 .3 0 .03477 57 351 17 .6 14 685 14 000 0 50 100 .8 0 .0 3600 62 131 IS .4 14 675 34 .300 0 50 100 .8 0 .33477 62 760 19 .0 14 667 34 300 0 5 0 100 .8 3 .03118 58 667 19 .a 14 659 34 .000 0 50 100 .8 0 .02546 49 687 M . i 14 .651 34 .000 0 JO 100 .8 0 .01800 36 . 190 : o .6 14 .642 14 .000 0 . 50 100 .8 0 .30932 19 137 (a) TIME (HR) igure (1), except aks at hours 7 and 13.50 1H.00 14.50 15.00 IMP. [RELATIVE TO -!RST) IS. 50 16.00 IS. 50 TOO 6 . 0 14. 9S6 34 000 0. so - 3. s - 03600 -22 140 6 9 14. 937 34 000 0. 50 -100. 8 - 03477 -24 417 7. 3 14 932 34 000 0. 50 -184 3 - 03118 -23 2 70 7 a 14 334 3 4 000 0. 5 0 -248. 4 - 02S46 -20 008 3 l 14 942 34 000 0. 50 -288 7 - 01800 -14 652 3 3 14 949 34 000 0. 50 -302 s - 00932 - 7 308 3. 7 14 959 34 000 0. 5 0 -288 9 3 0 0 0 9 1 14 965 34 000 0 so -248 7 0 00932 a 440 9 5 14 966 34 000 0 so -134 7 0 01800 17 029 10 1 14 960 34 000 3 5 0 -101 3 0 02546 25 370 .: 7 14 348 34 000 0. 50 4 1 0 03118 32 978 .1 s 14 923 34 000 0 50 100 2 0 01477 19 220 12 2 14 911 34 000 0 so 100 3 0 03600 41 iao .: 0 14 396 34 000 0 5 0 100 8 0 03477 44 276 13 7 14 382 34 000 0 5 0 100 a 0 03118 41 902 14 3 14 369 34 000 0 50 100 8 0 02546 35 393 14 3 14 357 34 000 0 5 0 100 8 0 01800 26 426 IS 2 14 344 34 000 0 so 100 8 0 00932 14 111 15 S 14 833 34 000 0 50 100 8 0 0 0 0 15 6 14 322 34 000 0 50 100 3 - 00912 -14 562 15 5 14 an 34 000 0 50 loo 3 - 01300 -28 200 15 4 14 900 34 000 0 so 100 8 - 02546 -39 680 IS 2 14 739 34 000 0 50 100 8 - 03118 -48 077 14 9 14 776 14 000 0 50 100 8 - 03477 -52 860 14 6 14 771 34 000 0 50 3 5 . 0 36O0 -53 604 14 3 14 771 34 000 0 so -100 8 - 03477 -50 534 14 0 14 776 34 000 0 50 -184 3 - 03118 -44 329 11 7 14 736 34 000 0 50 -248 4 - 02S46 -35 447 . ! 6 14 798 34 000 0 50 -288 7 - 0 1300 -24 635 13 5 14 810 34 ooo 0 50 -30 2 5 - 00932 -12 633 13 6 14 32: )4 300 0 50 -288 9 0 0 0 0 13 9 14 831 34 000 0 so -248 7 0 00932 12 864 14 2 14 837 34 000 0 50 -184 7 0 01800 25 415 14 a 14 337 34 000 9 50 -101 3 0 02546 37 112 IS 4 14 831 34 000 0 50 4 1 0 03118 47 309 16 2 14 313 34 000 0 50 100 2 0 33477 55 256 17 0 14 308 34 000 0 50 100 3 0 03600 60 002 17 a 14 798 34 000 0 50 100 8 0 03477 60 692 .3 s 14 739 34 000 0 50 100 8 0 03113 56 796 19 2 14 781 34 000 0 50 100 8 0 32546 48 153 .3 7 14 773 14 300 0 5 0 100 8 0 .0 1300 15 109 . : 0 14 764 34 000 0 50 100 8 0 00932 18 583 IS 2 14 756 34 000 0 50 100 a 0 .0 0 0 .: 2 14 749 14 000 0 50 100 3 - .00912 -13 903 :o 0 14 741 34 000 0 50 100 a - .01800 -36 339 19 7 14 733 34 000 0 SO 100 a - 32546 -50 746 19 3 14 725 34 000 0 50 100 a - .01118 -60 996 IB 1 14 .715 14 000 0 5 0 100 a - .03477 -66 499 Ca) TIME THR) (b) gure (1), except ks at hours 1 and 13.50 14.00 14.50 15.00 TEMP. RELATIVE ~3 FIRST) 101 1 1 6. 1 14. 956 34. 000 0. 50 - 3. s 0. 0 0. 0 1 2 7. 4 14 939 34 000 0. 50 -100. 8 0. 00932 6. 322 1 3 S. 2 14 93S 34 000 0. 50 -184. 3 «0 01800 14 652 1 4 a. ) 14 940 34 000 0. 50 -248. 4 0 02546 22 424 1 5 9 6 14 950 34 000 0. so -288. 7 0 03118 29. 404 1 6 10 2 14 961 34 000 0. so -302 s 0 03477 34 962 1 7 10 9 14 972 34 000 0. so -2 88 9 0 03600 38 490 i a 11 S 14 9S1 34 000 0. 5a -248 7 0 03477 39. 380 I 9 .: 1 14 985 34 000 0 it -184 7 0 03113 37 250 1 10 12 7 14 994 34 000 0. 50 -101 3 0 02546 31 966 1 11 13 3 14 976 34 000 0 50 4 1 0 01800 23 638 1 12 1} 7 14 962 34 000 0 so 100 2 0 00932 12 695 1 13 14 0 14 949 34 ooo 0. 50 100 8 0 0 0 0 1 14 14 2 14 936 14 0 00 0 50 100 8 - 00932 -13 260 1 15 14 2 14 924 34 000 0 so 100 8 - 01800 -25 308 1 16 14 2 14 912 34 ooo 0 50 100 8 - 02546 -36 503 1 17 14 0 14 899 34 000 0 50 100 8 - 03118 -44 469 1 IS 13 9 14 385 34 000 0 so 100 8 - 03477 -49 174 1 19 U 7 14 872 34 000 0 so 100 8 - 03600 -50 291 1 20 13 6 14 859 34 000 0 50 100 8 - 03477 -47 98S 1 21 13) 4 14 846 34 000 0 50 130 8 - 03113 -42 548 1 22 13 4 14 823 34 000 0 50 100 8 - 02546 -34 564 1 23 13 S 14 319 34 000 0 so 100 3 - 01800 -24 505 1 24 13 7 14 S03 34 000 0 so 100 8 - 00932 -12 832 2 1 14 0 14 797 34 000 0 so 3 5 0 0 0 0 2 2 14 3 14 797 34 000 0 5 0 -101 8 0 00932 13 288 2 3 14 7 14 302 34 000 0 50 -184 3 0 01800 26 278 2 4 IS 2 14 812 34 000 0 50 -248 4 0 02546 33 240 2 5 IS 3 14 924 34 000 0 50 -288 7 0 03118 48 394 2 9 16 4 14 836 34 000 0 5 0 -302 S 0 03477 55 952 2 7 17 0 14 348 34 000 0 50 -288 9 0 03600 60 169 2 a 17 7 14 3SS 34 000 0 50 -248 7 0 03477 60 411 2 9 18 } 14 86 4 34 000 0 50 -184 7 0 03118 56 227 2 10 IS 9 14 366 34 000 0 so -101 3 0 02546 47 504 2 11 19 4 14 862 34 000 0 50 4 1 0 01800 34 578 2 12 19 7 14 354 14 000 0 50 ♦ 100 2 0 00932 18 302 2 1) 19 9 14 346 34 000 0 50 100 S 0 .0 0 0 2 14 19 9 14 ass 34 000 0 50 100 3 - 00932 -18 611 2 IS 19 7 14 331 34 000 0 5 0 100 8 - .01300 -35 756 2 16 19 4 14 323 34 000 0 50 100 8 - .02546 -49 893 2 17 IS 9 14 315 34 000 0 10 100 8 - .03118 -59 922 2 IS 18 4 14 306 34 .000 0 50 100 8 - .03477 -65 250 2 19 IS .0 14 .797 34 .000 0 50 100 8 - .03600 -6S .315 2 20 17 5 14 739 34 .000 0 50 100 .8 - .03477 -61 .954 2 21 17 .1 14 7 79 34 .000 0 50 100 8 - .03118 -54 291 2 22 u .9 14 . 