A numerical study of wind forcing of eddies and jets in the California Current System

Transcription

1 Calhun: The NPS nstitutinal Archive Faculty and Researcher Publicatins Faculty and Researcher Publicatins Cllectin 1989 A numerical study f wind frcing f eddies and jets in the Califrnia Current System Batteen, Mary L. Jurnal f Marine Research, 47, pp ,

2 Jurnal f Marine Research , 1989 A numerical study f wind frcing f eddies and jets in the Califrnia Current System by Mary L. Batteen/ Rbert L. Haney,2 Terrance A. Tielking 1 and Philip G. Renaud' ABSTRACT A high-reslutin, multi-level, primitive equatin cean mdel is used t examine the respnse t wind frcing f an idealized flat-bttmed ceanic regime alng an eastern cean bundary. A band f steady alngshre, upwelling favrable winds, either with r withut alngshre variability, is used as frcing n bth anf-plane and a,a-plane. n each experiment a wind-driven equatrward castal jet and a pleward undercurrent are generated. n time the castal jet and undercurrent becme unstable and lead t the develpment f eddies and jets with relatively strng nshre and ffshre directed flws. The alngshre variatin in alngshre wind stress plays a rle in determining the lcatin f eddy generatin regins. A cmparisn f mdel results with available bservatins shws that the time-averaged mdel castal jet and undercurrent are cnsistent in scale and magnitude with the bserved data. Althugh the instantaneus eddies and jets are weaker than the crrespnding bserved features, they have hrizntal scales typical f the bserved scales. The results f this study supprt the hypthesis that steady wind frcing is ne f several pssible imprtant generatin mechanisms fr eddies in the Califrnia Current System. 1. ntrductin The climatlgical mean Califrnia Current System (CCS) cnsists f fur currents: the Califrnia Current, the Califrnia Undercurrent, the Davidsn Current, and the Suthern Califrnia Cuntercurrent (Hickey, 1979). The Califrnia Current is a brad, surface equatrward flw that can extend ffshre t km. The Califrnia Undercurrent is a subsurface pleward flw ver the cntinental slpe. The Davidsn Current is defined as a surface pleward flw that ccurs during the fall and winter nrth f Pint Cnceptin. The furth current, the Suthern Califrnia Cuntercurrent, is a surface pleward flw that ccurs suth f Pint Cnceptin and inshre f the Channel slands in the Suthern Califrnia Bight. Recent bservatins have shwn that, superimpsed n the brad, slw (-10 cm S-), climatlgical mean flw in the CCS are highly energetic, messcale. Department f Oceangraphy, Naval Pstgraduate Schl, Mnterey, Califrnia, , U.S.A. 2. Departmentf Meterlgy,Naval PstgraduateSchl,Mnterey,Califrnia, , U.S.A. 493

3 494 Jurnal f Marine Research [47,3 eddies and meandering jets (Bernstein et al., 1977; Mers and Rbinsn, 1984; Rienecker et , 1988). The meanders, which have wavelengths f up t several hundred kilmeters, can intensify ver several mnths and be "cut ff," becming islated eddies (Bernstein et al., 1977). Strng barclinic jets with peak velcities f -80 cm S- are embedded in this field f cyclnic and anticyclnic eddies. These jets are -70 km wide at the surface, extend t at least 100 m depth, and have ffshre excursins f several hundred kilmeters (Mers and Rbinsn, 1984; Rienecker et al ; Flament et ; Ksr and Huyer, 1986). The dynamical prcesses respnsible fr the generatin and evlutin f these intense and cmplex eddy and jet patterns in the CCS have yet t be fully identified. A pssible generative mechanism arises frm the barclinic and/r bartrpic instability f the mean castal Califrnia Current System which, during the upwelling seasn (frm - April t Octber), cnsists f an equatrward-flwing surface current r castal jet with mean speeds f -10 t 30 cm S- verlying a pleward-flwing undercurrent with a mean speed f -10 cm S- (Hickey, 1979; Cheltn, 1984; Huyer and Ksr, 1987). Bth barclinic and bartrpic instabilities have been shwn t generate eddies and jets in the nrtheast Pacific (Wright, 1980). Barclinic instability is an imprtant mechanism fr eddy generatin ff Vancuver [sland (Emery and Mysak, 1980; Thmsn, 1984), and ff the cast f Oregn and nrthern Califrnia (lkeda and Emery, 1984). n particular, keda and Emery (1984) have hypthesized that current meanders are triggered by alngshre variatins in the castline (capes) and grw as a result f the barclinic instability f the castal, equatrward, near-surface jet (-40 km wide and assciated with castal upweling) and the pleward Califrnia Undercurrent. As these unstable meanders intensify, they carry the cl, upwelled water ffshre and are ften cut ff, creating pairs f islated eddies r "vrtex pairs" cnsisting f a cyclnic and an anticyclnic eddy (Bernstein et al., 1977). Evidence fr bartrpic instability as a viable mechanism is still frthcming, althugh ne case f eddy-eddy-jet interactin bserved by the OPTOMA (Ocean Predictin Thrugh Observatins, Mdeling and Analysis) Prgram in the summer f 1983 shwed characteristics f bartrpic instability (Rbinsn et al., 1984). There is evidence fr bth prcesses ccurring ff Vancuver sland where a cyclnic eddy was frmed by a primary cntributin frm barclinic instability and an additinal, yet secndary, cntributin frm bartrpic instability (Thmsn, 1984). The rle f wind frcing in the generatin f eddies and jets in the CCS has nt been systematically investigated and may be the mst imprtant generatin mechanism fr eddy and jet frmatin. Satellite infrared imagery has shwn evidence f eddies and jets in the CCS during perids f winds favrable fr upwelling. These bservatins prvide evidence fr wind frcing as a pssible imprtant mechanism fr eddy and jet frmatin. Eddies and jets culd be caused by either a respnse t the seasnal mean wind field r t shrt-lived, strng wind events ccurring during the upwelling seasn.

