ANALYSIS AND SIMULATION OF OF WIND-DRIVEN CURRENTS DURING THE MIXED LAYER EXPERIMENT (MILE) Jose M. Fernadez Lopez NAVAL POSTGRADUATE SCHOOL Monterey, California THESIS ANALYSIS AND SIMULATION OF WIND-DRIVEN CURRENTS DURING THE MIXED LAYER EXPERIMENT (MILE) by Jose M. Fernandez Lopez March 1981 Thesis Advisor: R. W. Garwood Approved for public release; distribution unlimited ■ UW OJ SECURITY CLASSiriCATlON OF THIS PAGE (Whon Data En farad) REPORT DOCUMENTATION PAGE i peport numICh 2. GOVT ACCESSION NO 4. TITLE (and Subtllla) Analysis and Simulation of Wind-Driven Currents During the Mixed Layer Experiment (MILE) 7. AUTHORft) Jose M. Fernandez Lopez 9. PERFORMING ORGANIZATION NAME AND ADDRESS Naval Postgraduate School Monterey, California 93940 READ INSTRUCTIONS BEFORE COMPLETING FORM 1. RECIPIENTS CAT ALOG NUMBER 5. TYPE OF REPORT * PERIOD COVERED Master's Thesis March 1981 S. PERFORMING ORG. REPORT NUMBER • • CONTRACT OR GRANT NLMSERri 10. PROGRAM ELEMENT. PROJECT TASK AREA • WORK UNIT NUMBERS ' 1 I. CONTROLLING OFFICE NAME ANO AOORESS Naval Postgraduate School Monterey, California 93940 12. REPORT DATE March 1981 13. NUMBER OF PAGES 52 14 MONITORING AGENCY NAME * AOORESSy block numbot) The wind stress calculated from wind velocities measured during the Mixed Layer Experiment (MILE) was used as input to a one-dimensional wind-drive current model. These model results are compared with observed currents from the MILE-1 bouy, showing a qualitative agreement. MILE was an examination of the upper ocean carried out near Ocean Weather Station Papa during a 20-day period, August and September of 1977, which was characterized by two major wind events. do ,; FORM AN 73 1473 COITION OF I NOV •■ IS OBSOLETE S/N 0 102-014- 6«0 1 | SECURITY CLASSIFICATION OF THIS PAGE (9non Dot* Kniotod) »— jjgtj tmtmtmt ■ The observed currents have been analyzed to obtain information about their behaviour that could be used in the tuning of the model. For a simulation of the entire period the results are considered only satisfactory. 3 , Fornj„ 1473 t 1 Jan , 3 N 0102-014-6601 ueuaivv classification o* t«h ^40tr«Mn o«« »«••»•** Approved for public release; distribution unlimited Analysis and Simulation of Wind-Driven Currents During the Mixed Layer Experiment (MILE) by Jose M. Fernandez Lopez Lieutenant Commander, Spanish Navy Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN OCEANOGRAPHY from the NAVAL POSTGRADUATE SCHOOL March 1981 ABSTRACT The wind stress calculated from wind velocities measured during the Mixed Layer Experiment (MILE) was used as input to a one-dimensional wind-driven current model. These model results are compared with ob- served currents from the MILE-1 bouy, showing a qualitative agreement. MILE was an examination of the upper ocean carried out near Ocean Weather Station Papa during a 20-day period, August and September of 1977, which was characterized by two major wind events. The observed currents have been analyzed to obtain information about their behaviour that could be used in the tuning of the model. For a simulation of the entire period the results are considered only satisfactory. TABLE OF CONTENTS I. INTRODUCTION 7 A. PURPOSE OF THE STUDY - - 7 B. IMPORTANCE OF THE PROBLEM 8 C. LITERATURE REVIEW 9 II. THE MILE DATA 14 A. DESCRIPTION - -- 14 B. ANALYSIS - - 17 III. DESCRIPTION OF THE MODEL --- 36 A. THEORETICAL EQUATIONS — 36 B. NUMERICAL METHOD OF SOLUTION 37 IV. RESULTS - 42 LIST OF REFERENCES - 49 INITIAL DISTRIBUTION LIST - 50 ACKNOWLEDGEMENTS The author wishes to express appreciation to Dr. R. W. Garwood, Department of Oceanography, Naval Postgraduate School, for his guidance throughout this study, and to Dr. D. Halpern for providing the MILE data I. INTRODUCTION A. PURPOSE OF THE STUDY The objective of this research was to investigate how well an one- dimensional model of the wind driven current could explain the observed near surface current during the Mixed Layer Experiment (MILE). Measure- ments of the near-surface currents were