770 34 .000 0 50 100 .8 - .02546 -43 .5S7 2 23 16 .a 14 .760 34 .000 0 50 100 .8 - .01800 -30 .470 2 24 16 .8 14 .750 14 .000 0 5 0 100 .8 - .00932 -15 . 729 (a) TIME fHR) (b) igure (27) , except directions . 12. CD '.3.50 TEMP. :u..oo m.so :s.oo ^E_ATIVE TO FIRST) 102 1 I 6 5 ] 4 956 34 000 0 50 3 s 0 03600 22 951 1 2 7 7 J 4 940 34 000 0 50 -101 8 0 03477 26 415 i J 3 7 ] 4 939 34 000 0 50 -184 3 0 03118 26 S86 1 4 9 4 J 4 944 34 000 0 50 -248 4 0 02546 23 S83 1 5 9 9 ] 4 954 34 000 0 so -288 7 0 01800 17 697 1 6 u 3 1 4 966 ;< 000 0 50 -302 5 0 00932 9 5SS 1 7 10 6 4 977 34 000 0 so -288 9 0 0 0 0 1 3 u 7 1 4 985 34 000 0 so -248 7 - 00932 -10 049 1 5 10 3 j 4 989 14 000 0 so -184 7 - 01800 -19 669 1 10 10 3 4 986 34 000 0 so -101 3 - 02546 -27 938 1 11 13 3 1 975 34 ooo 0 50 4 1 - 03118 -34 248 1 12 10 3 4 956 34 000 0 so 100 2 - 03477 -38 188 1 13 10 3 4 937 34 000 0 50 100 a - 03600 -39 433 1 14 10 7 4 919 34 000 0 50 100 8 - 03477 -37 988 I 15 10 7 4 900 34 000 0 50 100 3 - 03118 -34 041 1 16 L8 3 4 382 14 000 0 50 100 8 - 02546 -27 890 1 17 11 0 4 36 3 34 ooo 0 so 100 8 - 01300 -19 902 1 13 11 2 4 34 4 34 000 0 5 0 100 a - 00932 -10 469 1 19 11 5 4 926 34 000 0 so 100 3 0 0 0 0 1 20 12 0 4 310 34 000 0 so 100 8 0 00932 11 115 i 1 21 12 5 4 794 34 000 0 50 100 a 0 01800 22 316 1 22 13 1 4 779 34 000 0 so 100 a 0 02S46 33 028 w 1 2] 13 9 .4 765 34 000 0 so 100 a 0 03118 42 562 X 1- 1 24 14 6 L4 751 34 000 0 50 100 8 0 03477 50 051 2 1 15 4 L4 716 34 000 0 50 3 5 0 03600 54 497 0- UJ 2 2 16 1 4 746 34 000 0 so -101 a 0 03477 55 139 Q : 3 16 3 4 ■52 34 ooo 0 50 -134 3 0 03118 51 466 2 4 17 3 .4 762 34 JOO 0 so -248 4 0 02546 43 409 2 5 17 6 4 774 34 000 0 50 -288 7 0 01800 31 424 2 6 17 9 l4 786 34 000 3 50 -302 S 0 00932 16 505 2 7 17 9 4 -97 34 000 0 50 -288 9 0 0 0 0 2 3 17 7 L4 907 34 000 0 5 0 -248 7 - 00932 -16 565 2 9 17 5 L4 313 34 000 0 50 -184 7 - 01800 -31 717 2 10 17 1 14 314 34 000 0 so -101 3 - 02S46 -44 198 2 11 16 3 L4 810 14 000 0 so 4 1 - 03118 -53 128 2 12 16 4 L4 799 34 000 0 50 -100 2 - 0 3477 -58 058 2 13 15 0 .4 T89 34 000 0 5 g 100 8 - 0 3600 -58 805 2 14 15 7 L4 779 34 000 0 so 100 8 - 03477 -55 626 2 IS 15 5 14 768 34 000 0 so 100 8 - 03118 -49 008 2 16 15 3 L4 757 34 000 0 so 100 8 - 02546 -39 543 2 17 15 3 L4 746 34 000 0 5 0 100 a - 01800 -27 338 2 13 15 5 L4 731 34 000 0 50 100 a - 00932 -14 472 2 19 15 7 L4 720 34 000 0 5 3 100 8 0 0 0 0 2 20 16 2 14 709 34 000 0 so 100 a 0 00932 15 001 2 21 .6 7 L4 699 34 000 0 50 100 3 0 01800 29 709 2 22 17 3 L4 689 34 000 0 so 100 3 0 02546 43 403 2 23 18 0 L4 679 34 000 0 50 100 8 0 03118 55 248 : 24 13 9 L4 670 34 000 0 50 100 a ) 03477 64 267 4.9580 4.9*00 ».9370 4.9430 4.9540 4.3S50 4.9750 4.9850 4-9990 4.9350 ..9750 4.3SS0 4.9370 4.3190 4.9000 4.8810 4.9830 4?250 4.6090 4.7930 . "'30 4. 75SO 4.7510 (a) 5.4903 '. "292 9.6SI3 9.3826 9.9200 ■.0.3023 ,0.5659 .0. -348 10.9293 :0. 4,362 10.8I',7 10.7922 10.7577 10.7357 10.7491 10.9174 10.9569 . :. 1831 1.524 7 I 1 . 3859 12.5101 13. 1406 13.8658 14.6453 TIME (HR) 3^ (b) jure (28) , except irections. 13. SO IH.OO 14.50 15.00 EMP. fRELPTIVE T0 c ^St; 103 DIST /(KX) (C) _ ' 1 1 1 1 1 II t I -13.4*0- - -12.557- I I ! I I I ■^-U- OIST. IKX) Figure 31. Contours as in figure (1) , except for Case Ilia in two dimensional mode. (»)» (b) , (c), and (d) are hour 6, 12, 18 and 24 respectively. 104 HOUR o '.2.00 12.30 .00 13.50 TEMP. iM.OO 14.50 !5.00 iRE'.PTIVE T0 FIRST) s as in figure ( 1) , a) and (b ) are hour 105 mCJUR IS una "eip. l_RTE« OEP'm it. ano 1 1 . 3989 ..sj:.- ::.3tOS '.4.B1S0 11.1131 i.aoaa : 1.6490 H.79SO n.3S«i :«.T970 12. BIOS :».»oto 13.300M - . M50 I3.5OTI 19.00 :3.50 14.00 14.50 15.00 "EMP. RELATIVE *C fIRST) HOUR 24 gure 32 , except for 14.00 14.50 ;relstive ro - 106 1 1 49 5 IS 001 14.000 0 5 0 - 5S 7 0 0 0 0 1 2 17 9 IS 009 14.000 0 50 -201 s - 00932 -16 793 1 3 13 9 IS 024 14.000 0 50 -326 a - 01800 -28 950 I 4 12 7 IS 047 !4. 