»»»&! i m « BeSSs ffiffil mChBD mm m iffSHg&l &>j Hi Jsc H ■ ' '■ BBS SB) .'■«••'.. .'."■■.; ■nil bkp$8 HBii OH ' Boms flflffiBW ■■•v..."' :,■;■/' ■ ,'-', Dudley Knox Library, NPS Monterey. CA 93943 NAVAL POSTGRADUATE SCHOOL Monterey, California THESIS OC2A. on the unsteady response op . ::ig front to local atmospheric by Christopher James Hall June 19S3 PC] ICING Thes. is Advisor: Roland 7. Garwood, Jr. Approved for public release; distribution unlimited T209048 SECURITY CLASSIFICATION Of THIS PAGE (Whan Date i Sntered) REPORT DOCUMENTATION PAGE READ INSTRUCTIONS BEFORE COMPLETING FORM 1. REPORT NUMBER 2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER 4. TITLE (end Subtitle) Cn the TTnsteady Response of an Oceanic Front to Local Atmospheric Forcing 3. TYPE OF REPORT & PERIOD COVERED Master's Thesis June 1983 6. PERFORMING ORG. REPORT NUMBER 7. AUTHORO) Christopher James Hall 8. CONTRACT OR GRANT NUMBERf*; » PERFORMING ORGANIZATION NAME ANO AOORESS Naval Postgraduate School Monterey, California 93940 10. PROGRAM ELEMENT. PROJECT, TASK AREA & WORK UNIT NUMBERS II. CONTROLLING OFFICE NAME AND AOORESS Naval ^Postgraduate School Monterey, California 93940 12. REPORT DATE June 1^3~ 13. NUMBER OF PAGES 120 14. MONITORING AGENCY NAME * AOORESSf*/ different from Controlling Of Hca) 15. SECURITY CLASS, (ot thla raport) Ma. DECLASSIFICATION/ DOWNGRADING SCHEDULE '« DISTRIBUTION STATEMENT (el Oil a Report) Approved for public release; distribution unlimited 17. DISTRIBUTION STATEMENT (at tha act-tract entered in Block 30, tl dltlarant from Raport) It. SUPPLEMENTARY NOTES It. KEY WOROS (Conllnua on reyerae aida ii nacaaamty and Identity by block number) oceanic front density front 20. ABSTRACT (Continue on reverae aide It necoeamty end Identity by block number) The unsteady res -ens e of two oceanic density fronts to local atmospheric forcing, using combinations of wind stress and surface" heat flux, is investigated with an embedded mixed layer-general circulation model. The adjustment of the frontal structure is dependent uoon the wind stress direction and whether there is surface heating or cooling. In cases of an aoolied wind stress alone where denser water is transported do,'; FORM AN 7S 1473 EDITION OF 1 NOV «S IS OBSOLETE S/M 0102- LF- 014-6601 1 tprilBITV CLASSIFICATION OF THIS PAGE fWhon Data Kntarec SECURITY CLASSIFICATION OF THIS PAGE fWhan Dmlm Bnfntf) to v/ard less dense water, the frontal structure diffuses, the mixed layer depth ceepens, and cross-frontal nixing occurs. In cases where less cense water is transported to ware denser water, the frontal strucure is ^reserved, mixed layer depth is preserved ana cross-frontal mixing is minimized. The adcition of surface heating shallows the mixed layer and inhibits vertical mixing. Inertial oscillations are observed in the across-frcnt velocity field. S'N 0102- LF- 014- 6601 SECURITY CLASSIFICATION OF THIS P AGEfWT»»n DMm Bnfrmd) Approved fcr public release; distribution unlimited On the Unsteady Response of an Oceanic Front to Local Atmospheric Forcing by Christopher J. Hall Lieutenant, united States Navy E.S., United States Naval Academy, 1975 Subnitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN METEOROLOGY AND OCEANOGRAPHY from the NAVAL POSTGRADUATE SCHOOL June 1983 Dudley Knox Library. NPS Monterey, CA 93943 ABSTRACT The UESt«ady response of two oceanic density fronts -.0 local atmospheric forcing, using combinations of wind stress and surface heat flux, is investigated with an embedded mixed layer-general circulation model. The adjustment of the frontal structure is dependent upon the wind stress direction and whether there is surface heating or cooling. In cases of an applied wind stress alone where denser water is transported tcward less dense water, the frontal struc- ture diffuses, the mixed layer depth deepens, and cross- frontal mixing occurs. In cases where less dense water is transported toward denser water, the frontal structure is preserved, mixed layer depth is preserved and cress-frontal mixing is nir.iirized . The addition of surface heating shal- lows the mixad layer and inhibits vertical mixing. Inertial oscillations ars observed in the across-front velocity field. TABLE OF CONTENTS I. INTECDDCTICN 11 A. EACKGECUND AND PURPOSE 11 B. CBSEEVATIONAL STUDIES 12 C. MODEL STUDIES 16 II. DESCRIPTION OF THE PROBLEM 19 A. GENEBAL 19 B. HYPOTHESES 21 C. METHOD 29 D. DESCRIPTION OF THE MODEL 33 III. MODEL RESULTS FOR FRONT 1 CASE I 40 A. ANALYSIS AND DISCUSSION 40 B. SUMMAEY — CASE I 46 IV. MODEL RESULTS FOR F5CNT 1 CASE II 48 A. ANALYSIS AND DISCUSSION 48 B. SUMMAEY — CASE II 52 V. MODEL RESULTS FOR F5CNT 1 CASE III 57 A. ANALYSIS AND DISCUSSION 57 B. SUMMARY -- CASE III 62 VI. MODEI FESULTS FOR FBCNT 1 CASE IV 66 A. ANALYSIS AND DISCUSSION 66 B. SUMMARY -- CASE IV 74 VII. MODEL RESULTS FCR FFCNT 2 CASE I 75 A. ANALYSIS AND DISCUSSION 75 B. SUMMARY — CASE I 82 VIII. MODEL BESULTS FOR FRONT 2 CASE II 86 A. ANALYSIS AND DISCUSSION 86 3. SUMMARY — CASE II 90 IX. MODEL RESULTS FOR FBCNT 2 CASE III 93 A. ANALYSIS AND DISCUSSION 93 B. SUMMARY — CASE III 97 X. MODEL RESULTS FCR FRCNT 2 CASE IV 101 A. ANALYSIS AND DISCUSSION 101 B. SUMMARY -- CASE IV 104 XI. CONCIUSICNS AND RECOMMENDATIONS 110 A. GENERAL 110 B. BECCMMENDATIONS 112 LIST OF BEEEBENCIS 115 INITIAL DISTRIBUTION LIST 118 LIST OF TABLES TABLE I. Atmospheric Forcing used in Model Runs ... 30 TABLE II. Model Constants and Variables 35 LIST OF FIGURES Figure 1. Frcnt 1 Figure 2. Frcnt 1 Figure 3. Front 1 Figure 4. Frcnt 2 Figure 5. Frcnt 2 Figure 6. Front 2 Figure 7. Frcnt Figure 8. Front Figure 9. Frcnt Figure 10. Frcnt Figure 1 1. Front Figure 12. Front Figure 13. Frcnt Figure 14. Front Figure 15. Frcnt Figure 16. Frcnt Figure 17. Front Figure 18. Front Figure 19. Frcnt Figure 20. Front Figure 21. Front Initial Temperature 22 Initial Mixed Layer Depth 23 Initial U-Geostrophic Velocity. ... 24 Initial Temperature 25 Initial Mixed Layer Depth 26 Initial U-Geostrophic Velocity. ... 27 Case I 12-Hour Temperature 43 Case I 12-Hour O-Velocity 44 Case I 12-Hour V-Velocity 45 Case II 36-Hour Temperature 50 Case II 36-Hour U-Velocity 53 Case II 12-Hour V-Velccity 54 Case II 24-Hour Mixed Layer Depth. . 55 Case II 48-Hour Mixed Layer Depth. . 56 Case III 12-Hour Temperature 59 Case III 12-Hour Mixed Layer Depth Case III - T vs z Profile. . . . Case III 36-Hour V-Velocity. . . Case III 48-Hour Mixed Layer Depth Case IV 12-Hour Temperature. . . Case IV 12-Hour Mixed Layer Depth. . 60 . 61 . 63 . 64 . 68 . 69 Figure 22. Front 1 Case IV 12-Hour U-Velocity 70 Figure 23. Front 1 Case IV 12-Hcur V-Velocity 71 Figure 2a. Front 1 Case IV 36-Hcur Temperature 73 Figure 25. Front 2 Case I 36-Hour Tsmperature 77 Figure 26. Ficnt 2 Case I 36-Hour Mixed Layer Depth. . . 79 Figure 27. Front 2 Case I 12-Hour 0-Velocity 80 Figure 28. Front 2 Case I 24-Hour V-Velocity 83 Figure 29. Front 2 Case II 36-Hcur Temperature 37 Figure 30. Front 2 Case II 48-Hcur Mixed Layer Depth. . 89 Figure 31. Front 2 Case II 48-Hcur V-Velocity 91 Figure 32. Frcnt 2 Case III 36-Hour Temperature 94 Figure 33. Front 2 Case III 36-Hour Mixed Layer Depth. . 96 Figure 34. Frcnt 2 Case III 36-Hour U-Velocity 98 Figure 35. Frcnt 2 Case III 24-Hour V-Velocity 99 Figure 36. Frcnt 2 Case IV 36-Hcur Temperature. . . . 102 Figure 37. Frcnt 2 Case IV 36-Hour Mixed Layer Depth. 103 Figure 38. Frcnt 2 Case IV 12-Hcur V-Velocity 106 Figure 39. Frcnt 2 Case IV 24-Hcur 7-Velocity 107 Figure 40. Frcnt 2 Case IV 36-Hcur V-Veiocity 108 Figure 41. Frcnt 2 Case IV 48-Hcur V-Velccity 109 ACKNOWLEDGEMENT The authcr is especially grateful to Dr. R. W. Garwood, Jr. for sharing his knowledge and giving guidance in the preparation of this thesis. A special thanks is owed to Mr. D. A. adamec fcr his programming expertise in setting up the model and in preparing the graphics package. My wife Annette has stood by the entire time and without her support and encouragement the task would never have been completed. Computer support was provided by the W. R. Church Com- puter Center at the Naval Postgraduate School, Monterey, California. 