taken during MILE, August- September 1977, in the vicinity of Ocean Weather Station (OWS) PAPA. During this period, the data show the response of the upper ocean to the passage of two wind events. This study investigates the hypothesis that surface wind can account for a large part of the energy and variability of inertial oscillations near the ocean surface and that these oscillations are predominantly locally generated, as was demonstrated by Pollard and Millard (1970) at another site. To accomplish this task, a one-dimensional wind-driven current model was solved numerically using a modified "leapfrog" scheme. The modifi- cation involved employed current values, u and v, which were vertically averaged at each time step to a depth equal to that of the observed mixed layer, simulating strong boundary layer mixing. The mixing depth used was a time-average of the mixed layer depth obtained from buoy temperature records and verified with Plessey CTD data taken from the R/V 0CEAN0GRAPHER. The data used to check the response of the model were those obtained by nine near-surface current meters, at depths from 5 to 32m, of the MILE-1 Mooring. The wind stress was computed from wind speed and di- rection as recorded by the R/V OCEANOGRAPHER during the experiment. It was hoped that the non-wind-driven current would be sufficiently small and invariant so that the hypothesis could be tested. In the next section, the current meter observations are analyzed by using a Fast Fourier Transform. The power spectra of currents from three significant depths illustrate how the currents are dependent on the surface wind stress. In section three the equations on which the model was based are given. It is shown how from those equations a numerical solution is obtained to solve the initial value problem that we are dealing with and how the model results were computed. In the last section the results and conclusions are given. If there is no other indication, the abscissa in all figures gives time in hours from the start of the experiment, 0500 GMT hours August 18th. There are 460 hours of recorded currents in all. B. IMPORTANCE OF THE PROBLEM As Csanady [1981] explains: "The problem of circulation is to de- scribe and understand the pattern of the residual or longer-term water particle displacement. The distribution of important water properties, e.g., temperature, salinity (...), depends critically on the pattern of circulation." The capability of modeling wind-driven currents could help to explain one component of that pattern of circulation. Modeling wind-driven current is needed in order to improve upper ocean thermal structure models, which have great importance in ASW. Fisheries, search and rescue operations, and control of pollution in the ocean are other fields where wind-driven currents must be considered. 8 C. LITERATURE REVIEW Horizontal inertia! currents occur in thin layers with a relatively reduced horizontal extent, Webster [1968] concludes that inertial oscillations are essentially transient phenomena. For a fixed location inertial oscillations at different depths may have diverse origins. According to Pollard and Millard [1970], Gonella [1971] and Kundu [1976], for the surface layer of the ocean, the wind stress is the principal mechanism for their generation. Inertial currents rotate clockwise (Northern Hemisphere) with a period T = ir/(|y| sin 0), where n is the earth's rotation vector and 9 is the latitude of the observation point. The transmission of the movement from the surface to deeper layers may normally be carried out either by turbulence in an unbounded homogeneous medium, or by boundary effects in a strongly stratified medium. To test the dependence of inertial oscillations as a function of wind stress the theory of Ekman [1905] was applied in an impulsive system. In this theory, the wind provides a stress on the sea surface, and the motion is viscously transmitted to lower layers. Figures 1 and 2 show four typical examples of the measured vertical structures. In figure 1 both temperature and velocity profiles are con- tinuously stratified: the negative gradients of temperature show that there is no mixing. However, the profiles in figure 2 show a change in temperature of less than 0.2° C in the upper 28m, indicating that the water is nearly homogeneous and the current is also nearly uniform. The more the ocean is stratified, the greater is the tendency for agreement with Ekman' s model which was developed for a homogeneous ocean. As o o o o 2 o °b.oo 3'. 