4 1989) Balteen et al.: A numerical study f wind frcing 495 n this study, a high-reslutin, multi-level, primitive equatin cean mdel is used t examine the respnse t climatlgical wind frcing f an idealized ceanic regime alng an eastern cean bundary. A band f steady alngshre winds, either with r withut alngshre variability, is used as frcing n bth anfplane and a {1-plane. t is seen in all experiments that bth a wind-driven, equatrward castal jet and a pleward undercurrent develp, which becme unstable, resulting in the generatin f eddies and jets. t is als seen that the alngshre variatin in wind stress can playa rle in determining the lcatin f eddy generatin regins. 2. Mdel descriptin and specific experimental cnditins a. Mdel equatins. The numerical mdel used in this research was develped by Haney (1985), mdified by BaUeen (1989), and is a multi-level, primitive equatin (PE) mdel. The mdel uses the hydrstatic, rigid lid, {1-plane and Bussinesq apprximatins. The gverning equatins are as fllws: du - ap' a 2 u - = -- + fv - Am'iJ 4 u + Km- + iu) dt P ax az 2 dv -1 ap' a 2 v - = -- - fu - Am'iJ 4 v + Km- + Av) dt P y az 2 1 z (au av) w= d~ -H ax ay () (2) (3) 10 p' = pgd~ - ~ 1 [ 1 pgd~] dz z H -H z p = P (1 - a (T - T» dt 4 a 2 T di = -AH'iJ T + KH az2 + Qs + Od(T) (4) (5) (6) n the abve equatins, t is time, (x, y, z) is a right-handed cartesian crdinate system with x pinting tward shre, y alngshre, and z upward. The crrespnding velcity cmpnents are (u, v, w), T is temperature, p is density and p' is the departure f the pressure frm the vertically averaged pressure. n Eqs. (3) and (4), ~ is a dummy variable f integratin. Eq. (4) includes the assumptin that the depth-averaged pressure is a cnstant (assumed zer); i.e., the bartrpic mde is ignred in this study. Eq. (5) assumes that density is a functin f temperature nly, cnsistent with the regin f the CCS being mdeled (e.g., the temperature, salinity and density figures frm CalCOF Line 60, i.e., pp. 107, 115 and 123 flynn et al. (1982), shw that density is primarily a functin f temperature). Althugh salinity may be a gd tracer

5 496 Jurnal f Marine Research [47,3 fr water masses in the CCS (Huyer and Ksr, 1987), it is nt essential fr a zer-rder descriptin f the CCS, since there are n majr salinity surces r sinks (such as majr rivers) in the regin being mdeled. due t slar radiatin, with n (6), Qs = as pcaz is the heating Here S is the dwnward flux f slar radiatin at the surface (see belw), R =.62 is the fractin f slar radiatin absrbed in the upper few meters (z) = 1.5 m) and ( -' R) = 0.38 is the fractin that penetrates t smewhat deeper levels (22 = 20 m) as given by Paulsn and Simpsn ( 977). The terms Au), Av) and Od( T) represent the vertical turbulent mixing f heat and mmentum by a dynamic adjustment mechanism. This adjustment, a generalizatin f the cnvective adjustment mechanism, is based n the assumptin f a critical Richardsn number, and it serves t maintain dynamic stability in the water clumn (Adamec et al., 1981). The bundary cnditins at the tp (z = 0) f the mdel cean are: au K -=0 m az (7) (8a) av K - = Tp m az 0 (8b) (8c) w=, (8d) and at the bttm (z = -H) they are Km :~ = CD (u 2 + V 2 )1!2 (u cs 'Y - v sin 'Y) (9a) (9b) (9c) w= O. (9d) n (8b), T is the alngshre cmpnent f the surface stress which is varied in different experiments as described belw. n (8c), QB is the net upward flux f lngwave radiatin, sensible and latent heat acrss the sea surface which is described belw. n (9a, b), CD = X 10-3 is a bttm drag cefficient and 'Y = 10 is a gestrphic inflw angle (Weatherly, 1972). The bttm stress in (9a, b) represents ne f the simplest pssible parameterizatins f a bttm Ekman layer. Table prvides ther