000 0 50 -423 0 - 02546 -32 8S6 1 5 11 7 IS 075 14.000 0 50 -483 s - 03118 -37 199 1 6 11 4 IS 104 14.000 0 50 -S04 2 - 03477 -40 436 1 * 11 3 IS 132 14.000 0 50 -483 7 - 03600 -41 530 x a 11 4 15 154 14.000 0 50 -423 5 - 03477 -40 316 1 9 11 6 15 168 14.000 0 50 -327 S - 03118 -36 30 3 1 10 12 0 IS 174 4.000 0 so -202 4 - 02546 -30 875 I U 12 S IS 169 14.000 0 50 - 56 6 - 01800 -22 641 1 12 -i 2 IS 1SS 14.000 0 $0 99 9 . 00932 -12 376 1 U 14 1 IS 142 4. 000 0 so 100 8 0 0 0 0 1 14 IS 1 15 130 4.000 0 so 100 8 0 00932 14 028 1 15 16 3 15 119 14.000 0 50 100 8 0 oiaoo 29 156 1 16 17 7 IS 110 4.000 0 so 100 8 0 02546 44 423 1 11 19 2 IS 101 4.000 0 50 100 8 0 03118 58 aoa 1 IS ia § 15 093 4.000 0 so 100 8 0 03477 71 045 1 19 22 S IS 086 14. 000 0 so 100 8 0 03600 79 525 1 20 :* 2 15 0 80 4. 000 0 50 100 a 0 03477 32 342 i :i 26 0 IS 074 4.000 0 so 100 8 0 03118 79 704 s l 22 27 6 IS 069 4. 000 0 5 0 100 a 0 02546 69 3S7 1 23 29 1 15 064 4.000 0 50 100 a 0 01300 51 356 1 24 10 3 :s 060 4. 000 0 5 0 100 8 0 00932 28 137 X 2 1 30 8 15 060 14.000 0 5 0 - 55 7 ) 0 0 0 0. : : ; : 9 15 068 4.000 J 50 -201 5 - 00932 -19 593 LlI 2 1 .5 1 15 083 4.000 0 5) -326 a - 01800 -27 473 o : 4 12 9 15 106 4.000 0 50 -423 0 - 0 2 S 4 6 -13 187 1 5 11 IS 134 4.000 0 50 -483 s - 03118 -36 969 2 6 11 IS 164 4.000 0 50 -504 2 - 03477 -39 896 0 .1 IS 191 4.000 0 50 -483 5 - 03600 -41 192 2 8 11 IS 213 4.000 0 50 -423 5 - 03477 -40 094 2 9 11 15 228 4.000 0 50 -327 5 - 03113 -36 673 2 10 :: 15 234 4.000 0 50 -202 4 - 02S46 -30 800 2 11 12 15 229 4.000 0 50 - 56 6 - 01800 -22 569 2 12 1 J 15 215 4.000 0 SO 99 9 - 00932 -12 336 2 13 14 15 202 4.000 0 50 100 8 0 0 0 0 2 14 19 15 190 4.000 0 SO 100 8 0 00932 14 013 2 IS 16 15 179 4.000 0 so 100 8 0 01800 29 163 2 16 17 IS 169 4.000 0 so 100 a 0 02S46 44 461 2 17 19 IS 160 4.000 0 5 0 100 8 0 03113 58 869 2 ia 20 15 153 4.000 0 50 100 8 0 03477 71 122 2 19 22 IS 146 4.000 0 50 100 8 0 03600 79 577 2 20 24 IS 139 4.000 0 5 0 100 a 0 03477 32 321 2 21 -5 IS 114 4. 000 0 SO 100 a 0 03113 79 552 . 27 IS 128 4. 000 0 50 100 8 0 0 2546 68 385 2 2] 28 i :5 124 4.000 0 50 100 a 0 01800 51 351 2 24 29 8 is 119 4.000 (a 0 \ J 50 100 a 0 00932 27 646 .5.3000 :s.:ow I5.J2H0 .s.:»»o :5.3>S0 :s.:o<40 .5. :JIO :5.1530 .5. 1680 ;S.;"40 :5..590 15.1S50 :5.;.20 .5. .300 .5.:;30 :s. :090 :5. ;cco :5.C930 5 :iS' :s.0790 s.;'. :s.oseo :s.06«o .S.3SM .9.5:S2 -.7.939<1 15.9392 ;2. i.3l . I. H65 :l.'<2 73 : 1.3297 : 1.3914 ::.62:5 ::.3'S: .2. .655 :3.2201 .4. .02' :S. 1250 :s.3«40 17.6743 :9.158S 20. "981 22.4906 24.2400 25.3659 ••• 29.0692 30.3383 gure 34. Same as figure 11), except for ase 1 1 1 b with peaks at hours 7 and 19. ,.;; .1.50 :5.ao 15.50 :s.oo ~Ewo. RElhTIVE TO FIRST) 107 3>t an ■ T S TAU 8MBT WDD OB 1 ,- 1 1 47. 3 IS. 001 34.000 o.so - 55.7 -. 03600 -175.086 t 1 2 17. 7 IS 009 34.000 0.50 -201.5 -.03477 - 62.530 [ 1 3 15.3 15. 024 34.000 0.50 -326. 9 -.03118 - 50.044 c 1 4 12.3 15. 047 34.000 0.50 -423.0 • -.02546 - 32.932 1 5 11.9 IS 075 34.000 O.SO -483.5 -.01800 - 21.607 lOf I 6 11.7 IS 104 34.000 0.50 -504.2 -.00932 - 10.945 1 7 12.0 15 131 34.000 O.SO -483. 7 0.0 0.0 l a 12.4 15 154 34.000 0.50 -423.5 0.00932 11.542 l * 13.1 15 168 34.000 O.SO -327. S 0.01800 23.408 1 10 14.0 15 175 34.000 O.SO -202.4 0.02 546 35.288 l 11 15.2 15 172 34. 000 O.SO - 56.6 0.03118 46. 708 1 12 16. 7 IS 161 34.000 o.so 99.9 0.03477 56.954 1 13 18.0 15 152 34.000 0.50 100.8 0.03600 63. 705 1 14 19.4 IS 143 34.000 0. 50 100.3 0.03477 66.297 I 15 20.8 15 135 34. 000 0.50 100.8 0.03118 63. 716 :o.- 1 16 22.0 15 128 34.000 O.SO 100.8 0.02546 5S.248 1 17 21. 1 15 122 34.000 J. 50 100.8 0.01800 41. 146 1 13 24.0 IS 116 34.000 0.50 100.3 0.00932 22.239 1 19 24. 7 15 110 34.000 O.SO 100.8 0.0 0.0 ^. 1 20 25. 1 15 104 34.000 0.50 100.8 -.00932 - 23. 531 2 " i 21 25 .4 15 099 34.000 O.SO 100.8 -.01800 - 46. 145 w r 1 22 25.5 IS 093 34.000 O.SO 100.8 -.02546 - 65. 790 1 23 25.5 15 383 34.000 O.SO 100. 8 -.03118 - 80.740 I " 1 24 25.4 15 383 34.000 O.SO 100.3 -.03477 - 89.380 £»■ 2 1 25.0 IS 08} 34.000 O.SO - 55.7 -.03600 - 31.646 w Z 2 2 22.1 15 090 34.000 o.so -201. 5 -.03477 - 73.064 Q . 2 3 14.7 IS 106 34. 000 0.50 -326.8 -.03118 - 46.456 2 4 13.0 IS 128 14. 000 o.so -423.0 -.02546 - 33.442 2 5 11.8 15 157 34.000 o.so -483.5 -. 01800 - 21.441 2 6 11.7 15 186 34.000 2.50 -S04.2 -.00932 - 10.915 2 7 11.9 15 214 34.000 0.50 -483. 7 0.0 0.0 2 3 12. 