00 16.00 211.00 32.00 '40.00 — f-o 4 3?J00 C2 CD O CL 2£ • a 2 o • a w x w C r i 3 o "b.oo 00 16.00 24.00 (*H)Hld30 32.00 40.00 48.00 c o 3 o a cm o a a a □ o 03 00 CD 10 U3 Ld o O O) o o t— LD "4- O s_ Q. O O O O T3 0) ■b.oo 8.00 16.00 24.00 32.00 40.00 48.00 !T3 » o n o o 2 01 -1000. 21 CJ -2OO0 100. 200. 300. TIME (HOURS) 400 500 2000 O. 1000. s: a i 5 0. en ^ -100Q. CJ ■200Q. 100 200. 300. TIME (HOURS) 400 500. Figure 4. Wind speed vs time, u and v comDonent. 16 were low pressure disturbances which developed rapidly in the Gulf of Alaska and moved toward land in an East-Northeast direction. The center of the low on 31 August passed directly over station P, causing calm conditions for a few hours. That is shown by the double pulse in figure 3. B. ANALYSIS Figure 5 shows hourly temperatures at the studied levels and illus- trates the variability of the temperature structure of the layer above the seasonal thermocline. Homogeneous layers are indicated in this figure when temperature traces from two or more depths coincide. During stratified conditions, the vertical or horizontal movement of the water column past the sensors causes apparent temperature variability. Most of this vari- ability appears to be due to tidal -period internal waves. Above the 30 meters level, homogeneous and stratified conditions alternate in re- sponse to atmospheric conditions, as can be seen in the power spectra in figure 5a. With the rapid increase of the wind early on 22 August, at about 95 hours on the time axis, the temperature at 5m dropped and within four hours the upper 23m of the water column became vertically homogeneous due to strong mixing. During this strong wind event, the mixed layer deepened to nearly 35m. After the storm died, by 24 August stratifi- cation was reestablished between 17m and the base of the earlier 30m mixed layer. During the second storm the weaker wind event of 27-28 August mixed the upper layers to about 22m (figure 6). Figures 7, 8 and 9 are the power spectra for the u and v com- ponents of the observed current at three different levels, 11 , 23 and 17 o o m o o ZT s time. 6,29,32m. ■ ^-^ > CM o en to 00 o en OC -C CM -t-> « =) CD CM o -a « in CTi 1— -t-> 1 — to <— • UJ o 0J ~^ S_ en C\J CD tD 3 Q3Q 18 2.0 r cr 1-5 UJ 1.0 i m 0.5 O.O JL I -■ — - 0.00 0.02 0.04 0.06 TEMPERATURE -i o.oa 3-r 2. UJ I ~ 1. J- 00 0.02 Q.QH 0.05 TEMPERATURE o.oa Figure 5a. Power spectrum of the temperature at two levels Frequency: c.p.h. 19 0. en en 10, -20, Q_ LU o ia. •40. 100. 200. 300, TIME (HOURS) 4 00. 500 Figure 6 Mixed layer depth variation with time, as computed from MILE-1 temperature data buoy. 20 32m, for three different time windows. In figure 7 the time window is from 0 to 260 hours, only the effects of the first storm are present. In figure 9, the time window is from 200 to 460 hours, and only the second storm is present. For the spectrum of figure 8, the time window is from 100 to 360 hours, and the time period includes both storms. Comparison between different depth levels in figures 7 and 9 indi- cates different amounts of kinetic energy for each depth at near-inertial frequencies. The first storm, as can be seen in figure 4, was charac- terized by a pronounced shift from steady easterly winds to strong westerly winds. That strong change after a period of at least 100 hours of steady winds could be the means by which part of the energy transfer between the ocean and the atmosphere could have eliminated the existing inertia! current