10 I . INTRODUCTION A. EACKGSCUNE AND PURPOSE Curing recent years, there have been a number of scien- tific studies that describe the nature and existence of oceanic frcnts. Cromwell and Reid (1956) identified a front by an abrupt horizontal density change at the saa surface. Roden (1976) stated that a front should be considered to exist wherever any oceanic state variable (density, tempera- ture cr salinity) reaches a relative maximum value in its horizontal gradient. The mctivaticn for studying fronts and ocean prediction has been stressed by Roden (1976) , Elsberry and Garwood (1979), and Niiler (1982). Elsberry and Garwood (1979) spe- cifically pcint out antisubmarine warfare applications, fisheries management and a resource for climate research data, as viable and pertinent reasons for further study, tfany important physical processes which are accompanied by attendant air-sea interactions occur in frontal regions. Latent and sensible heat transfer, evaporative and precipi- tative processes, barcclinic currents, salt fluxes, mass and momentum transport, inert ial-int ernal wave activity and mix- ing all can occur. Oceanic frontal areas are areas of sound 11 speed changes and often are areas of increased biological activity. This thesis examines the time-dependent response of a numerically- simulated oceanic front to local atmospheric forcing. The model used in this work incorporates the forc- ings of wind stress and surface heating with a 20-levsl primitive equation ocean circulation model with embedded mixed layer dynamics. B. CBSERVATICBAL STUDIES Cromwell and Eeid (1956) described a simple case of an upper layer of warm, less dense water overlying a layer of cool, denser water in the ocean. The front in this case is a density front formed by the horizontal temperature gradi- ent. Observations shewed surface convergence along the front, sinking motion in the immediate vicinity of the front and divergence at lower depths. They observed that the wind affected the front by mixing the upper layer, reducing the horizentai surface temperature gradient, and enhancing the temperature jump at the base of the mixed layer. Vcorhis and Hersey (1S6U) observed a wintertime thermal front in the Sargasso Sea. They found an average tempera- ture gradient of 1 deg C/10 km, and a maximum in one 12 instance cf 1.5 deg C/5 km. This was accompanied by a 60 cm/s jet flowing to the east alcng the edge of the front. The depth of the front corresponded to the mixsd layer depth. The water on either side of the front was found to be well-mixed. Katz (1969) continued the work of Voorhis and Hersey and derived temperature-salinity correlations for a front observed in the Sargasso Sea in May. He found the front to be a separation cf two distinct water masses, with a tran- sition zone cf only a few meters in the vertical. He deduced that water transport along the front maintained the sharp Transition. Although not observed, Katz presumed mix- ing must occur at the interface, but the along-front current prevented any build-up of well-mixed waters in that area. He also hypothesized that a vertical component to the cur- rent must exist at the interface. Thus, the interface wculd be preserved by both horizontal and vertical motions, and the vertical velocity would account for the observed accumu- lation of well-mixed waters below the front. Eang (1973) studied a front at the southern end of the Benguela Current. This was an intense front with a horizon- tal temperature gradient cf 1.6 deg C/km and a temperature 13 change of 8-10 deg C across it. There was also local upwelling occurring due tc an offshore transport. As might be expected from Ekman theory, Bang found the front to intensify under southerly winds (Ekman transport being to the left of the wind in the Southern Hemisphere). Under a northwest gale, the front rapidly weakened. It reintensi- fied as the wind steadied from the south. Ecden has made significant and extensive contributions to the literature on oceanic fronts, especially on the large-scale fronts in the Pacific Ocean. In a series of papers, h€ has observed and examined the Pacific subarctic front (Roden 1975, 1977) , the subtropical front (Roden 1974, 1975, 1980), the doldrum front (Roden 1974, 1975), and the subarctic-subtropical transition zone (Roden 1971, 1972). In the 1971 paper, Roden concentrated on the subarctic-sub- tropical transition zone and found that the wind stress played an important role in determining the location of heat and salt flux divergence zones. Roden (1972) focused on the temperature and salinity fronts located at the boundaries of the transition zone; the subarctic front to the north and the subtropical front (which is also a density front) to the south. The oriains of bcth fronts were found to be related 14 to the wind stress, geostrophic flow fields and heat and salt flux divergence. The doldrum front was included in a study of the subtropical front (Rcden 1974) . Further work on all three fronts was conducted by Roden (1975) with ref- erence tc the wind and to the energy flux fields. He observed that the depth of the mixed layer changed dramati- cally across the subarctic front in winter and spring; from 100 m on the north side tc 300 m on the south side. The subtropical frcnt is highly dependent on the wind and energy flux fields at the sea surface, as the front occurs in an area of Ekman transport convergence. The doldrum front is a front due tc a salinity gradient only, with a baroclinic eastward- ilcwing current at the surface and a faster west- ward-flowing undercurrent. For the subarctic front, Roden (1977) found atmospheric forcing (that is, wind stress, radiative heat flux, precipi- tation and turbulent energy fluxes) to be the primary cause of frontal movement, intensification and decay. Roden has shown repeatedly that the roles of wind stress, Ekman trans- port and heating are inextricable from the dynamics of frcn- togenesis. Eoden (1980) again examined the subtropical frontal zone (within which are located a number of 15 individual fronts) and showed that Ekman transport led tc a concentration of the temperature and salinity gradients in the upper ocean. Thus, frontogenesis was due to horizontal convergence and confluence of the flow field. While Boden's work has dealt primarily with frontogene- sis ard in explaining the dynamics of several identified North Pacific frcntsr his findings are pertinent to this thesis, i.e., local atmospheric forcing plays a major role in the dynamics of oceanic fronts. C. MCDEL STUDIES Garvine has concentrated on a modelling, approach to fronts. In cne of his earlier papers (1974), he investi- gated the dynamics of small-scale fronts, though without regard to atmospheric forcing. Such fronts propagate into the ambient water via the unbalanced horizontal pressure gradient. Because of minimal cross-frontal mixing, he found strong convergence and sinking at the front. He later expanded this irodel to include the effects of wind stress (Garvine 1979a, 1979b) . However, because of zhe need to maintain steady state in the model, he prescribed wind stress to be of secondary importance relative to the hori- zontal pressure gradient. Buoyancy and energy budgets were added later tc the model (Garvine 1980). 16 Kao (1980) investigated the Gulf Stream as a large-scale density frcnt in the upper ocean. The heart of his work was performing a scale analysis, which revealed three length scales: an inertial or deformation length scale, a buoyancy length scale, and a diffusive length scale. Kao's conclu- sion was that the front was maintained by the cross-Gulf Stream circulation, but his model included no wind stress or heating. Cushman-Roisin1 s (198 1) model was based on Roden's work on large-scale frontogenesis, and it does have some similar- ities to the model used in this thesis because it includes mixed layer dynamics. An important difference is in the scales. Cushman-Roisin investigates large-scale and long- term spin-up cf a frcnt in response to a wind stress curl. The model in this thesis is used to investigate local response of a pre-existing front tc local winds and heating. Surface wind stress is a primary means of forcing in both models, but Cushman-Roisin applies a strong wind stress curl in the form cf a wind field that changes direction at the latitude cf the zonally-oriented front. Me, on the other hand, spin up a horizontally uniform wind stress over six hours, after which it maintains a constant value. The 17 results obtained by Cushman-Roisin depend much upon the curl of the wind stress. Cushman-Roisin finds the mixed layer depth is at a minimum in the middle of the front, while Ekman downwelling is at a maximum. This is probably due to a lack of any wind stress at the front itself, although the curl is large. Camerlengc (1982) studied the large-scale response of upper ocean fronts, specifically the Pacific subarctic front. His model has a variable-spaced horizontal grid with highest resolution in the frontal area. Vertical mixing was not included in the model. Assuming a pre-existing front, Camerlengc applied different wind stresses, and found that except in the case of the passage of a strong cyclone, the effects of wind forcing were limited to the upper 150 m. One case of a uniform wind stress did show Ekman transport and a horizontal displacement of the front. 18 II. DESCRIPTION OF THE PROBLEM A. GENERAL The response of a pre-existing oceanic front to local atmospheric forcing (wind stress and surface heating) over a time period of two days is examined. An embedded mixed lay- er-ocean circulation model is used, and two different fron- tal structures are treated. The first numerically-inserted front, hereafter referred to as Front 1, is somewhat of an artifact in that the isotherms become horizontal at a rela- tively shallow depth (see Figs. 1, 2, and 3 for the initial conditions) , so that Front 1 is manifested only within the upper 60 m. The temperature field is vertically stratified below approximately 70 m. The front is about 10 km wide. The maximum horizontal temperature gradient at the surface is 1.5 deg C/1.6 km. The mixed layer depth is a numerical- ly-inserted approximation to what the actual mixed layer depth would be. A geostrcphic along-front velocity is cal- culated from the initial temperature field. It has a maxi- mum speed of 32 cm/s with its axis located at the surface on the warm side cf the front. The across-front geostrophic 19 velocity is zero. Front 1 is a viable representation of a smaller mescscale upper layer front, and the model results will be important in this context. The second type of front, hereafter referred to as Front 2, is a simulation of a more typical front, similar to those reported by Rcden (1980). The horizontal temperature gradient at the surface is 1.5 deg C/3.2 km. The front is not only evident