4 15 236 34.000 0.50 -423.5 0.00932 11.456 2 9 12. 3 IS 251 34.000 O.SO -327.5 0.01800 23.239 40'- 2 10 13. i 15 257 34.000 o.so -202.4 0.02546 35.035 2 11 15.0 IS 254 34.000 o.so - S6.6 0. 03118 46. 159 2 12 16.4 IS .241 34.000 0.50 99.9 0.03477 56. 054 2 13 17.8 IS .233 34.000 O.SO 100.8 0.03600 63.043 2 14 19.2 IS .225 34.000 o. so 100.3 0.03477 6S.623 2 15 20.6 IS .217 34.000 J. 5 0 100.3 j . 0 3 1 1 3 63. 110 2 ie 21.8 IS .210 34.000 0.50 100.3 0.02546 54.870 ' 2 17 :2 . ) 15 .203 34. 000 0.50 100.3 0. 01300 40.923 2 ia 23.3 15 .197 34. 000 O.SO 100.8 0.00932 22. 134 sol 2 19 24.6 IS . 191 34. 000 o.so 100.3 0.0 0.0 2 20 25.1 15 .185 34.000 0. 50 100.8 -.00932 - 23.462 2 21 25. 3 IS .180 34.000 0.50 100. 3 -.01800 - 46.025 2 22 25.4 15 .175 34.000 0.50 100.8 -.02546 - 65.615 2 23 25. 3 15 . 169 34.000 0. 50 100.8 -.03118 - 80.218 2 24 25. 1 IS . 164 34.000 0.50 100.3 -.03477 - 38.884 5 UJ«n_ C3 (a) 5.3000 5.:090 ,s.;2»o 5. Mm :s.07so :s. :o0 .5.0820 IT. '6*3 '.7. 57 in .5.3027 .2. '129 '.9962 11.5913 2.;C32 '.2.»'<52 .3. 1221 IH.0397 15.2167 .6.6619 18.0166 19.2989 20.7512 21.9810 23.06H2 23.9787 ?4.5596 25. 1383 25.4065 25.5175 25.. 958 25.H299 TIME (HR) (b) Figure 35. Same as figure (1), except for Case 1 1 lb wth peaks at hours 1 and 13. '. 4 . 50 TEMP. 15.00 15.50 15.00 ?E_3TIVE TO FIRST) 16. SO 17.00 108 1 1 49 .5 15 -ooi 34 .000 0 .so - 55 .7 . .00000 - 0 .004 1 2 18 . ] 15 .009 34 .000 0 .so -201 .5 0 .00932 16 .951 1 3 16 .4 15 .024 34 .000 0 .50 -326 .8 0 .01300 29 . 308 I 4 1) . 3 15 .047 34 .000 0 50 -423 .0 0 .02546 33 .425 1 S 12 .4 15 .076 34 .000 0 50 -483 .5 0 .03113 33 . 007 1 6 12 .1 IS . 105 34 000 0 .50 -504 2 0 .03477 41 .405 1 7 12 . 7 IS .133 34 000 0 50 -483 .7 0 .03600 44 .390 : 3 . > .5 15 .155 34 000 3 50 -423 s 0 .03477 46 079 1 9 14 3 15 .169 34 000 0 50 -327 s 0 .03118 44 043 1 10 IS 3 IS .176 34 000 0 so -202 .4 0 02546 33 499 1 11 16 4 IS 174 34 ooo 0 50 - 56 6 0 .01800 29 185 1 12 17 3 15 164 34 000 0 5 0 99 9 0 .00932 16 060 i i; u 1 15 1SS 34 000 0 5 0 100 8 0 .0 0 0 1 14 IB 7 15 147 34 300 0 50 100 3 - .00932 -17 S21 1 15 19 2 15 139 34 000 0 5 0 100 a - 01300 -34 806 1 16 19 5 15 131 34 000 0 50 100 3 - 02S46 -50 246 1 17 19 7 15 123 34 occ 0 50 100 a - 03118 -62 429 1 18 19 3 IS 116 34 300 3 SO 100 8 - 33477 -70 201 1 19 .: 0 IS 108 34 000 3 50 100 8 - 33600 -73 174 1 20 20 1 IS 101 34 000 0 so 100 8 . 03477 -71 243 1 21 :o 4 15 C94 34 000 0 50 100 a - 03118 -64 744 1 22 20 9 15 086 34 000 0 50 100 3 - 02S46 -53 760 i 13 21 5 IS 079 34 coo 0 50 100 a - 01800 -58 968 1 24 22 1 15 373 34 300 3 SO 100 8 - 00932 -20 873 2 1 2] 0 15 073 34 000 0 SO - 55 , 0 0 0 0 2 2 22 2 15 080 34 300 0 50 -201 S 0 00932 21 5C0 : J 15 2 15 .96 14 ooo 0 50 -326 8 0 01800 27 045 2 4 1] 5 IS 119 34 000 0 5 0 -423 0 0 02546 34 017 2 5 12 3 IS 147 34 300 0 50 -483 5 0 03118 37 696 2 6 12 1 15 177 34 000 0 5 0 -504 2 0 03477 41 2C7 2 7 12 6 IS 204 34 .00 0 50 -483 7 0 03600 44 728 2 a 12 4 IS 226 34 300 0 50 -423 5 0 03477 45 938 2 9 14 4 15 241 14 000 0 5 0 -327 S 0 03118 44 14 7 2 10 .5 4 15 247 34 300 0 SO -202 4 0 02546 36 760 2 11 16 4 IS 246 34. 000 0 50 - 56 6 0 01800 29 171 2 12 17 ] 15 216 34 000 0 50 39 9 0 00932 16 osi 2 1} -- 1 IS 227 34. 300 &. 50 100 a 0 0 0 0 2 14 18 7 IS 218 34. 000 0. SO 100 s - 00932 -17 491 2 15 19 1 IS 21C 34. 000 G. 30 IOC. 8 - 01800 -34 714 I 16 19 4 IS 202 34 000 0. 5C 100. 8 - 02546 -50 044 2 17 13 6 15 19S 34 ooo 0. 50 100. 8 - 01118 -62 132 2 18 19. 7 15 187 14. 000 :. 50 100. i - 03477 -69 824 2 19 19 9 15 180 14. 000 0. 50 100. 3 - 03600 -72. 794 2 20 20. 1 15. 172 14 000 0. 50 100. 8 - 03477 -70 952 2 21 M 4 15. 16S 34. 000 0. 53 100. 8 - 03118 -64. 569 2 22 it 8 IS. 1S8 34. 000 0. 50 100. 8 - 32S46 -S3. 691 2 2] 21. 4 15. 1S1 14. 000 0. 50 100. 8 -, 018CO -33. 970 2 24 22. 1 IS. 144 34. 000 0. 50 100. 8 -. 00932 -20. 717 (a) - - _9te« torn. -='E" 3£» 5.3CC0 49.5152 .5.3090 18.2758 ; s. :j«o i..234 o o 15.94 70 : 3.2981 15.0750 .2.3919 :s.:oso I. :53 : 5 . : 320 I 5953 .5. :5<0 : 3. 4930 .S. .590 :4.i-93 IS.I7S8 -.5.3173 :s. .".0 .S.3606 o is. taw 17.3167 .s.isso H.IOIS = .5.. .60 18.71S9 -*- :5.:)90 19.1832 .S.:300 .9.4886 IS. .290 19.7135 :s..:so 13.9392 a :5.:390 19.362H a IS. .300 20.1317 ,r\i_ .5.2930 23. .441 : 5. 0960 20.8511 JE ' .5.3790 21.4543 5.2123 22.2966 ro — o B-Ol _ n , 2Z ure 56. Same as figure (34), except for versel of peans. 