before generation of a new inertia! current. Since the upper ocean is assumed to be one-dimensional there must be some unsteady mechanism by which the vertical transfer of momentum is modulated in time, causing the observed phase and magnitude differences between the 32 meter level current and the surface. The response of the current in the upper layers to the second storm was quite different from the response to the first storm. In this latter case the wind shifted from having a northerly component to a strong southerly one and, in a few hours, to a northerly component again (figure 4). The upper level currents initially appear to be attenuated by the southern component winds but then are reinforced when the wind di- rection shifts toward the south. Also these winds have a smaller inten- sity and duration, and as it is shown by figure 6 the mixed layer did not deepen as much as in the first storm. 21 60. r _l 40. (X U.J A 20. o. — - . I > .1 — I -1 0. J20.04 0.ObO.uUU. 100. I 20. 14 OEPm ii m. 60. r _i 40. cr UJ ac i 1 ,i I ■ - ■ I I cr a 20. 0. 020. 04 0.06 0.08 0. 1 00. 120. 14 DEPTH 23 M. 60. 40. LU I 1 ■ ■ ' 1 0. 020.04 0.06 0. 080. 100. 120. 11 DEPTH 32 M. 60. r 40. 20. 0. •■■-llA. i i i a. j<;u.04b'.uu.oao.ioo. 120 14 DEPTH 11 M. 60. 40. 20. in j.i 1 1 „ 1 0. . 120.04 0. 06 0.08 0. 100. 120. U DEPTH 23 M. 60. 40. i 20. k I t -*-~. a 0.020.04 0.06 0.08 0. 10 0. 12 0. 14 DEPTH 32 M. Figure 7. Power spectrum of observed current. Time window 0 to 260 hours. « (Abscissa: c.p.h.; ordinate: (cm/s) ) 1 : inertia! frequency. 22 60. p 0.02 0.04 0.06 0.08 0. 10 0. 12 0. 14 DEPTH 11 M. 60. r 40. S» 20. 0. »k *-ij/li —■■''' 0.02 0.04 0.06 0.08 0. 100. 120. 14 DEPTH 11 M. 60. r 0.02 0.04 0.06 0. CeO. 100. 12 0. 14 DEPTH 23 M. 60. 40. i 20. t -« I J 0.02 0.04 0.060.Q8 0.100.120.14 DEPTH 32 M. 60. r 40. cc i 20. 0. J ^1^1 -1 I ■ J 0.02 0.04 0.06 0.080. 100. 12 0. 14 OEPTH 23 M. so. r 40. QC i 20. b ' ' 111 0.020.04 0.060.08 0. 100. 120. 14 OEPTH 32 M. Figure 8. Power spectrum of observed current. Time window : 100 to 360 hours. 2 (Abscissa: c.p.h.; ordinate: (cm/s) ) 1 : inertia! frequency. 23 cr LU i cr i 411. 20. i. C . T? cr _. cc I r\ h 1 1 > i l 0. >2 0.04.0.CbO.Gtt0.lQO.I20.l4 DEPTH 11 M. oO. 40. 20. LI - k c M cc I t^ll, I 1 I j. :2Q.cso. ooo.aao. too. 1 2 o. 14 DEPTH 23 M. 60. _J 40. cr LU cc i 20. cr LU CC 60. r 40. 0. iJJ.u4G.uoU.udO. 100. 12 0. 14 DEPTH 1 1 M. 60. 40. 20. 0. 1 .1 ifwl tmimmi UJ 0. J2 0.04 0.uo0.0d0. 100. 12 0. 14 DEPTH 23 M. 50. r 40. n ^°': A J_i 0. ,2 0. 04 0. u6 0.08 0. 100. 12 0. 14 DEPTH 32 M. a. 120.040. 060.080. 1 0 0. 120. 14 DEPTH 32 M. Figure 9. Power spectrum of observed current. Time window : 200 to 460 hours. ? (Abscissa: c.p.h.; ordinate: (cm/s) ) 1 : inertia! frequency. 24 Because the mixed layer had undergone a shallowing process as dis- cussed earlier, the transfer of energy to the 32m level was hindered by stratification. Figures 10 and 11 are the power spectra for the u and v compon- ents of the current for the total period of observation. The spectra for 32m level exhibit a double-peaked feature at the near-inertial period As Pollard [1970] suggests, at that depth it is unlikely that the ampli- tude of inertia! oscillations can be generated by the action of a single storm. The time series of observed currents are shown in figures 12 to 19. In those figures, the plotted running mean, an average over one inertia! period, shows the non-inertia! current at each level. It should be recognized here, that an undetermined part of this non-inertial current may be quasigeostrophic and not directly related to the local wind conditions. 25 u: UJ Q i o I 0- o (_> i 3 <"->■ r 20. lb, 1U. A I, J Q.000 0.Q2S 0.0S0 0.07S 0.100 0.125 0.150 0.175 TOTAL PEfllOO-DEPTH 23M. AC o I Z3 20. IS. 10. 5. ■ 0. 1.1SL-1 I 1 , I >-^ l, it J' I li i I i J Lft 1 J i I I I i l I 0.000 0.025 O.OiU 0.075 0.100 0. :S 0.150 0.175 TOTAL PLfllOO-UEPTH 32M. Figure 10. Power spectrum of observed current. Total period (u-component) . « (Abscissa: c.p.h.; ordinate: (cm/s) ) 1 : inertial frequency. 