at the surface, but also its effect on the temperature field extends throughout the thermocline of the model (see Figs. 4, 5, and 6 for the initial conditions) . The mixed layer depth again is a numerically- ins erted approximation based en the shape cf the temperature field. It is felt that adjust- ments which occur shortly after the start of integration of the Eodel will compensate for any errors in the initial field. A gecstrophic along-front velocity is calculated from the initial temperature field. Its maximum value is 100 cm/s and the axis lies at the surface on the warm side of the frcnt. The acrcss-front gecstrophic velocity is zero. With both fronts oriented in a right-hand coordinate system, z increases upwards, y increases to the right, and x increases out cf the page. 20 3. HYPOTHESES It is expected that the direction of the wind relative to the orientation of the front plays an important role in the near-f rental circulation and density structure. Ekman transport across the front should cause upweliing and down- welling features near the surface manifestation of the front. Jchannessen, et al (1977) observed that the thermo- cline through the Maltese front shallowed in certain areas, which indicated upweliing, and also that -he thermocline spatially deepened after isotherms surfaced. In Johannes- sen's case, this was attributed to the presence of an eddy. If the water masses had been of similar types, it would have been indicative cf downwelling. With regard to one-dimensional mixing, Niiier's (1975) mixed layer model used an impulsive wind stress and no heat- ing, and showed that initially the mixed layer deepened rap- idly. Strong inertial motions can be generated which car lead to a large increase in available turbulent energy and thus to a rapid (within the first half pendulum-day) deepen- ing cf the mixed layer. Mellor and Durbin (1975) also used 2 2 an impulsive wind stress of 2 cm /s (approximately 2 dynes/cm^) and no heating. They showed that the mixed layer 21 T at hour 0 o.o 25.0 50. o-; 75.0- 16.0 Q. CD Q 100.0- 125.0- 150.0- 175.0- 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Figure 1. Frcn-t 1 Initial Temperature. Only the middle section of the grid and the upper 175 m are shewn. Contour interval is 0.5 deg C. 22 H at hour 0 25.0- 50.0- 75.0- (D Q 100.0 125.0- 150.0- 175.0 1 — r— — i — i — i" i i i i i i i i 25.0 35.0 45.0 55.0 65.0 75.0 Y-distance (km) Figure 2. Brent 1 Initial Mixed Layer Depth. 23 U at hour 0 o.o 25.0- 50.0- 75.0- a a 100.0- 125.0- 150.0- 175.0 2 i i i i J o X 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Figure 3. Frcnt 1 Initial U-Geo strophic Velocity. Contour interval is 8 cm/s . 24 T at hour 0 05 Q 25.0- 50.0- 75.0 - 100.0 125.0- 160.0- 175.0- 200.0- 225.0 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Figure 4. Front 2 Initial Temperature. Only the middle section of the grid and the upper 225 m are shewn. Contour interval is 0.5 deg C. 25 H at hour 0 o.o 25.0- 50.0- 75.0- E 100.0- Q. Q 125.0- 150.0- 175.0- 200.0 225.0 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Figure 5. Frcut 2 Initial Mixed Lay€r Depth. 26 U at hour 0 CD Q 0.0 25.0 J 50.0- 75.0- 100.0- 125.0 150.0- 175.0- 200.0- 225.0 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Figure 6. F-cn+- 2 Initial U-Geostrophic Velocit interval is 20 cai/s. Dashed lines negative values. inai Contour cate 27 deepened and that the temperature jump also increased slightly. In a two-dimensional model, De Szoeke (1980) examined the effects of wind stress only in his version of the Niiler (1975) model and found that in the case of constant wind stress, the mixed layer deepened rapidly in the first half pendulum-day (t=Pi/f), and then slowed. An additional effect of the wind stress is the possible augmen- tation of a guasi-gecstrcphic frontal shear (in the along- front direction) which could increase vertical mixing as prescribed by the initial value of the Gradient Richardson Number: Ri = £ x (dynes/cm ) t_y (dynes/cm ) Q (deg C-cm/s) Case I ♦ 1.0 Case II -1.0 Case III + 1.0 Case IV -1.0 0 0 0 0 0 0 -.004 -.004 In the cases above, Tx is the along-front (x-direction) com- ponent of wind stress, Ty is the cross-front (y-directicn) component of wind stress, and heat flux Q is applied to the ocean uniformly at the surface (heat flux is positive upwards, so the negative value indicates warming of the ocean from the air) . All four cases are examined for both Front 1 and Frcnt 2. Cases I and II examine the effects of wind stress paral- lel to the frcnt only, which will eventually generate a steady Ekman transport perpendicular to the front. The wind stress of 1 dyne/cm^ corresponds to a wind speed of 7-3 m/s. In all cases the wind stress is spun-up from 0 at t=0 to its 2 maxiium absolute value (1.0 dynes/cm ) by hour 6. From hour 6 to hour 48 it remains constant. Such a shcrt spin-up time is net unreasonable, as winds can change on a shorter time scale, for example, when an atmospheric cold front passes. Cases III and IV impose a constant surface heating on each 30 of the twc preceding cases. As indicated by the earlier one-dimensional mixed layer models, we expect that the heat- ing value will net be overwhelmed by the wind stress, and that the effects of both dynamic and thermodynamic forcing will te evident. The initial conditions for Front 1 are shown in Figs. 1, 2, and 3. Warmer, less dense water resides on the left, and cooler, denser water resides on the right. The initial con- ditions for the velocity are determined by the associated initial density field, which is balanced by a geostrophic along-front current directed out of the figure (u positive) (see Fig. 3). The mixed layer depth varies from a uniform depth in the far field to a shallowing through the front. The model is run for a 48 hour time period for each of the specified atmospheric forcings shown in Table I. In Case I we expect tc see water from the cold (right) side transported to the warm (left) side, upwelling en the cold side at the front and dcwnwelling due to connective and turbulent mixing en the warm side. The mixed layer depth should deepen, and the front should diffuse. In Case II we expect the warm water to be transported on the surface to the ccld side, but convective mixing to be absent due to the 31 suable condition of the less dense water overriding the den- ser water. Opwelling shculd occur on the warm side at tha front, and only minor downwelling should occur on the cold side due to the effect cf wind stirring alone. In both Cases III and IV the heating should have a shallowing influ- ence on the mixed layer depth tending to offset deepening and ether effects caused ty turbulent mixing. The initial conditions for Front 2 are shewn in Figs. 4, 5, and 6. In this configuration, the warmer, less dense water resides en the right and the cooler, denser water resides on the left. The accompanying along-front gecs- trcphic current is directed into the page (u negative) with its maximum value at the surface. The mixed layer depth follows the ccntcurs of the upper -hermociine, shallowing across the frcnt. The mcdel is initiated and integrated in time as it was fcr Front 1. In Case I (wind stress positive, directed out of the figure) , we expect the Ekman transport to be toward the left. The results fcr this case should be analagous to the expected results for Case II applied to Front 1 as previ- ously noted. Case II should be compared to Case I for Front 1 and Cases III and IV should be compared to Cases IV and III respectively cf Front 1. 32 The inertial pericd fcr our model is 27T ' T. = ^j-~ 20 hours at the latitude cf 36 deg N. Considering that in this model wind stress dees not attain its steady maximum value until 6 hours have elapsed, we should find a maximum in inertial motion somewhat later than half an inertial period after time zero, at perhaps t=15 hours cr so. D. EESCHIETICN CF THE MODEL The primary documentation for the model is in Adamec, et al (1981). In that paper, the model is cast in radial coor- dinates to investigate the oceanic response to a stationary radially-symmetric hurricane. In our case, the model is in right-hand Cartesian coordinates and it is two-dimensional (y and z) . It is believed that this model is particularly well-suited tc the study cf upper ocean fronts because it incorporates the Garwood (1977) bulk mixed layer model into the Haney (1980) primitive equation model. The ocean is assumed hydrostatic and incompressible, where density is a function of temperature alone. The Coriolis parameter is constant and there are no fluxes of mass, momentum or heat 33 normal to any boundary except at the surface, where atmos- pheric forcing is applied. The horizontal grid spacing is 125 m and the vertical grid spacing is variable over 20 lay- ers from 6m at the top layer to 64 m at the bottom layer. The domain size in y and z is 100 km by 500 m, respectively. With the frcnt pre-existing as an initial condition, the initial u-ccmponert of velocity is in geostrophic balance, and the initial v-component is initially set to zero. Drawing upcn Adamec, et al (1981), highlights of the model are outlined below. Table II lists the pertinent model variables and constants used in the governing equations . The governing eguations in their two-dimensional form are as follows: St ay dz 8zv \i) &t *y dz j.iy MB 2 fa 5t ^y az T^y2 ^z ^; 34 TABLE II Model Constants and Variables at AM Km R M To At J K z=-D y u T hr H coefficient of thermal expansion hcrizcntal eddy conductivity coefficient for heat hcrizcnxal eddy diffusion coefficient for momentum vertical eddy conductivity coefficient for heat vertical eddy diffusion coefficient for momentum latitude Ccriclis parameter gravity reference density of seawater reference temperature racdel tircestep horizontal grid array size vertical arid array size basin depth basin width x (along-front) component of velocity y (across-front) component of velocity temperarure mixed layer depth 2.0E-5 /degC 2.5E+5 cm2/s 2.5E+5 cm2/s 0.5 cm2/s 0.5 cm^/s 36 N 8. 