13.50 1Y.00 11.50 15.00 IS. 50 15.00 16.50 17.00 17. SO TEMP. (RELATIVE TO FIRST] 109 :»* hr H r 5 I 1 51 3 is 001 14 000 i 2 18 6 15 009 4 000 i 3 16 6 15 024 >4 000 1 4 13 3 15 048 4 000 i 5 12 2 15 076 14 000 1 6 11 8 15 105 14 000 1 7 12 3 15 132 14 000 1 3 12 5 15 1S4 4 000 1 9 12 8 15 168 4 000 1 10 13 1 IS 174 1 000 1 11 13 4 15 171 4 oco 1 12 13 8 15 158 4 000 1 13 14 2 15 146 4 coo 1 14 14 7 15 134 4 000 1 15 15 1 15 123 4 000 1 16 15 7 15 112 4 000 1 17 16 4 15 102 4 000 1 18 11 3 IS 092 4 300 1 19 18 4 15 084 4 000 1 20 19 7 15 075 4 000 1 21 21 2 15 068 4 000 1 -2 13 0 15 061 4 000 1 23 25 0 IS 055 4 000 1 24 27 1 IS 050 4 000 2 1 23 a IS 050 4 ooo 2 2 22 4 15 058 4 iOO : :s 5 15 074 4 000 2 4 13 5 15 096 4 000 2 5 12 1 15 125 4 000 2 fi 11 8 IS iSJ 4 ooc 2 7 11 a 15 183 4 000 2 3 12 2 15 205 4 000 2 9 12 5 15 219 4 000 2 10 12 8 IS 225 4 000 2 11 13 2 :s 222 4 000 2 12 :i 6 15 209 4 000 2 13 14 0 is 196 4 000 2 14 14 4 IS 184 4 000 2 15 14 9 15 173 4 000 2 16 15 5 15 162 4 300 2 17 .6 3 15 151 4 ooo 2 18 17 2 15 142 4 000 2 19 18 4 15 133 4 000 2 20 .3 7 IS 125 4 ooo 2 21 11 2 15 117 4 000 2 22 23 0 15 111 4 000 2 23 24 > 15 105 4 000 2 24 :6 a 15 099 4 000 (a) Jtcp --•* 3T=9 CE»TH 51.3302 IS. 3090 19.5593 1S.0210 5.5587 IS. 3470 >3.2S7<4 1S.37S0 12.226V :S.:0SO 1 1.9129 15.131G 12.3051 is.isio .2.5322 ;5. :S80 12.8171 :5.:7>40 13.0528 15.1710 1 3.3795 15.1S90 13.9298 IS.IHSO H.219S 15.1340 H.S7H1 :s.i220 IS. 1020 IS. 1 120 IS. 7173 15.1020 15.1H2I - 17.3251 1 5 . 08 JO 19.U007 1.5921 :S.06»0 21.2U8 IS. 0610 J2.98W1 15.0550 24.9S83 15.0490 3'. :?3> 55 7 0 C3600 181 soo 201 5 0 03477 63 428 326 8 0 03118 50 859 423 0 0 02S46 33 347 483 5 0 .1800 21 811 504 2 0 00932 10 983 483 7 0 0 0 0 42 3 S - 00932 -11 731 327 5 - 01300 -23 2 79 202 4 - 02546 -33 653 56 6 - 03119 -42 370 99 9 - 03477 -48 937 100 8 - 03600 -52 123 100 8 - 03477 -51 925 100 8 - 03118 -47 952 100 8 - 02546 -40 601 100 8 - 01800 -29 366 100 8 - 00932 -16 219 100 8 - 00000 - 0 001 100 8 0 00932 18 261 100 3 c 01800 37 644 100 8 0 02546 57 770 IOC 6 0 03118 76 611 IOC 8 0 03477 32 697 55 7 0 03600 101 942 201 5 D 03477 76 651 326 8 0 03118 47 686 423 0 0 02S46 33 908 483 S 0 01800 21 659 504 2 0 00932 10 958 483 7 0 0 0 0 423 5 - 00932 -11 400 327 S - 01800 -22 716 202 4 - 02S46 -33 12 3 56 6 - 03119 -41 676 99 9 - 03477 -48 187 100 a - 03600 -51 414 100 a - 03477 -51 021 100 a - 03118 -47 297 100 8 - 02546 -40 053 100 8 - 01900 -29 606 100 8 - 00932 -16 140 100 8 - 00000 - 0 001 100 8 0 00932 18 264 100 a 0 01800 37 375 100 8 0 02546 57 776 100 8 0 03118 "6 284 100 8 0 03477 91 479 TIMioT (HR) (b) Figure 37. Same as figure 1.35), except for reversel of peaks. '.4.50 TEMP. is. oa RELPT] 15.50 IS. 00 VE TO FIRST! 16.50 17.00 17.50 no ~ ■/.— —J2 24 (C) E oistr (KX) i rr Dlsr"(KX) DIST.~(KX} Figure 38. Same as figure (31), except for Case I lib. in =*„ .(ITER TEHP. u»TEB 3EPT .5. 1340 11.7510 is.iono 11.6610 15.10*0 11.5787 3 3 15. :o«) 1 1 . 5096 :s. :n*o 11. .579 :s.io*o 11.4273 15.10*0 11.*I9S LS. 10*0 11. -i 350 IS. ::*o .1.-1731 '.5.1 3*0 11.5311 _ IS. IMC U.605S O IS. low 11.6913 iS.io*o 11.7927 30 is.ino .1.9738 — - is.ioio 11.958! .5. 13*0 12.0296 IS. IBM 12.0832 15.1050 :2. 1153 O 15. 1 350 12.1293 3 15. 1050 12.10S7 15.1050 12.0668 IS. 1050 15.1050 12.306* 1 1 . 9300 15.10S0 1 1 . 9*29 — a — - 16.00 R5T) J4 .RTF" ■■•" .(ITER OE1"* 15.1570 1 3.363* :5.:560 13.07*1 15.1550 1 2 . 9 1 2S O 15. 1S»0 12.9*38 ^ .5.15*0 12.9*18 :5.1550 13.2201 1S.1SS0 13.5*77 15.1560 3.3981 .5.1570 H.5378 15.1580 15.193* o o 5. ItM 15.7*0* 15.1510 16.66*9 15.1610 16.3966 — 11.50 "E*p. 15.00 IS. 50 IS. 00 (RELATIVE TO FIRST) »4 L«rEB TEHP. 15.0000 1S.M9C 15.0210 15.0170 15.0750 15. 1010 IS. 1310 15. 1530 15.1990 15.1710 15.1720 15.1610 15.1520 15.1110 IS. IMS 15.1290 IS. 1220 15.1160 15.1100 15.1050 15.0990 15.0930 15.09*0 15.0920 -»J«n. tSTEK OEPTH 17.9230 17.7297 15.9779 12.9S21 11.9931 11.7927 12.2999 12. 7909 13.5399 19.1999 15.6907 .5.9969 19.3693 .9.7236 20.9975 22.0330 11. 9596 23.6S53 29.1370 21.1229 21.5550 29.5509 21.5009 21.1705 Figure 12. Profiles as in figure (1), -* except for Case IVa. it ind ~ 13. OC U.50 15.00 15.50 16.00 rEMP. (RELPTIVE TO FIRST! 16 Li DISTV (KX) ' | 1 ' ! 7";" ' t i ! — tj (c) : ?> I ft) .I, r\t I,!.' v V/V.V, y-/£5 (d) b dist: (kxj oist: , except for Case IVa. 117 <*i~ o o J. ^RYER TENP. 15.1040 15.1040 15.1040 LATER oepim 1 1 . 6820 11.5909 11.5129 15.1040 11.4400 (a) 15.1010 11.3494 15.1040 11.4243 15.1040 15.1040 15.1040 15.1040 11.4397 11.4712 11.4691 11.6077 1 15.1040 11.6922 / / '///////// o 15.1040 15.1040 1 1 . 