26 u U J cr i- o cj I X UJ az 0- r. o u I ;> ?u. lc.. 10. 5. - ,^A- 1^1. >.r O.UOO 0.Q2S 0.US0 0.0?S 0.10Q 0.1^5 0.150 0.17S TOTfiL PEfllOO-OEPTh 1 IM. 30. r 20. 10. . iVt-j uaC ^i,i. a 0.000 0.025 O.OSO 0.075 0. 100 0.125 0. ISO 0.175 TOTAL PEfllQD-QEPTH 23M. cr UJ cc 0_ r o Figure 11 25. 20. IS. 10. 5. - L_ 1'U. . 1 0.000 Q.Q2S 0.050 0.0/5 0.100 0.125 0.150 0.175 TOTAL PEFHUQ-OEPTH 32M. Power spectrum of observed current. Total period (v-component) . « (Abscissa: c.p.h.; ordinate: (cm/s) ) 1 : inertia! frequency. 27 40. . 20. (T) C_) -20. -MO. 40. 100. 200. 300. 400. HOURS. (DEPTH 11 M.) 1 i i 500. 500. 400. 500. HOURS. (DEPTH 32 M Figure 12. Observed current, total period (.u-component) . Running mean (*), average over 1 inert, period 28 Q_ CD 40. 20. 0. -20. •40. h U C, n. R A^T!! •/''ill I ■'{'* •■,' ' n _i_ 100. 200. 300. 400. 500. HOURS. [DEPTH 11 M. 40. . 20. Q_ O u en -20. ■40. J 1 I L 100. 200. 300. 400. J 1 500. HOURS. (DEPTH 23 M 40. • 20. o CO 0. -20. •40. ilULjUlJlll Uj . ■' I ! 1 H II I 0. 10c. ]0. 400. soo. HOURS. (DEPTH 32 M.l Figure 13. Observed current, total period (v-component) . Running mean (*), average over 1 inert, period 29 io. r . 20. o C_3 IT) ■20. -40. 50. 100. 150. 200. HOURS. (DEPTH 11 M. 250. 300. HO. p 20. CD cn -20. -40. 50. 100. 150. 200. 250. HOURS. (DEPTH 23 M.J 10. 20. CD -20. ■40. ■J\ i /i .n i ' ;»IHP I - 0. 50. !00. 250. HOURS. (DEPTH 32 M.) 300. Figure 14 Observed current: 0 to 260 hours (u-component) Running mean (*), average over 1 inert, period. 30 10. 20. O CO - -20. -40. J I 1 1_ J . . . L 50. IOC HCURS. (DEPTH 11 M. 100. 150. 200. HQURS. (DEPTH 23 M, 50. 100. 150. 200. HQURS. (DEPTH 32 M. 250. I I ' 300. 300. 300. Figure 15. Observed current: 0 to 260 hours (v-component) Running mean (*), average over 1 inert, period. 31 10. r 20. Q_ U I in 0. Z; -20. -40. no. 20. Q_ ' 0. in -20. -40. 100. 150. 200. HOURS 250. 300. [DEPTH 23 M 10. ■40. 100. 150. 200. 250. 300. 350. HOURS. [DEPTH 32 M.) 400. 350. 400. 400. Figure 16. Observed current: 100 to 360 hrs. (u-component) Running mean (*), average over 1 inert, period. 32 Q I CO '10. 20. 0. -20. -40. 40. 20. Hfiv vi 100. 150. 200. 35C HOURS. (DEPTH 11 M.) o <_> J o. CO 2: CJ -20. -40. 30. 20. 10. - > 100. 150. 200. 250. 300. HOURS. (DEPTH 23 M.J 350. CO -10. 2: u -20. -30. 100. 150. 200. 230. 300. HOURS. (DEPTH 32 M 350. 400. 400. 400. Figure 17. Observed current: 100 to 360 hrs. (v-component) Running mean (*), average over 1 inert, period. 33 40. 20. o CD ■20. •40. 200. 250. 300. 350. 400. HOURS. [CEPTH 11 M. 450. 500. 40. 20. CO X -20. -40. 200. 250. 300. HOURS 35G. 400. 450. [DEPTH 23 M.) 500. 40. 20. O ' o. en ^ -20. o . -40. 200. 250. 300. 350. 400. 450. HOURS. (DEPTH 32 MJ 500. Figure 18. Observed current: 200 to 460 hrs. (u-component) Running mean (*), average over 1 inert, period. 34 40. 20. en ■20. -40. H, ^ i M ft !i il V 200. 250. 200. 350. 400. 450. HOURS. (DEPTH 11 M.) 500. 40. 20. ED J 0. CO CJ •20. -40. 200. 250. 300. 350. 400. 450. HOURS. (DEPTH 23 M.) 500. 40. . 20. 2: o o 2, -20. -40. J ' ' ' I : I 200. 250. 300. 350. 400. HOURS. (DEPTH 32 M.) 450. 500. Figure 19 Observed current: 200 to 460 hrs. (v-component) Running mean (*), average over 1 inert, period. 35 III. DESCRIPTION OF THE MODEL A. THEORETICAL EQUATIONS In this study, one-dimensional conservation of momentum in the mixed layer is assumed. This conservation of momentum and the condition of incompressibility are reflected by the Navier-Stokes equations of motion, Dv Dt 1 * 2-*- x v = - ^ Vp + G + vV v 3u. 3)T = 0 setting: u = u + u + u1 g V = V + V + v1 g where u and u1 are the horizontal mean and fluctuating components of x-component of non-geostrophic velocity, and u is its geostrophic component; similarly v, v' and v are the corresponding y-components. y With the Boussineq approximation and Reynolds averaging, ft vG + u,) f(v + V + v') - — f^ g PQ 3x 3uV 3u'v' u'u 3z 3y 3x + v 92u + ±J_ + 32w 2 ' 2 ' 2 [Zxc dyc 3z^J ^(vg + v + V) = •f(u + G + u1) - — I2- g po 9y 3v'w' 3v'v' 3u'v 3z 3y 3x + v 32u 3^v + 32w 2 2 2 3x 3y 3z J Assuming (a) Reynolds stresses are much greater than viscous stresses (b) Vertical velocity field vanishes, w=0. (c) Geostrophic flow is separable from wind driven flow, and neglecting the horizontal density gradient - 1 3p g p0 3x Then the equations for wind-driven flow become 3u r- 3 — r— r Tqr = fv - t- u'w' at dl 3v -= - fu - — v'w [1] [2] B. NUMERICAL METHOD OF SOLUTION To solve equations [1] and [2] a vertical grid from the surface to 35m, was used. The values of u(z,t) and v(z,t) were then solved numerically as an initial -value problem. 37 Taking the equations for wind-driven flow and applying an eddy viscosity closure, — i — r I 3u -U W = k ir- dZ -v'w' = k and assuming k constant, gives: 8v 3z | = fv + k 4- [3] Sv .- 82v 67. The boundary conditions are a. At the surface: [4] -u'w' = 3uigi= Tx(t) 3z p v'«0 = k 3iM , Ld!i 3z p b. where x (t) and x (t) are wind stress in x and y directions respectively at time t and p is the density of sea water. At z = -D < -h, a "slip" condition is prescribed, u'w'(-D) = 0 v'w'(-D) = 0 38 With the eddy viscosity closure, | (-D) = § (-D) = 0 The numerical model used to simulate the current was based on a "leapfrog" scheme, with m indicating space (depth) and n time, then u(z,t) = u(mAz,nAt) = u(m,n). In this manner the component of equations [3] and [4] can be written: 3u u(m,n+1 ) - u(m,n-l ) 3t " 2At 3v ., v(m,n+l ) - v(m,n-1 ) 3t "' 2At fv = fv(m,n) fu = fu(m,n) k ^-4 = — ~* (u(m-l,n-l) - 2u(m,n-l) + u(m+l,n-l)) dzz (Mr k ^4 = — ^T (v(m-l,n-l) - 2v(m,n-l) + v(m+l,n-l)) 3z^ (Azr Solving for the (n+1) values, u(m,n+l )=Ru(m-l ,n-l )+(l-2R)u(m,n-l )+Ru(m+l ,n-l )+2fAtv(m,n) v(m,n+l )=Rv(m-l ,n-l )+(l-2R)v(m,n-l )+Rv(m+l ,n-l )-2fAtu(m,n) where: R = 2kAt/(Az)2. At the surface m = M and application of the boundary conditions gives: 39 u(M,n+l) = 2Ru(M-1,n-1) + (l-2R)u(M,n-l J + 2fAtv(M,n) + 2RAz xx(n)/(kp) v(M,n+l) = 2Rv(M-l,n-l) + (l-2R)v(M,n-l ) - 2fAtu(M,n) + 2RAziy(n)/(kp) The numerical model is stable when the value of R is equal to or less than 0.5. Assuming an eddy viscosity coefficient k of 23 cm/s and an increment of depth of Az = 1m, and a time step At = 100 seconds gives an R equal to 0.46. The initial conditions were established as those observed values of the current speed for each component, u and v, at time 0500 GMT August 19th, at the first recorded peak of the v-component of the current. The surface stresses xx and xy were computed eyery hour as a function of the hourly wind speed data for each component w and w , using 2 2 1/2 T = W (W + W ) Cnp x xx y' Da 2 2 1/2 Ty = Vwx + V CDpa with a value for the drag coefficient Cn of 1.3 x 10 . Values for the u and v components were calculated for each level, from the surface to 35m at intervals of lm, at time steps of 100 seconds. Every hour a new input of wind stress was applied, setting as initial conditions for the next run an integrated value for depth in the mixed layer. 40 Mixed layer depth as a function of time was deduced from the Mile-1 temperature time series and checked with Plessey CTD data taken from the R/V OCEANOGRAPHER. The model was initially run without any damping term, and the results were acceptable until the onset of the second storm. At that time a clear shift in phase between the recorded and modeled currents was observed. In an attempt to avoid a steadily worsening phase problem a linear damping term was introduced. According to Pollard and Millard [1970], this decay factor models the dispersion effect. Then the equations for wind driven flow become: 3u -- 3 at - fv - 37 (u'W) - cu 3v ,- 3 /— r— r\ _= _fu . ^-(vV) - cv -5 -1 A damping coefficient of c = 5.03 x 10 sec was chosen from Pollard [1970]. Thsi gives an e-folding decay time of 2.3 days. 41 IV. RESULTS Figure 20 through 22 show the modeled currents compared with the recorded ones at three differents levels. As was discussed earlier, the dominant frequencies of the model and the