55E-5/S 981.0 cm/s2 1.0276 g/cm^ 5 degC 30 s 800 20 500 m 100 km 0 = " n ~ ?g (5) e . ^ ( 1 -*(i - I ) ) (6) The tcundary conditions are: u = ° • AM^ " ATif " ° ® y = 0 , 100 km (7) w=0@z=0,-D (8) 35 .w'T1 = -2- , -u'w1 = ~ . -v'w'=0@z = o ?oc to -w'T ' = -u'w' = -V ' w ' = 0 © Z a -D (9) An equation fcr the depth, h, of the well-mixed layer is derived by integrating the continuity equation and applying the rigid lid boundary condition (Eq. 8) : H + w-h = we (1°) The vertical turbulent fluxes are parameterized in two different Banners depending upon where in the water column they are located. Below the mixed layer, the vertical fluxes are parameterized by eddy viscosity and conductivity coefficients : »'w' " "K^z ▼•*■ = -^M on 'M3z WT" - -KT|f Above the mixed layer, turbulent mixing makes such a method which assumes Kj, and K™ constant unrealistic and inaccurate. Thus the Garwood (1977) turbulence closure model is invoked using bulk turbulent kinetic energy equations. 36 The entrainmer.t buoyancy flux is given by: 1 .-. <*g(v/'T')_h = -/h (12) where and are the vertical and total components respectively cf the turbulent kinetic energy. The mixed layer total turbulent kinetic energy equation and the verti- cal component of turbulent kinetic energy equation are: h£Z = mi: I - «Sh(;7^).il/(2Ri*) - (4 + fh)(E> (13) JL at h(\v'w!) = *gh((w'T')_h - (WT')0)/2 + ( - 3(v7m7'))<2)* - (/3 (H) where u* = is the friction velocity and Ri*= 0 becomes the new nixed layer depth. During mixed layer shal- lowing, heat, momentum and potential energy are conserved. To prevent the levels beneath the mixed layer from becoming unstable in the numerical process, a dynamic stability con- dition is imposed such that the Gradient Richardson Number is always greater than 1/4. The embedding of the mixed layer model within the gen- eral circulation model requires communication between the two. The general circulation model is the dynamic portion which calculates changes of u, v, and T at each depth level 38 due to advective and diffusive processes. These values ar<= then acted upon by the mixed layer model, which in tarn cal- culat€s the changes due tc surface fluxes and entrainment mixing, and calculates the new mixed layer depth. These values are then used by the general circulation model. 39 0 III. MODEL RESULTS FCR FRONT 1 CASE I A. ANALYSIS AND DISCUSSICN Although the front is initially in geostrophic balance, the imposition of atmospheric forcing causes the front t undergo a variety of adjustments. In Case I, a positive wind stress cf 1 dyne/cm^ is applied. The front and the u-component field undargo diffusion, thereby giving rise to an ageostrophic u-component, which in turn creates a v-ccm- ponent. As diffusion occurs through mixing, and as the sur- face expression of the front is advected to the left in response to the wind stress, the along-front jet decreases in magnitude as well as in horizontal extent. A small count^rcurrent is present at hour 24 due to a reversal in the slope of the isotherms in the vicinity of the front. This effect disappears by hour 36, but then reappears at hour 48. The base cf the front en the right side deepens (as evi- dent by the isotherms becoming vertical to greater depths) from about 30 or initially to about 50 m as a result of the effect of turbulent mixing and the creation of ageostrophic 40 velocities while undergoing dynamic adjustment (see Fig. 7). kn ageostrcphic u-component is evident in Fig. 8 in the area of y=53 km to 61 km. The mixed layer depth increases as the upward sloping thermccline erodes within the front because water is transported across the front, right to left. The mixing of the coder water with the warmer water causes the mixed layer depth to deepen on the left (warm) side. The axis of maximum v-values lies just above the bottom of the mixed layer near y=53 km. If the v-profile is examined (Fig. 9) , it is seen that dv/dy > 0 on the right (cold) side of the frontal axis, and dv/dy < 0 on the left side. The gradients cf v are much stronger on the left side of the front than they are on the right. The maximum v-velocity is -8 tc -10 cm/s. From continuity, dw/dz < 0 (downwelling) on the right side cf the axis and dw/dz > 0 (upweiling) in a thin layer on the left side that closely follows the mixed layer depth. It is noted also that the mixed layer depth has deepened at the right side of the front. This phenom- enon is present throughout the model integration. Though such a conditicr was not anticipated prior to the running of the model (we expected an upweiling in the mixed layer on the right side as a result of the mass transport over the 41 front towards the left) , this depression in deptn is believed tc be physically realistic. It is suspected that this increase in the mixed layer depth occurs in response to non-staticnary adjustment to the atmospheric forcing, as it also occurs in Case II where the oppositely-directed wind stress is applied. Because the mixed layer depth responds to the vertical integral of transport, the fact that the mixed layer is shallcwer within the front than in the far field blocks the flow frcm penetrating to depth. As the water encounters this "obstacle", it "backs up" on the right side and thus forces a depression in the mixed layer. This explanation must be tempered by the fact that these figures are instantaneous snapshots in time, and can be deceiving in attempting tc describe processes that have been evolving over a length of time. Another possibility is that some type of internal standing wave has been excited which is causing fluctuations in the mixed layer depth. The influence of the ageostrophic u-veiocity, the core of the v-velocity lying along the well-mixed layer and the depression of the mixed layer on the right side of the front is felt at depths greater than 100 m. Upwelling and down- welling are evident at these depths (Fig. 7) beneath the right edge cf the front. 42 T at hour 12 o.o 25.0 J 50.0 75.0- Ql (D Q 100.0 125.0- 150.0- 175.0 15.20 14.40 i i 25.0 35.0 45.0 55.0 65.0 Y-distance (km) 75.0 Figure 7. Frcr.t 1 Case I 12-Hour Temperature. Ccatou: interval is 0.2 deg C. 43 U at hour 12 o.o 175.0 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Figure 8. Frcr.t 1 Case I 12-Hour U-Velocity, interval is 8 cm/s. Contour 44 V at hour 12 o.o 25.0 50.0- 75.0- Q. CD Q 100.0- 125.0- 150.0 175.0 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Figure 9. Front 1 Case I 12-Hour V-Vexocity. . C interval is 2 cra/s. Dashed lines ma negative values. Contou: icare 45 Interesting patterns in the v profiles evolve at hours 24 and 48. At 24 hours a small positive v exists. This is contrary to the expected Ekman transport direction in the surface layer, and is prctably the result of an oscillation created by the inertial mction. Furthermore, at both 24 and 48 hours, two cores of a positive v-component are present symmetrically centered about the base of the mixed layer on either side cf the front. These are not present in the front, but form outside the frontal area and extend to the far field where the mixed layer is relatively stable. The across-front velocity component is in consonance with the direction of the net Ekman transport at all times except hour 24. As noted, this velocity is at a maximum at the base of the mixed layer rather than at the surface. It is ncn-zerc beneath the mixed layer in the middle of the front as well. Thus, it appears that interfacial mixing does occur in this case, and it may be contributing to the vertical mixing cf heat in the thermocline at this location. B. SUMMAEY — CASE I Under the influence of positive wind stress and no heat- ing, the frcnt has diffused and has been advected in the direction of the surface Ekman transport. Because the frcnt 46 is unsteady under an applied wind stress, ageostrcphic velocities are created. Fart of the response is fricticnai due to the turbulent boundary layer or mixed layer pro- cesses, and part is inertial due to the applied wind stress boundary condition. A noticeable deepening of the mixed layer occurs at the front en the right (cold) side, and the horizontal variability in mixed layer depth and temperature are reduced significantly under the influence of both verti- cal and cress-frontal mixing. 