7927 11.9731 oo 15.1040 11.9567 ' 15. 1040 15.1040 15.10S0 1S.10SO 12.0277 12.0811 12.1127 12.1207 o 15.1050 12.1042 Q 15.1050 12.0644 Si 2: 15.1050 12.00 7/ / / / / n Jp / A' / / / / ■". Jyjyy/ // / / 3 jp£f/ / / / / / / / //// O w* //J/ ' / / / / Iff/ /// O rf& //? Av / //////// /// ID- 1 1 1 :3.0a 13.50 m.so TEMP. 15.00 15.50 16.00 _ -T I VE TO FIRST) lOTER 'EBP -ATER OEPTH IS. 1590 : 3.0929 IS.1SS0 12.9205 IS. 1540 I2.9S12 IS. 1550 : 2. 940 7 15.1550 19.2019 1S.1S50 13.5550 15. 1560 14.0055 1S.1S70 14.5439 15.1590 15.1700 IS. 1600 15.7514 15.1610 19.6775 IS. 1610 5 MM 15.1620 17.6907 15.1630 17.9083 15.1640 17.9S67 15.1640 17.6690 15.1640 17.3140 15.1640 17.0423 15. 1630 '.6.3067 15.1620 1S.S942 15. 1610 15.0196 15.1590 14.2732 15.1590 13.9293 15.1570 13.3634 Figure 4S. Same as figure (32), except tor Case IVa. 11.50 "EMP. 15.00 15.50 'RELATIVE TO F] 16.00 RST1 118 TEA 'EBP. LATER DEPTH '5.0880 17.9701 15.0870 18.5*06 15.0880 19. 1877 .5.090: 19.9373 15.0930 20.77*7 15.0960 a 1.5570 IS. 1000 22.*033 15.10*0 22.9616 15.1080 23.*7*9 IS. 1110 23.7210 15.1150 23.9888 15.1150 23.6553 15.1180 23.*009 15.1190 22.6999 15.1190 21.7820 IS. 1170 20.7*09 15.1150 19.9318 15.1130 19.0*3* 15. 1090 18.2*7* 15. 1010 17.821* 15.1000 17.*0S3 IS. 0950 17.2*39 IS. 0920 17.3290 15.0890 17.5*71 U.50 15.00 15.50 16.00 TEMP. (RELPTiVE TO HRST) OTEfl -in' LUTE" CEPTh 15. 0*60 29. 1686 15.0*90 29.9396 1S.0S20 30. 3808 15.0550 30.4908 15.0590 30.3239 15.0630 29.9063 15.3680 29.2106 15.0720 29.3660 15.0780 27.390* 15.0790 26.3353 15.0820 2S.*357 15.3820 2*.* 70S IS. 3930 23.7107 15.0820 23.02** 15.0800 22.SS13 15.0760 22.3515 22.3265 IS. 0690 22.6186 15.06*0 23.39S9 IS. 3590 23.8939 IS. 0560 2*. 786 7 1S.05IC 25.9839 s. mo 27.1281 .s.o*ao 28.2036 Figure 46. Same as figure (33), except for Case IVa. 1U.50 TEMP. 15.00 15.50 16.00 [RELPTIVE TO FIRST) 119 : s . aooo : 5 . :o90 :5. 3240 15.0170 15.0750 :5.I050 IS. 1330 -.5. 1550 15.1590 15. I'M ;3. ITW) 15.1520 :s. isoo : 5 . 1 wc 15.1370 15. 1170 15. 1380 15.1000 : 5 . 0910 1 5 . OMO 15.0830 15.0780 15.0730 is.oen .flTER OEPTm (bU 13.30 DC 1-..50 '-S.00 15.50 16.00 TEMP. (RELATIVE '0 FIRS" TIME"(HR) -1 7- I.RTER 'EHP. _«TER 0EP7 15.0000 52.7009 15.0090 19. 4187 IS :;«: .5.2699 5 5 . i>4 7« 12.5775 IS. J750 11.4191 15.1030 : .3432 15.1300 10.7783 15.1520 . 0 . 885 7 15.1870 II.43SO 15.1720 12.S033 => 15.1680 14.0180 .5.1580 IS. 9019 IS. 1460 17.-155 IS. 1370 19.107H IS. 1290 19.9240 15.1220 19.9197 is. 1:43 .9.3323 15. 13'C 18. '612 a 15.0990 19.4635 3 15.:9O0 18.7537 15.39J0 19.7878 15.0750 15.08*0 21.6277 l-t. . '5< IS. 0630 27. 1,56 T.n — _ a-« i». 3 Fijure >' . iaae is figure except for Case IVb »ith phaaa snift fro* . . 111.50 15.00 15.50 16.00 "EMD. ^RELATIVE TO FIRST) 120 -ft' S MiliMy^A^yvt^ M;&'~M OIST. (KX) DIST""CKX) Figure 48. Same as figure (31), except for Case IVb. 121 a-™ \Litn. Q LOTEB 'EBP. 15.1030 15. 1030 :5.:030 i mi .5. 10S0 IS. 1050 15. 1050 15. 1050 15. 1050 15.1010 15.1030 15.1030 15.1030 15. 1010 15.1C3C 15.10X0 : s . : 050 '.5. 1050 15.1050 15.1040 15. 1030 .(iTEn depth 1 0 . 3962 11.1597 1 1 . '60S 12.1991 2.1313 :2.ij'9 12.3623 12.0665 11. '017 11.3615 11.1336 11. 0192 10.9962 1 1 .1591 1 1 . '601 12.1391 12. 1313 12.1979 1 2 . 3621 i2. oses 11.7017 11.3615 11.1336 "->- 13.00 14. 50 TEM°. 15.00' 15.50 15.00 aE-AT[VE TO F!RST1 _- 3 IS. 1620 IS. 1S10 '.5.1610 :s. ;S30 IS. 162(1 1S.1S90 15.1560 15.. 530 15.1520 15.1510 IS. ISM IS. 1600 15.1620 - 5. IHO '.5. ;i20 IS. 1590 :S.156C .5. .510 5. :52: 15. 1510 :S. :5»0 L«TEH OEPTN S.CS'C 18.0172 '339' s.ao'i 11.2016 13.2059 ■2. 1'96 12.7100 13.1230 11.1601 15.9019 17. 1511 16.0370 16.0171 :'.339' ; 5. 30 72 -.1.2017 13.2059 !2.'796 12.7108 13.1230 ...(0. IS. 9015 Figure 19 . Sue as figure except for Case IVb. : "..50 TEMP. 15.00 15.50 '.RELATIVE TO F 16.00 :rsti 122 IE5" "EXP. LATER DEPTH :s. 1100 17. SOU 15.1110 17.5283 15.1110 17.8974 15. 108C 13.9729 15. 1040 20.3467 15. IQOO 21.8374 15.0930 23.0410 15.0970 23.5225 15.C9S0 23.0122 15.0990 21.780S 15.1030 20.1336 15. 1070 18.7612 15.1100 17.6014 15.1110 17.5281 IS. 1110 17.39714 15.1090 13.9723 IS. 1040 20.3*66 15.1000 21.3373 15.0990 23. otae 15.0910 23.5224 15.0990 23.0122 15.0990 21.7806 15.1030 20.1337 15.1070 13.7509 U. 50 rEMP. 15.00 15.50 16.00 (RELATIVE TO FIRST) — 3 — :~i_ 3 • c a • j *p . lOTEP. oep 15.0670 28.5736 15.0 700 29.5813 15.0720 29.1300 15.0730 28.4193 15.0710 26.6727 15.0670 24.9127 15.0640 23.5775 IS. 0610 22.9500 IS.CS80 23.1028 15.0SO0 23.9S28 is.;s90 25.3930 IS. 0630 27.14.56 I5.OS70 28.5735 15.0700 29.5919 .5.: 720 29.1300 IS. 0730 28.4194 15.0710 25.6725 IS. 0670 24.9127 :i.C640 23.5771 15.0610 22.9499 15. 