ocean are slightly different, see figures 23 and 24. There- fore when the wind decreases and the current is almost totally inertial under small forcing the modeled and observed oscillations will drift out of phase. This is most apparent in the period before the second storm, when the wind speed dropped to a minimum. The model does not have the capability to reproduce the observed current driven by the sharp change in directions of the wind during the second storm. The modeled and observed currents become out of phase at about time 330 hours. After the wind again becomes more steady in direction, the modeled and observed currents again agree in phase. Other discrepancies between observed and modeled current could be caused either by observational errors or by failure of the model to properly treat the physics of the problem, such as neglecting advection It is clear that the dissipation of mean kinetic energy is too much in the model using R = 1/2.3 days. Figure 22 shows that at the 32m level the modeled current is stronger than the recorded one. At the other levels the opposite happens. The model needs to be tuned to get a better amplitude comparison in the mixed layer. Doing this tuning by only comparison with observed currents is difficult because of the probable errors in the measurements. As 42 40. 20. Q_ 0. o I -20. -40. "■*%wto A 1 I ' ■ ' ! I : I I 0. 100. 200. 300. 400. 500. DBS. (-) 4 MdCELEQt..) CURRENT (11 M.) 40. 20. 0. o =3 -20. - -40. 100. 200. 300. 400. 08S. (-) S, MODELED!..) CURRENT (11 M.l 500. Figure 20. Comparison between observed and modeled currents. 43 o Q_ O (_> 40. 20. 0. > -20. -40. 100. 2C0. 300. 400. OBS. !-) & MODELED!..! CURRENT (23 M.) 500. 40. 20. LU _ Q _ o (_) I _ -20. -40. I L Mwww _______________ I I 100. 200. 300. 400. 500. OBS. (-) 4 MODELED!..) CURRENT (23 M.) Figure 21. Comparison between observed and modeled currents 44 40. p 20. LU o a. o 0. > -20. - -40. 0. 4wf§lfh 100. 200. 300. 400. OBS. (-) 4 MODELED!..) CURRENT (32 M.) 500. 40. 20. o Q_ 0. o I -20. -40. \4imm i. n \ J L. J I L 100. 2Q0. 300. 4Q0. DBS. (-) 4 M0DELEDL.) CURRENT (32 M.J 500. Figure 22. Comparison between observed and modeled currents 45 12.5 — 10.0 Q 7.5 a. 5.0 2.5 0.0 A...N-, -■^> ■•■' 0.000 0.0^5 0.030 0.075 0.100 0.125 0. i TOTAL PERIOD-QEPTH-1 1M. so. r SO 2.175 - 40. LlJ a ° 30. Ql 20. o u 10. 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 TOTAL PERIQ0-0EPTH-23M. a o z: 60. 60. 40. Q_ 2: o <-■ 20. 1 : ' ' ' ' ! ' ■ 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 TOTAL PERI0D-DEPTH-32M. Figure 23. Power spectrum of modeled current (u-component) 2 (Abscissa: c.p.h.; ordinate: (cm/s) ). 46 I2.S ~ 1 G . 0 1 7.5 Q_ 5.0 o 2.5 0.0 ~ 40. 30. - Q_ 20. O 10. - 0. _i_ _i_ 1 , I I i I 0.C00 0.025 O.OSC 0.075 0.10C 0.125 0.150 0.175 TOTAL =ERI0D-DEPTH-1 1M 50. r I ' ■' I i i : ' i ! I 0.000 0.025 C.0SC 0.075 O.'.OO 0.125 0.150 0.175 T3TPL PERICD-DEPTH-23M 90. p LU o o 2: 40. ED <-> 20. 0. L _l_ 0.C00 0.025 0.050 0.075 O.iOO 0.125 0.150 0.175 rOTRL PEPI0D-QEPTH-32M. Figure 24. Power spectrum of modeled current (v-component) (Abscissa: c.p.h.; ordinate: (cm/s) ). 47 suggested by Halpern et al LI 981 3 » there is spurious rotation of the rotor of the current meters produced by motions of the surface- following buoy mooring. Tuning could be done with a different treatment of the eddy vis- cosity as well as alternate parameterization of the mean kinetic energy. The first approach would be possible when turbulent viscosity of the water as a function of depth and stratification is better known, per- mitting detailed quantitative calculations of the vertical stress profile. Two other factors that could have a relative important effect on the currents and are not included due to the limited scope of this study is the process of inertial-gravitational wave propagation and the resultant horizontal dispersion of mean kinetic energy. 