47 IV. MCDEL HESCITS FOR FRONT J. CASE II A. ANALYSIS 5ND CISCUSSICN In this case, a negative wi nd stress (directed into the page) is applied. Wind stirring must overcome static sta- bility as the warmer water will override the cooler water. It will be seen that the wind stress cf 1 dyne/cm^ is suffi- cient to mix the warmer water which is transported toward the cooler water. There is no evidence of stratification of shallow waters. Recall from Case I that, as the denser water from the right side was being transported to the left, it had to overcome static stability in order to upwell and override the front, and that the mixed layer depth profile posed a vertical barrier to the transport. In this case, the base cf the mixed layer is at an incline in the direc- tion of transport and static stability need not be overcome in the transport process. This leads to the expectation that cross-frontal mixing may be minimal in this case. Diffusion in the temperature field again is evident over the 48 hours, but this time it occurs primarily at the edges of the front. A strong horizontal temperature gradient of 48 0.6 cleg C/1.2 km in the middle of the front is maintained up through 48 hours (see Fig. 10 as representative of this) which was not present in Case I. This lands credence to the hypothesis that cross-frontal mixing is minimal. Noticeable mixing occurs on the cold side of the front. The isotherms are vertical to greater depths than they were in Case I (see Fig. 10) . The turbulent mixing alone not only cverccmes static stability but is also able to mix to a relatively greater depth en the right side of the front. The water that is being transported across the front is apparently immediately mixed by wind stirring as no plume of the warm, less dense water is present on the right side. The alcng-front current again forms an ageostrophic com- ponent as it ur.dergoes adjustment, and is especially evident on the right side of the front around y=55 km (Fig. 11) where it exists to a greater extent both horizontally and vertically than was seen in Case I. The core of the alcng- front jet dees decrease in speed and diffuse in time. By hour 36 the maximum value cf u has been reduced to slightly more than 8 cm/s. The creation of this ageostrophic veloc- ity accompanied by a v-compenent leads to strong downwelling around y=55 km underneath the front (Fig. 10) and remains 49 T at hour 36 o.o 25.0- 50.0 75.0- Q. 0 Q 100.0- 125.0- 150.0 175.0 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Figure 10. Front 1 Case II 36-Hour Temperature. Contour interval is 0.2 deg C. 50 over the 48 hcur integration. A strong core of negative across-front velocity of ever -6 cm/s is created in this area (Fig. 12) , and there is an attendant sharp upwelling in the isctharms at 75 m and wave-like fluctuations present to depths beyond 175 m. In the areas where dv/dy > 0 (dw/dz < 0) , downwelling is seen in the front, and where dv/dy < 0 (dw/dz > 0) , upwelling is seen. In the surface layer, the v-component is positive and in the direction of Ekman trans- port. It is concentrated in a jet in the area of the tight- est horizontal temperature gradient over the shallow peak in the nixed layer depth. All of these tendencies and trends persist over the 48 hcur integration. A deepening in the mixed layer occurs to the right of the front near y=55 km and progresses outward in time. The shallow peak in the mixed layer depth within the front is mostly preserved, though some erosion and mixing obviously has occurred (compare Figs. 13 and 14). This further sup- ports the hypothesis that minimal cross-frontal mixing occurs. Examination of the corresponding v-fields also show little cress-frontal nixing. 51 B. SUMMARY -- CASE II In this case of a forcing of a negative wind stress and no heating, the temperature structure of the front retains a strong horizontal gradient over -he U8-hour integration. Diffusion cf the front occurs, but it is concentrated at the boundaries of the front. Kind stirring overcomes the static stability cf transported water once it crosses the front. The cieaticr under adjustient of a large ageostrophic u-ve- locity and an accompanying v-velocity give rise to strong upwelling and dcwnwelling features within the front. The shallcw peak cf the mixed layer depth within the front is preserved ever time. The fact that this peak is maintained, the hcrizcntal temperature gradient retains a tight struc- ture, and the v-field is mainly constrained to the ageos- trophic areas an3 surface layer, suggests that interfacial or cress- f rental mixing is minimal. 52 U at hour 36 o.o 25.0- 50.0 *c 75.0 Q. © Q 100.0- 125.0- 150.0- 175.0 25.0 35.0 45.0 55.0 65.0 Y-distance (km) 75.0 Figure 11. Fzcnt 1 Case II 36-Hour U-Velocity. Contou: interval is 4 cm/s. 53 V at hour 12 o.o Q. CD Q 25.0^ 50.0- 75.0- 100.0- 125.0 J 150.0- 175.0 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Figure 12. Front 1 Case II 12-Kour V-Velocity. Contou: interval 2 cm/s. 54 H at hour 24 o.o 25.0 50.0 75.0-1 Q. CD Q 100.0- 125.0- 150. On 175.0 25.0 35.0 45.0 55.0 65.0 Y-distance (km) 75.0 Figure 13. Frcnt 1 Case II 24-Hour Mixed Layer Depth, 55 H at hour 48 o.o 25.0- 50.0- 75.0-1 Q. (D Q 100.0- 125.0- 150.0- 175.0 ' i i i i { i i i i | ■ i i i 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Fiqure 14. Fxcnt 1 Cass II U8-Hcur Mixed Layer Depth, 56 V. MCDEL RESULTS FOR FRONT J. CASS III A. ANALYSIS AND CISCUSSICN A unifcrm surface heating is applied with the identical wind stress cf Case I. The magnitude of each forcing is such that influences frcm both are expected to be mani- fested. In examining Figs. 15 and 16, the obvious effect of heating is the adjustment cf the temperature structure on either side cf the front. At first examination, it appears that the heating is having the opposite effect of what is expected - that is, it appears to cool the mixed layer rather than warm it. In reality, the heat is carried dcwn to depths cf 50 id and warms the water there. Cooling occurs between 32 and 50 m depth, which is readily seen in Fig. 17. Mixing may create a dynamic instability in the thermocline, and vertical diffusion of heat by Rp*d2T/dy^ may cause the intermediate water to be ccoled and the deep mixed layer to be warmed. This basic structure remains over the 48-hcur integraticn. The front undergoes diffusion and is advected to the left, as occurred in Case I. The front is manifested to a lesser depth in accordance with the heating process - downwelling and mixing have been moderated by the heating. Though some wave-like mction is seen in the temperature 57 field beneath the mixed layer, the magnitude is not as great as in the case of wind stress alone. The mixed layer depth has shallowed to about 43 m under heating alone in the areas outside the front (see Fig. 16). This shallowing occurs because the atircspheric forcing (heating and wind) is input as a body force ever the entire mixed layer. The heating has the effect of making the mixed layer depth more uniform. The narked deepening in the mixed layer depth that occurred in Cases I and II at the right (cold) side of the front is not present in this case. The deepening of the mixed layer affects the u-field. The ageostrophic u-component does not develop to as great an extent as it did in Case I. The gen- eral along-front current appears much as it did in Case I, except that its vertical extent is also constrained by the shallower mixed layer depth. In both cases, maximum speeds agree ever the 48-hour integration, and they ar a advacted with the front as it responds to the mass transport. The v-field follows the same trends as it did under wind stress alone. At 12 hours, v is directed to the left as expected following the transport, and at 24 hours the v-ve- locity reverses and establishes the layers of concentrated positive v-values centered symmetrically about the mixed 58 T at hour 12 o.o 25.0 50.0 75.0- Q. CD Q 100.0 125.0- 150.0 175.0 16.00 15.20 14.40 25.0 35.0 . 45.0 55.0 Y-distance (km) 65.0 75.0 Figure 15. Frcnt 1 Case III 12-Hcur Temperature. Contour interval is 0.2 deg C. 59 H at hour 12 o.o 25.0- 50.0- 75.0 Q. © 100.0- 125.0- 150.0- 175.0 -J 25.0 35.0 75.0 Y-distance (km) Figure 16. Front 1 Case III 12- Hour Mixed Layer Depth 60 Temperature (°C) 16 • 17 18 Figurs 17. Front 1 Case III - T vs z Profile. Profile taken at y=35 km for t=0 and t=12 hours. 61 layer depth. At 36 hcurs, v returns to a negative value ana at 48 hours, though still negative, v is much decreased in magnitude. Again, cells cf positive v-velocities are pres- ent at about the mixed layer depth. The across-front veloc- ity does penetrate the front and the shallow peak of the mixed layer (see Fig. 18) which is indicative of cross-frcn- tal nixing. The shallow section of mixed layer itself is eroded and smoothes cut ever the 48-hour integration as it did in Case I (Fig. 19) . B. SUMMABY -- CP.SE III The effects cf both wind stress and heating are clear in this case. The wind stress induces a mass transport to the right, moving cooler, denser water into warmer, less dense water. This water not only apwells and moves over the front, but also moves acrcss the frontal interface. At 24 and 48 hours, the v-field appears to be influenced by inertial oscillations with a reversal in direction occurring in the surface layer at 24 hours and a near-reversal at 48 hours. Cores cf positive velocities are established cen- tered about the mixed layer depth outside of the front. The front both diffuses and mcves to the left in time. 62 V at hour 36 Q. CD Q 0.0 25.0- 50.0 75. On 100.0- 125.0- 150. OH 175.0 ! ! I 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Figure 18. Frcnt 1 Case III 36-Hour V-Velocity. Con-our interval is 2 cm/s. 63 H at hour 48 o.o 25.0^ 50.0^ 75.0 J Q. CD Q 100.0^ 125.0 J 150.0 175.0 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Figurs 19. Frcct 1 Case III 48- Hour Mixed Layer Depth. 64 Heating shallows the mixed layer depth as expected, and thereby restricts the vertical extent of the velocity fields. Heating also prevents the immediate deepening of the irixed layei on the right side of the front, which was also seen in fccth Cases I and II. The heat manifests itself at the initial mixed layer depth where the isotherms become more stratified. 