590 23.1029 is. :sac 23.9526 ■.5.:S90 25.3826 1S.C530 - - (b) Figure 50. Sue as figure except :'or Case [Vb. 14.50 15.00 15.50 16.00 rtMP. relative to first) 123 dist:"(kx) Disf.; (KX) (c) (d) oist: ckx) oisr.'(KX) Figure 51. Same as figure (31), except for Case Va. 124 lAies oe»th 15.1030 15.1030 15. 1330 :s. ioio 15. 10X0 is. :oio 15. 1050 15. .350 15. 1C10 15.1310 15. 1330 15.1030 15.1330 15. 1030 15. 1330 15.1340 15. 1353 1S.13S0 15.1060 15. 1060 I5.1D60 IS. 1050 15.1050 IS. . MS 1S.00 15.50 16.00 »RE'_0T!VE TO FIRST) L»TEB •■"'" •.ATER OEP 15.1560 11.7709 15.1590 15.2911 .5.1600 15.2SS3 15.1600 11.6251 15.1600 3.3698 15.1560 12.9867 15. 1550 1 2.12S5 15. 1520 12.2S38 15.1S10 12.9916 15.1530 11.1212 1S.1SS0 15.8713 15.1530 ' 3532 15.1530 19.9975 15.1550 21.5396 15.1560 21.8675 15. 1670 20.3833 15.1660 17.3065 '.. 1610 15.6012 15.1620 13.8012 ■5. 1590 12. '595 5.15.10 2.<579 .5. 1530 12.36 39 13.2535 15.1540 11.1172 (b) rigure il. ^ame except tor Jase ;l*.5C !5.00 15.50 16.00 fEMP. RELATIVE TO FIRST) 125 LfSTEH TEMP. l«TEB 3EPTH IS. 0910 15. '061 15.0950 15.9515 :5.39l0 '.S.9598 15.0930 19.8392 15.3930 20.9116 : 5. 0930 23.1667 IS. 0930 2S.60S3 15.0940 2S.96V1 IS. 3990 27.0191 is.ioso 25.8566 IS. • 120 21.1361 : s . n 90 22. 1956 IS. 1210 20.9310 IS. 12S0 19.9996 IS. 1210 19.7337 15.1200 19. 6216 :s. .uc 20.1178 is.io'0 20.6061 15. 1000 20.8121 15.0950 20.5771 1S.092O 19.7871 15.3930 19.6379 15.0920 '.'.266 7 IS. 0930 .5.2290 £'- 3 15.3190 :s.:seo IS. 3600 IS. 0610 1S.36S0 1S.OSS0 I S . 3680 ,5.3-50 IS. MM .S.JS1C IS. 389C S MM 15.3830 15.0690 .5 1813 .5.3170 IS. 0180 • • 15.0160 32.5661 J1.S099 33.6225 31 .5119 29.3909 2S.9S25 2i.2'Sl 21.1953 2-..333S 25.8301 25.31S2 26.5701 2S 3393 It. '599 >3. 21 '5 21.3906 21.3166 • 22.S132 21.2969 ?'.3639 29.9617 (b) figure 53. iame js figure 33) except for Case Va. m.SO rEMP. :5.00 '.5.50 15.00 15.50 (RELATIVE TO FIRST! 126 BIBLIOGRAPHY Adamec, D. , R. L. Elsberry, R. W. Garwood and R. L. Haney, 1981: An embedded mixed-layer-ocean circulation model. Dynamics of Atmos- pheres and Oceans, 6_, 69-96. Apel , J. R. , 1982: Personal communication. Bell, T. H., 1978: Radiation damping of inertial oscillations in the upper ocean. Journal of Fluid Mechanics, 88, 289-308. Butler, W. A., 1981: A study of horizontal sea surface temperature variability. M.S. thesis, Naval Postgraduate School. Cushman-Roisin, B., 1981: Effects of horizontal advection on upper ocean mixing: A case of frontogenesis. Journal of Physical Oceanography, 11 , 1345-1356. De Szoeke, R. A., 1980: On the effects of horizontal variability of wind stress on the dynamics of the ocean mixed layer. Journal of Physical Oceanography, 10, 1439-1454. Dillon, T. M. and D. R. Caldwell, 1977: Temperature microstructure profiles at ocean station P: Preliminary results from the MILE experiment. School of Oceanography Oregon State University. Foo, E., 1981: A two dimensional diabatic isopycnal model-simulating the coastal upwelling front. Journal of Physical Oceanography, 11 , 604-626. Garwood, R. W., 1976: A general model of the ocean mixed layer using a two-component turbulent kinetic energy budget with mean turbulent field closure. Ph. D. thesis, University of Washington, (NOAA Tech. Rep. ERL 384-PMEL 27). Garwood, R. W., 1977: An oceanic mixed layer model capable of simu- lating cyclic states. Journal of Physical Oceanography, _7, 455-468. Garwood, R. W., R. W. Fett, K. M. Rabe and H. W. Brandli, 1981: Ocean frontal formation due to shallow water cooling effects as observed by satellite and simulated by a numerical model. Journal of Geo- physical Research, 8£, 11000-11012. Holloway, G., 1980: Oceanic internal waves are not weak waves. Journal of Physical Oceanography, 10, 906-914. 