48 LIST OF REFERENCES Csanady, G. T. , 1981: Circulation in the coastal ocean. EOS, 62, 8-15. Ekman, V. W. , 1905: On the influence of the earth rotation on ocean currents. Arks. Nat. Astron. Fys., 2, 11 . Garwood, R. W. , 1976: A general model of ocean mixed layer using a two component turbulent kinetic energy budget with mean turbulent field closure. NOAA-TR-ERL-384, NTIS, Dept. of Commerce, Springfield, Va. Garwood, R. W. , 1977: An oceanic Mixed Layer Model capable of simulating cyclic states. J. Phys. Oceanogr. , 7_, 455-468. Gonella, J., 1971: A local study of inertia! oscillations in the upper layers of the ocean. Deep-Sea Res. , 18, 775-788. Halpern, D., 1974: Observations of the deepening of the wind-mixed layer in the Northeast Pacific Ocean. J. Phys. Oceanogr. , 4, 454-466. Halpern, D., R. A. Weller, M. G. Briscoe, R. E. Davis, and J. R. McCullough, 1981: Intercomparison tests of moored current measurements in the upper ocean. J. Geophys, Res. , 86, 419-428. Kase, R. H. , 1979: Calculations of energy transfer by the wind to near- inertial internal waves. Deep-Sea Res. , 26, 227-232. Kundu, P. K. , 1976: An analysis of inertia! oscillations observed near Oregon coast. J. Phys. Oceanogr. , 6_, 879-893. Kroll, J., 1975: The propagation of wind-generated inertia! oscill- ations from the surface into the deep ocean. J. Mar. Res. , 33, 15-51. McPhee, M. G., 1980: A study of oceanic boundary-layer characteristics including inertia! oscillation at three drifting stations in the Artie Ocean. J. Phys. Oceanogr. , 10, 870-884. Pollard, R. T., 1970: On the generation by winds of inertial waves in the ocean. Deep-Sea Res. , 17, 795-812. Pollard, R. T. and R. C. Millard, 1970: Comparison between observed and simulated wind generated inertial oscillations. Deep-Sea Res. , 17, 813-821. Pollard, R. T. , 1980: Properties of the near-surface oscillations. J. Phys. Ocanogr. , ]_0, 385-398. Webster, F., 1968: Observations of inertial period in deep sea. Rev. Geophys., 6_, 473-490. 49 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 3 Department of Oceanography Naval Postgraduate School Monterey, CA 93940 6. Professor J. Wickham, Code 68Wk 1 Department of Oceanography Naval Postgraduate School Monterey, CA 93940 7. Jose M. Fernandez Lopez 3 Capitan de Corbeta Institute Hidrografico de la Marina Cadiz, Spain 8. Antonio Ruiz Canavate 1 Teniente de Navio Instituto Hidrografico de la Marina Cadiz, Spain 9. Director 1 Naval Oceanography Division Navy Observatory 34th and Massachusetts Avenue NW Washington, D.C. 20390 50 No. Copies 10. Commander 1 Naval Oceanography Command NSTL Station Bay St. Louis, MS 39522 11. Commanding Officer 1 Naval Oceanographic Office NSTL Station Bay St. Louis, MS 39522 12. Commanding Officer 1 Fleet Numerical Oceanographic Center Monterey, CA 93940 13. Commanding Officer 1 Naval Ocean Research and Development Activity NSTL Station Bay St. Louis, MS 39522 14. Office of Naval Research (Code 480) 1 Naval Ocean Research and Development Activity NSTL Station Bay St. Louis, MS 39522 15. Scientific Liaison Office 1 Office of Naval Research Scripps Institution of Oceanography La Jolla, CA 92037 16. Library 1 Scripps Institution of Oceanographv P.O. Box 2367 La Jolla, CA 92037 17. Library 1 Department of Oceanography University of Washington Seattle, VIA 98105 18. Library 1 CICESE P.O. Box 4803 San Ysidro, CA 92073 19. Library 1 School of Oceanography Oregon State University Corvallis, OR 97331 51 No. Copies 20. Commander 1 Oceanography Systems Pacific Box 1390 Pearl Harbor, HI 96860 21. Chief, Ocean Service Division 1 National Oceanic and Atmospheric Administration 8060 Thirteenth Street Silver Spring, MD 20910 22. Almirante Director 2 Instituto Hidrografico de la farina Cadiz, Spain 23. Dr. David Halpern 1 Pacific Marine Environmental Laboratory 3711 15th Ave. NE Seattle, WA 98105 52 c.l 5S' LoPe2 '9374 7 currents during the Thesis L8225 Lopez c-1 Analysis and simula- tion of wind-driven currents during the Mixed Layer Experiment (MILE). 193747 thesL8225 Analysis and simulation of wind-driven c III II 111! I II II I 3 2768 002 12647 6 DUDLEY KNOX LIBRARY