65 VI. MODEL RESULTS FOR FRONT J, CASE IV A. ANALYSIS AND EISCUSSICN Case IV combines a negative wind stress and a uniform surface heating. The mixed layer shallows noticeably and heat is carried to the bottom of the mixed layer at depths of 55 -co 70 m as in Case III (see Figs. 20 and 21). The heating dees have an interesting effect when compared with the wind- stress-only forcing of Case II. The sharp dip ir. the isotherms in the middle of the front is not evident here as it was in Case II. Horizontal diffusion of the tempera- ture structure occurs more rapidly and attains a gradient of 1.6 deg C/5.6 km by hour 12 (see Fig. 20) . The along-frcnx velocity is limited in its vertical development on the right side of the front near y=57 km (Fig. 22) and follows both the horizontal and vertical diffusion tendencies of the den- sity front. The across-front velocity has a narrow, verti- cally-oriented cere of negative values with a maximum of -6 cm/s en the right side cf the front between 25 and 50 m depth as in Case II. Since this maximum of v-velocity exists in an area where there is little u-velocity, its 66 existence cannot be attributed to a response to the agecs- trophic a- component. The position of this v-velocity corre- lates well with the upwelling/do wnwelling pattern evident in the isotherms in Fig. 20, and also with wave patterns in the isotherms over the entire depth extent in rhe right half of Fig. 23. We suspect that such a large area of v-component created below the mixed layer is a response to rhs warming of the water at the initial mixed layer depth which has shoaled, re-oriented the isotherms and created vertical velocity. Furthermore, wind-generated mixing forces verti- cal motions in the water mass to a great depth, inducing a v-component there. In this case, the front diffuses horizontally more rap- idly than under wind stress forcing alone. The front spreads like a warm, less-dense plume overriding the cocl, denser water (compare Fig. 24 to Fig. 20) . The along-frcnt current shifts with the front. The mixed layer loses its shallow section within the front and smoothes out, which did not happen in Case II. The peak in the mixed layer was maintained much longer. With heating, there is less of a temperature difference and less of a shallowing from the far-field mixed layers to the shallow mid-frontal mixed 67 T at hour 12 o.o 25.0- 50.0- 75.0- Q. CD Q 100.0 125.0 150.0- 175.0 14.40 25.0 35.0 45.0 55.0 65.0 75.0 Y-distance (km) Figure 20. Front 1 Case IV 12-Hcur Temperature. Contour interval is 0.2 deg C. 68 H at hour 12 Q. CD Q • 25.0- . JL r^y \ ~~^~^ \ 50.0- -rir r\ • 100.0- 125.0- • 150.0- - - 175.0- I — , — , — ,__, — — p. . , . — , — , — .... — , — , — , — , — — , — ,.^_ 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Figure 21. Frcnt 1 Case IV 12-Hour Mixed Layer Depth 69 U at hour 12 o.o a o Q 25.0- 50.0- 75.0 100.0- 125.0 150.0 175.0 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Figure 22. Front 1 Case IV 12-Hour O-Valocity. Contour interval is a cm/s. 70 V at hour 12 o.o CD Q 25.0- 50.0- /y.ui 100.0 125.0- 150.0- 175.0 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Figure 23. Fiont 1 Case IV 12-Hcur V-Velociry. Contour interval is 2 cm/s. 71 layer, which probably accounts for the quicker breakdown of the shallow section of the mixed layer. The v-field in the surface layer is advected to the right, with a maximum value located at the surface within the front. Ey hour 24, strong horizontal cells of a v-ccm- ponent have formed about the mixed layer depth. In this case, the values are negative, whereas in Cases I and III they were positive. (Case II never formed them.). These cells disappear at hour 36 and reappear at hour 48, as they did in Cases I and III. The mechanism that explains the appearance of negative v values is unclear. The trends to 48 hours show further diffusion and advec- tion of the warm frontal plume to the right. There is smoothing of the horizontal distribution of mixed layer depth. The surface front patterns of u- and v-velocity are all advected to the right. 72 T at hour 36 25.0-1 50.0- /u.u Q. Q 100.0- 125.0- 150.0- 175.0 J 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Figure 24. Frcnt 1 Case IV 36-Hcur Temperature. Ccntcu: interval is 0.2 deg C. 73 B. SDMMABY -- CilSS IV Application cf a negative wind stress and surface heat- ing results in the front moving as a warm overriding plume to the right. The mixed layer initially shsllows due to the heating, and ever the 48 hour integration breaks down and smoothes cut in the horizontal. The along-front velocity is advected and diffused in the mixed layer. The pattern cf across-front velocity shifts to the right in the surface layer, with its maximum value centered over the shallowest portion of the mixed layer. A v-cemponent develops to quite a great depth en the right side of front due -co motion gen- erated by heating and turtulent mixing. Cells of negative v- component are formed at hours 24 and 48 which ar a centered about the mixed layer depth. 74 VII. MODEL RESULTS FOR FRONT 2 CASE I A. ANALYSIS 3ND LTSCOSSICN The initial conditions for Front 2 are shown in Figs. 4, 5, and 6. The front extends throughout the depth of the basin and is oriented such that warmer, less dense water is on the right and cooler, denser water is on the left. Many of the dynamical features of Front 1 are expected to be repeated fcr Front 2. In comparing Front 2 to Front 1 , the horizontal axes are oppositely-directed to the frontal ori- entation. The thermocline slopes upward in the positive y-directicn for Front 1, but downward for Front 2. The wind stress cf Case I applied to Front 2 creates a transport directed to the left. Warmer, less dense water moves towards the cooler, denser water. In this case, dif- fusion in the temperature field is present for the duration of the integration. The horizontal temperature gradient remains large (1.0 deg C/1.2 km) in the middle of the front with the majority of the diffusion occurring at the right boundary. Mixing on the cool (left) side of the frcnt extends frcm the surface to 135 m which is below the initial 75 depth of the mixed layer. Results of downwelling are seen at the left frontal boundary, near y=42 km. Apparently, there is no chance for a stable, overriding warm plume to develop before it is mixed into the ambient cool water peel. These phenomena in the temperature field were also seen in Case II for Front 1. Much more dramatic oscillations occur in the isctherms, primarily on the right side between 53 km and 70 km, where the entire field is inclined. They are also visible en the left side superimposed upon an inclina- tion of the entire field sloping downward -co the right (Fig. 25). The isctherms show a definite trend towards becoming more uniformly inclined beneath the mixed layer across the entire horizontal expanse, with the steeply-inclined field on the right teccming more horizontal. Downwelling causes the left side tc slope downward to the right and upweliing lifts the isctherms on the right side. The mixed layer depth undergoes major changes over the entire domain. Cn the left side, it deepens to where the depth in the far field is approximately 125 m (Fig. 26) . Since this deepening occurs by 3 hours of integration, such a drastic deepening probably resulted from the initial mixed layer depth being inserted at too shallow a depth in this 76 T at hour 36 o.o 25.0- 50.0- 75.0- E 100.0- Q. Q 125.0- 150.0 175.0 200.0- 225.0 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Fiqure 25. Frcnt 2 Case I 36-Hour Temperature. Contour interval is 0.5 deg C. 77 area- As in Frcnt 1 Case II, a downward bulge in the mixed layer extending to 155 m cccurs at the left frontal boundary at y=U3 km (Fig. 26) . In this case, the downward bulge does not correspond to xhe side on which -he waters would tend to "back up" prior to crossing over the front as in Front 1 Case I. As strong mixing is implied by the vertical orien- tation of the isotherms at that location, the bulge is believed to te associated with a cooling of the waters in that area as a result of enhanced vertical mixing caused by the ageostrophic along-front velocity shear (Fig. 27) . Within the frcnt, a shallcw peak in the mixed layer depth is maintained at th€ left boundary, though over time it does deepen slightly and erode through mixing. There is much variability in the mixed layer depths on the right side of the front, but it appears that the general trend is for deepening to cccur in the far field beyond y=55 km (Fig. 26) . Along with the isotherms, the along-front u-velocity diffuses and decreases its maximum speed over time. As already seen, an ageostrophic component forms on the left frontal bcundary and stimulates mixing there. The remnants of a tight hcri2cntal velocity gradient are seen after U8 78 H at hour 36 o.o 25.0 - 50.0-1 75.0 E 100.0- Q. Q 125.0- 150.0- 175.0- 200.0^ 225.0 25.0 35.0 45.0 55.0 65.0 Y-distance (km) 75.0 Figure 26. Frcnt 2 Case I 36-Hour Mixed Layer Depth 79 U at hour 12 Q. Q 0.0 25.0- 50.0- 75.0- 100.0- 125.0 150.0- 175.0 200.0- 225.0 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Figure 27. Frcnt 2 Case I 12-Hour U-Velocity, interval is 1C cm/s. Contour 80 hoars, though little cr nc advecticn of the along-front cur- rent occurs in response to the