127 Kantha, L. H., 1977: Note on the role of internal waves in thermocline erosion. Modeling and Prediction of the Upper Layers of the Ocean, Edited by E. 8. Kraus, Pergamon Press, 173-177. Kantha, L. H., 0. M. Phillips and R. S. Azad, 1977: On turbulent en- trapment at a stable density interface. Journal of Fluid Mechanics, 79, 753-768. Kraus, E. B. and J. S. Turner, 1967: A one-dimensional model of the seasonal thermocline. Tell us, 19, 90-105. Linden, P. F., 1975: The deepening of a mixed layer in a stratified fluid. Journal of Fluid Mechanics, 71 , 385-405. Pinkel, R., 1981: Observations of the near-surface internal wavefield. Journal of Physical Oceanography, 11 , 1248-1257. Price, J. F., 1981: Upper ocean response to a hurricane. Journal of Physical Oceanography, 11 , 153-175. Price, J. F., C. N. K. Mooers and J. C. Van Leer, 1978: Observation and simulation of storm-induced mixed-layer deepening. Journal of Physical Oceanography, 8, 582-599. Roth, M. W., M. G. Briscoe and C. H. Mc Comas III, 1981: Internal waves in the upper ocean. Journal of Physical Oceanography, 11 , 1234-1247. Shook, R. E., 1980: The one-dimensionality of the. upper ocean mixing and the role of advection during the POLE experiment. M. S. thesis, ilaval Postgraduate School. Simpson, J. J. and C. A. Paulson, 1979: Observations of upper ocean temperature and salinity structure during the POLE experiment. Journal of Physical Oceanography, 9_, 869-883. Simpson, J. J. and C. A. Paulson, 1980: Small scale sea surface temper- ature structure. Journal of Physical Oceanography, 10, 399-410. Spigel, R. H., 1980: Coupling of internal wave motion with entrainment at the density interface of a two-layer lake. Journal of Physical Oceanography, 10, 144-155. Townsend, A. A., 1968: Excitation- of internal waves in a stably- stratified atmosphere with considerable wind-shear. Journal of Fluid Mechanics, 32, 145-171. i^ii INITIAL DISTRIBUTION LIST No. Copies 1. Defense Technical Information Center 2 Cameron Station Alexandria, VA 22314 2. Library, Code 0142 2 Naval Postgraduate School Monterey, CA 93940 3. Chairman, Code 68Mr 1 Department of Oceanography Naval Postgraduate School Monterey, CA 93940 4. Chairman, Code 63Rd 1 Department of Meteorology Naval Postgraduate School Monterey, CA 93940 5. Professor R. W. Garwood, Code 68Gd 2 Department of Oceanography Naval Postgraduate School Monterey, CA 93940 6. Professor R. T. Williams, Code 63 Wu 1 Department, of Meteorology Naval Postgraduate School Monterey, CA 93940 7. Professor K. L. Davidson, Code 63 Ds 1 Department of Meteorology Naval Postgraduate School Monterey, CA 93940 8. Professor R. L. Elsberry, Code 63Es 1 Department of Meteorology Naval Postgraduate School Monterey, CA 93940 9. Professor R. L. Haney, Code 63Hy 1 Department of Meteorology Naval Postgraduate School Monterey, CA 93940 10. Mr. P. C. Gallacher, Code 63Ga 1 Department of Meteorology Naval Postgraduate School Monterey, CA 93940 129 11. Naval Oceanographic Office NSTL Station Bay St. Louis, MS 39522 Attn: Lieutenant R. J. Burger 12. Director Naval Oceanography Command Naval Observatory 34th and Massachusetts Avenue NW Washington, D. C. 20390 13. Commander Naval Oceanography Command NSTL Station Bay St. Louis, MS 39522 14. Captain C. H. Bassett Code 00 Naval Oceanographic Office NSTL Station Bay St. Louis, MS 39522 15. Commanding Officer Naval Oceanographic Office NSTL Station Bay St. Louis, MS 39522 16. Commanding Officer Fleet Numerical Oceanography Center Monterey, CA 93940 17. Commanding Officer Naval Ocean Research and Development Activity NSTL Station Bay St. Louis, MS 39522 18. Dr. S. Piacsek, Code 320 Naval Ocean Research and Development Activity NSTL Station Bay St. Louis, MS 39522 19. Commanding Officer Naval Environmental Prediction Research Facility Monterey, CA 93940 20. Chairman, Oceanography Department U.S. Naval Academy Annapolis, MD 21402 21. Chief of Naval Research 800 N. Quincy Street Arlington, VA 22217 130 22. Office of Naval Research (Code 420) Naval Ocean Research and Development Activity NSTL Station Bay St. Louis, MS 39522 23. Scientific Liaison Office Office of Naval Research Scripps Institution of Oceanography La Jolla, CA 93037 24. Library Department of Oceanography University of Washington Seattle, WA 98105 25. Library CICESE P. 0. Box 4803 San Ysidro, CA 92073 26. Library School of Oceanography Oregon State University Corvallis, OR 97331 27. Commander Oceanography Systems Pacific Box 1390 Pearl Harbor, HI 96860 131 Thesis B8814 c.l Burger Oceanic mixed layer response to tidal period internal wave motion. Thesis B8814 c.l 197951 BureSeanic mixed laver response to tidal period internal wave motion. thesB8814 Oceanic mixed layer response to tidal pe 3 2768 002 07935 2 DUDLEY KNOX LIBRARY JMeraR Mwsfifflfi KraHB raw mm fflSWln I nRHHS H ■'". ■■:kr'V/} HlBIHf mhH| Hi Hill HOT HP ■■""■'■:■ ■'■■■',; AH MB! .'••■•.'■ mat