wind-generated transport. Wave-like oscillations appear to propagate along the deeper extremities cf the u-field, but no phase relation between isotachs cr with ether fields is readily apparent. The across-front v-velocity does correlate with the direction cf transport up through hour 9. An oscillatory pattern exists in the v field over the 48-hour integration. At hour 12, the entire v-field is positive, but this may be a response to the agecstrophic u-velocity, and it is strong enough to overcome the acrcss-frcnt transport velocity. At 24 hours, v is in the direction cf transport and a maximum of -20 cm/s appears at the surface within the front over the shallowest secticn of mixed layer depths at y=43 km (Fig. 28) , and remains through hour 36 . This is reassuring as it was expected that the inherent static stability of the water masses would trinimize deep cross-frontal mixing, similar to what was seen in Front 1 Case II. The isotachs very defi- nitely terminate at the left boundary of the front, but they also exist beneath the mixed layer and do cross the front beneath the mixed layer. At hour 48, v is positive again, perhaps due tc inertial motions. It is proposed (though it 81 is certainly not as clear as it was for Front 1) that cross-frontal mixing, though inhibited, occurs here to a greater extent than it did for Front 1. The majority of the mass transport appears to exist in the mixed layer and passes over, rather than through, the shallow mid-frontal depth of the nixed layer. The reasons for the variations between the fronts may be due to the greater u-component (both in speed and in areal coverage) present with Front 2. B. SUMMABY — O.SE I Several complexities have been incorporated into the modeling of Front 2. First, the isotherms slope downward to the right ever the entire right half of the basin. Hence, the front not only exists at the surface but is "connected" through the depth of the tasin. This establishes an initial u-velccity which exists over the same area. Adjustment to the wind stress may not be confined solely to the upper few meters, as dynamic responses may be transmitted to depths beyond those directly affected in the surface layer. Also, the mixed layer depth is artificially inserted as an initial condition, and may net be the most perfect fit to the temp- erature field. Though this mixed layer configuration may exaggerate cr suppress actual features, it is nevertheless felt to be a reasonable approximation of an actual front. 82 V at hour 24 Q. (D Q 0.0 25.0- 50.0- 75.0- 100.0- 125.0 150.0- 175.0- 200.0- 225.0 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Figure 28. Front 2 Case I 24-Hour V-Velocity interval is 5 cm/s. Contour 83 The responses are much more complicated in structure in Front 2 than they were in Front 1. Beyond 12 hours, the front shows little advective response to the mass transport. One reason this occurs is because the front exists over such a great depth. The original thermal structure and tempera- ture gradient are maintained in the middle of the front, with horizontal diffusion occurring primarily at the right boundary. Mixing in the surface layer occurs as the isot- herms become vertical to greater depths over time. At the left boundary of the front, downwelling is quite evident and the waters mix easily due to the creation of an ageostrophic u-component which enhances the wind stirring. Wave-like oscillations are evident in the temperature field beneath the mixed layer, and the entire deep temperature field becomes mere uniform in slope over the 48-hour integration. The mixed layer depth must be considered in three sepa- rate regimes - left side, frontal, and right side. On the left, the mixed layer depth increases by almost 50 m at the frontal boundary, where mixing is enhanced due to the influ- ence of the ageostrophic current. The mixed layer bulges downward, then rises sharply to its shallow peak at the front. This shallow section remains throughout the 48 hour 84 integration though it dees deepen slightly due to mixing. On the right side, the mixed layer deepens and becomes more horizontal though there are strong fluctuations over inter- vals of 4 km and less. Two primary trends are observed in the along-front u-ve- locity: 1) the u-component diffuses in time, still retain- ing its basic shape but decreasing in speed and horizontal gradient; 2) an ageostrophic cemponent is evident, prima- rily extending outwards ficm the left boundary of the front and which is believed to "drive" the downward bulge in the mixed layer there. The across-front velocity cemponent is concentrated at the surface in the direction of transport between 0 and 9 hours and at 24 and 36 hours. The front poses no barrier to the v-velccity at 12, 24, or 48 hours. The 36-hour fields are the only cr.es which have essentially no cross-front velocity cemponent other than in the surface layer. Because the initial horizontal temperature gradient is preserved in the middle cf the front, and because the shallow portion of the mixed layer depth is still evident after 48 hours, sug- gest that little cross-f rental mixing occurs. 85 VIII. MODJL RESULTS FOR FRONT 2 CASE II A. ANALYSIS AND CISCDSSICN With the wind stress opposite from that of Case I, the net Ekman transport is left to right, and cooler, denser water will be transported toward warmer, less dense water. There are similarities here to the results of Front 1 Case I. The front bscomes much more diffuse at the surface and the horizontal temperature gradient is not preserved as it was in the preceding case (see Fig. 29) . It has decreased to 1.5 deg C/6.4 km. The horizontal field on the left side reorients ty inclining down to the right, and the inclined field on the right becomes more horizontal. The total effect is to make the temperature field more level beneath the mixed layer. Wave-like fluctuations are also seen in the isotherms (Fig. 29) . Vertical mixing can be readily seen to have occurred within the front by the steep slope of the isotherms. The mixed layer depth immediately adjusts in the left far field to around 125 m as it did in Case I, but a much greater downward bulge in the mixed layer forms at the left 86 T at hour 36 o.o 25.0 50.0- 75.0 E 100.0- c \ \ i » \ ■ i i / \ i \ s \ V _ \ X I \ / 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Figure 39. Frcnt 2 Case IV 24-Hcur V-Velocity. Contour interval is 5 cm/s. 107 V at hour 36 25.0- 50.0-1 75.0- £ 100.0- c CD Q 125.0- 150.0- 175.0- 200.0- 225.0- 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Figure 40. Frcnt 2 Case IV 36-Hcur V-Velccity. Contou: interval is 5 cm/s. 108 V at hour 48 o.o 25.0 50.0 75.0- £ 100.0 Q. Q 125. OH 150.0 175.0- 200.0 225.0 25.0 35.0 45.0 55.0 Y-distance (km) 65.0 75.0 Figure 41. Front 2 Case IV 48-Hour V-Velocity. Contour interval is 5 cm/s. 109 XI. CONCLUSIONS AND RECCMflEND ATIONS A. GENERAL This thesis has examined the unsteady response of two oceanic fronts to the lccal atmospheric forcings of wind stress and surface heat flux. The simplicity of Front 1 enabled identification of basic processes stimulated by the forcings, processes which were not so clearly seen in Front 2. Front 2 was a mere realistic simulation of an oceanic front, and, hopefully, it will serve as a stepping stone for further investigations intc fronts and testing of this fron- tal model. Ihere are a few very general properties that exist for both Fronts 1 and 2, and which bear out our hypotheses stated in Chapter 2.B.: 1) Wind direction plays a primary role in frontal adjustment. In the cases where warmer, less dense water is transported tc cccler, denser water, the structure of the front is preserved. The mixed layer depth is also pre- served, and little crcss-f rental mixing occurs. 2) In the cases where cooler, denser water is trans- ported to warmer, less dense water, the horizontal tempera- ture gradient is diffused, the mixed layer depth within the 110 front breaks dcwr and deepens, and much cross-frontal mixing occurs. Ccnvective mixing occurs along with wind stirring. 3) A uniform constant surface heat flux shallows the mixed layer outside of the frontal zone to a depth which is propcrtional tc the amount of heat flux. The combination of a +1 dyne/cm2 wind stress and a surface heat flux of -0.004 deg-cm/s mixes heat down to a depth of the initial mixed layer and leads tc stratification there. Stratification of the isotherms at the surface did not occur. For the cases in which the heat flux is applied, turbulent mixing is restrained in the vertical, which agrees with the results of Niiler (1975) and Mellor and Durbin (1975). 4) In areas of the frontal zona where ageostrophic velocities are created, vertical mixing is increased. 5) Mixed layers deepen rapidly within the first 12 hours under wind stress alone as the fronts undergo initial adjustment. Eeycnd 12 hours, adjustments are confined tc an area around the the basic depth attained during the initial adjustment period. Niiler (1975), Mellor and Durbin (1975) and Be Szceke (1980) all reported this phenomenon. 6) A time-dependent pattern in the direction and depth-influence of the acrcss-front velocity exists. It is 1 11 probably due to inertial oscillations created by the atmos- pheric forcing. It was surprising to see -he downward bulge in the mixed layer at the cold-side boundary of both fronts ir. the wind stress only cases. It is unclear as to why this happens, though some speculative reasons wars provided. In Front 1, the formation of cores of positive v-velcc- ity which are symmetric about the mixed layer depth are intriguing. Inertial oscillations may provide an ex planaticn. The tilting down to the right of the entire temperature field in Front 2 in all four cases is a major adjustment, and one which is independent of wind stress direction and heating. It would appear that this tilt is a response to the re-orientation of the oceanic current fields. B. EECOMMENEATICNS There is both further investigation that can be done with the results of this thesis, as well as new work which is suggested by these results. The results of these eight model runs could be further quantified by using a finer con- tour interval for the fields, and by producing fields for gradients, agecstrophic velocities, and the like. The 1 12 inertial motions could be investigated to encompass magni- tudes, directions, depths and areas affected. It would be instructive tc examine (y,z) streamf unctions. The model could be tested by conducting parametric sensitivity studies of the constants used in the governing equations and mixed layer equations. New work might include using different combinations of these atmospheric forcings both in magnitude and direction. Inclusion of a wind stress in the y-direction would cer- tainly prove to be of interest, as would a diurnal heating/ cooling cycle. Other atmospheric forcings could be applied. Evaporation and precipitation m ight be incorporated. The equation of state could be expanded to include salinity, and an initial salinity field could be inserted and monitored over time. Cf course, a three-dimensional version of this model would he valuable. More simulations of observed fronts using data acquired in the field would provide fur- ther insight into the applicability of the model. Data acquired by Jcharnessen, et al (1977) of the Maltese front would be a recommended starting point. Computer central processor unit (CPU) time was extensive for each of these model runs. They each averaged over four 113 hours of CFU time to run, providing no stopping and r?st^:-- ing were regaired. Such a model is far from being useful operationally for real-tine assessment of ocean structure to provide, for example, input for acoustic forecasting models. However, for tasic research, this model appears to be a pow- erful tool for deciphering the complexities of ocean frontal dynamics and thermodynamics. 1 14 LIST OF REFERENCES Adamec, D. , B.I. Elsberry, R.W. Garwood, Jr. , and R.L. Haney, 1981: An embedded mixed layer-ocean circulation model. £yjj. of Atmos. and Oceans, 5, 69-96. Bang, N.D.. 1973: Characteristics of an intense ocean frontal system in the upwell regime west of Cape Town. Tellus . 25, 256-265. Briscce, H.G., CM. Jchanressen, and S. Vincenzif 1974: The Maltese oceanic front: a surface description by ship and aircraft. Deep. Sea Res. , 2J, 247-262. Camerlengo, A., 1982: Larae-scale response of the Pacific Ccean subarctic front to momentum transfer: a numerical study. J. Ph^s. Oceanogr. , J2, 1106-1121. Cromwell, T. , and J.L. Reid, Jr., 1956: A study of oceanic fronts. Tellus, 8, 94-101. Cushman-Roisin , £., 1981: Effects of horizontal advection en upper ccean mixing: a case of f rontogenesis. J. Phys. Cceano^r. , VI, 1345-1356. De Szceke, R.A., 1980: On the effects of horizontal variability cf wind stress on the dynamics of the ocean mixed layer. J. Phis. Oceanogr. , ±0, 1439-1454. Elsberry, E.L., and R.W. Garwood, Jr., 1979: First- generaticn numerical ccean prediction models - goal for the 19e0«s. Naval Postgraduate School Report 63-79-007, 41 pp. Endoh, M., C. N. K. Mooers, and W. B. Johnson, 1981: A coastal upwelling circulation model with eddy visccs- ity depending on Richardson Number. Coastal Upwellinc, F. A. Richards, Ed. Am. Geophys. U., 57^~pp. Garvine, R.W., 1974: Dynamics of small-scale oceanic fronts. J. Fhys. Oceanogr. , 4, 557-569. Garvine, R.W., 1979a: An integral hydrodynamic model of upper ccean frontal dynamics: Part I. Development and analysis. J. Phy_s. Oceanogr ., 9, 1-18. Garvine, R.W., 1979b: An integral hydrodynamic model of upper ccean frontal dynamics: Part II. Physical char- acteristics and comparison with observations. J. PJiX§. Cceancqr . , 9, 19-36. 1 15 Garvire, R.W., 1S80: The circulation dynamics and thermodynamics of upper ocean density fronts. J. Phys. Cceano^r., JO, 2058-2C81. "" Garwood, R.W., Jr., 1977: An oceanic mixed layer model capable of simulating cyclic states. J. Phys. Ocean- cox., 7, 455-46 8. ~ L- Haney, R.L., 1S80: A numerical case study of the development of large-scale thermal anomolies in the cen- tral north Pacific Ocean. J. Phys. Oceanogr., 10, 541-556. " — *- *~ — Johannessen, CM., D. Good, and C. Smallenburger, 1977: Ofcservaticn cf an oceanic front in the Ionian Sea during early winter 1970. J. Gecpjjis. Res., 82, 1381-1391. Johnson, D. B. and C. N. F. Mooers, 1981: Internal cross-shelf flew reversals during coastal upwelling. Ccastal Up welling, F. A. Richards, 2d. Am. Geophys. U. , 5T9~pp7 Kao, T.W., 198C: The dynamics of oceanic fronts. Part I: The Gulf Stream. J. Ehys. Oceanogr., JO, 483-492. Katz, E.J., 1S69: Further study cf a front in the Sargasso Sea. Tellus, 2J, 25 9-269. Mellcr, G.I., and P. A. Durbin, 1975: The structure and dynamics cf the ccean surface mixed layer. J. Phys. Cceanoax., 5, 718-72 8. " — Mooers, C. N. K. , 1978: Cceanic fronts: A summary of a Chapman Conference. EOS, 59, No. 5, 484-491. Niiler, P.P., 1975: Deepening of the wind-mixed layer. J* *ar. Res., 33, 405-422. Niiler, P.P., 1982: •Fronrs-aO1 - a study of -he North Pacific subtropical f rent . Nav. Res. Rev., 3'i, No. 3, 41-50. Roden, G.I., 1S71: Aspects of the transition zone in the northeastern Pacific. J. Geophys. Res., 76, 3462-3475. Roden, G.I..e 1972: Temperature and salinity fronts at the boundaries of the subarctic-subtropical transition zone in the western Pacific. J. GeoDhys. Res., 77, 7175-7 187. " ~ Roden, G.I., 1974: Thermchaline structure, fronts, and sea-air eneray exchange of the trade wind region east cf Hawaii. J. Phys. Oceanogr. , 4, 168-182. 1 16 Roden, G.I., 1975: On North Pacific temperature, salinity, sound velocity, and density fronts and their relation to the wind and energy flux fields. J. Phys. Oceanogr., 5, 557-571. ~ — a~ Roden, G.I., 1S76: On the structure and prediction of oceanic fronts. Nav Res. Reviews, 29, No. 1, 18-35. Roden, G.I., 1S77: Oceanic subarctic fronts of the central Pacific: structure of and response to atmospheric forc- ing. J. Ehys. Oceanogr.. 7, 761-778. Roden, G.I., 1980: On the subtropical frontal zone north of Hawaii during winter. J. Phis. Oceanogr. , 10, 342-362. Suginchara, N., 1977: Opwelling front and two-celled circulation. J. Oceanogr. Soc. Japan. 33, 115-13 0. " *"• — ~ Voorhis, A.D., and J. 3. Hersey, 1964: Oceanic thermal fronts in the Sargasso Sea. J. Geophys. Res. , 69, 3809-3814. ~ 117 INITIAL DISTRIBUTION LIST No. Copies 1. Defense Technical Information Center 2 Camercn Station Alexandria, VA 22314 2. Library, Code 0142 2 Naval Postgraduate School Monterey, CA 93940 3. Chairman, Code 68Mr 1 Department cf Oceanography Naval Postgraduate School Monterey, CA 93940 4. Chairman, Code 63Rd 1 Department cf Meteorclogy Naval Postgraduate School Monterey, CA 93940 5. Professor B. tf. Garwood, Code 68Gd 2 Department cf Oceanography Naval Postgraduate School Monterey, CA 93940 6. Mr. D. A. Adamec, Code 63Ac 1 Department cf Meteorclogy Naval Postgraduate School Monterey, CA 93940 7. Professor B. L. Elsberry, Code 63Es 1 Department cf Meteorclogy Naval Postgraduate School Monterey, CA 93940 8. Professor B. L. Haney, Code 63Hy 1 Department cf Meteorclogy Naval Postgraduate School Monterey, CA 93940 9. LT Christopher J. Hall, USN 2 Naval Oc<=ancgra ohy Command Center Box 31 Ho t a S P FPO New York 09540 10. LTJG C. C. Durban, USN 1 Naval Postgraduate School SMC Box 2645 Monterey, CA 9 3 940 118 11 . Director 1 Naval Oc€ancgraphy Ccmmand Naval Observatory 34th and Massachusetts Avenue NW Washington, D. C. 20390 12. Commander 1 Naval Oceanography Ccmmand NSTL Station Eay St. Louis, MS 39522 13. Commanding Officer 1 Naval Oceanographic Office NSTL Station Eay St. Louis, MS 39522 14. Commanding Officer 1 Fleet Numerical Oceanography Center Monterey, CA 93940 15. Commanding Officer 1 Naval Ocean Research and Development Activity NSTL Station Bay St. Lcuis, MS 39522 16. Commanding Officer 1 Naval Environmental Prediction Research Facility Monterey, CA 93940 17. Chainan, Oceanography Department 1 U.S. Naval Academy Annapolis, MD 21402 18. Chief of Naval Research 1 800 N. Quincy Street Arlington, VA 22217 19. Office cf Naval Research (Code 420) 1 Naval Ocean Research and Development Activity NSTL Station Bay St. Louis, MS 39522 20. Scientific liaison Office 1 Office of Naval Research Scripps Institution cf Oceanography La Jclla, CA 92037 21- Library 1 Department cf Oceanography University cf Washington Seattle, WA 98105 22. Library 1 CICSSE P.O. Ecx 4803 San Ysidro, CA 92073 1 19 23. Library Schccl cf Oceanography Oregon State University Corvallis, OR 97331 24. Commander Oceanography Eox 1390 Fearl Harbor, Systems Pacific HI 96660 120 Thesis H1473 c.l 201612 Hall On the unsteady re sponse of an oceanic front to local atmo- spheric forcing. 201GU Thesis H1473 c.l Hall On e- the unsteady r 3ponse of an oceanic front to local atmo- spheric forcing. On the unsteady response of an oceanic f II I II 3 2768 002 07527 7 DUDLEY KNOX LIBRARY m am BBWMnBBffl ISHi ■■ in '■■■ : "!; 1