6 1989] Batteen et al.: A numerical study f wind frcing 497 Ta ble 1. Values f cnstants used in the mdel. Value cal gm- (OK) x C 1.23 x 10-3 gm cm gm cm x 10-4 (OK) x los cm 1 x 10 6 cm 4.5 x los cm 800 s 0.93 X 10-4 S- 980 cm S-2 2 x cm 4 S- 2 x cm 4 S- 0.5 cm 2 S cm 2 S- Definitin specific heat f sea water bttm drag cefficient cnstant reference temperature density f air density f sea water at T thermal expansin cefficient number f levels in vertical crss-shre grid spacing alngshre grid spacing ttal cean depth time step mean Crilis parameter acceleratin f gravity biharmnic mmentum diffusin cefficient biharmnic heat diffusin cefficient vertical eddy viscsity vertical eddy cnductivity symbls in the mdel equatins as well as values f cnstants used thrughut this study. b. Dmain size and reslutin. The dmain f the mqel is the rectangular regin extending frm apprximately 124 t l30w and frm 36.5 t 42.5N, cvering an area f 6 lngitude by 6 latitude (Fig. 1). The regin extends apprximately 500 km ffshre frm the west cast f Nrth America, and it spans the Califrnia castline frm Pint Sur in the suth t Cape Blanc in the nrth (640 km). The hrizntal reslutin f the mdel is 8 km in the crss-shre directin and 10 km in the alngshre directin. This hrizntal grid reslutin shuld allw realistic spatial reslutin f messcale features in the CCS, which have typical wavelengths f the rder f 100 km (Breaker and Mers, 1986). Althugh there are significant variatins in the castline and cean depth in the CCS, these variatins are mitted in the mdel in rder t fcus n the rle f steady wind frcing in the generatin f eddies. c. Finite difference scheme. n the hrizntal, a space-staggered B-scheme (Arakawa and Lamb, 1977; Batteen and Han, 1981) is used. There are 10 layers in the vertical, separated by cnstant z-levels placed at depths f 13, 46, 98,182,316,529,870,1416, 2283 and 3656 m. d. Heat and mmentum diffusin. The mdel uses biharmnic lateral mmentum and heat diffusin with the chice f cefficients listed in Table 1. Hlland and Batteen (1986) have shwn that Laplacian lateral heat diffusin can diminish the barclinic

7 498 Jurnal f Marine Research [47,3 43N 41N 39N 37N 35N 132W 130W 128W 126W 124W 122W Figure. Study dmain. The rectangle represents the primitive equatin (PE) mdel dmain. Bathymetry in meters, cntur interval is 200 m. signal assciated with messcale prcesses, making it less likely that barclinic instability prcesses can exceed the diffusive damping. Since biharmnic diffusin is scale selective and acts predminantly n scales smaller than thse f eddies (Hlland, 1978), the use f biharmnic, rather than Laplacian lateral diffusin, alng with the apprpriate cefficients, shuld allw messcale eddies t be generated via barclinic and/r bartrpic instability prcesses. e. Wind frcing. Using ship bservatins in ne-degree square areas, Nelsn (1977) cmpiled a cmplete descriptin f mnthly mean wind stress ff the west cast f the United States. These histrical marine wind stress fields were used t determine the wind frcing f the PE mdel. The wind stress data f Nelsn (1977) fr the summer mnths shw that the mean wind stress has an alngshre, equatrward cmpnent, implying cnditins generally favrable fr castal upwelling. T investigate the rle f

8 1989] Batteen et al.: A numerical study f wind frcing ,... Z Q) "'0 :::l -:;:: 0 -J ~ :: -Ul ' (dyne cm- 2 ) Figure 2. Wind stress (T) versus latitude and alngshre distance. The dashed line represents the unifrm alngshre cmpnent f the mdel wind stress used in Experiments and 2, while the slid line with dts represents the variable alngshre cmpnent f the mdel wind stress used in Experiments 3 and 4. this wind stress as a mechanism fr eddy and jet frmatin, the alngshre cmpnent f the wind stress field during summer (June-August) was averaged znally and meridinally in the area f the mdel dmain. The resulting equatrward wind stress frcing f dyne cm- 2 (equatrward mean wind f -8.3 ms- 1 ) was used in the mdel fr the experiments with cnstant wind frcing (Experiments 1 and 2). n additin t an equatrward wind stress fr the summer mnths, the wind bservatins f Nelsn (1977) shw that the mean equatrward wind stress can vary by 20-30% ver nly several degrees f latitude. Maximum values f surface wind stress ccur ff Cape Mendcin, where characteristic values can apprach 1.2 dynes cm- 2 (Fig. 2) ver a distance which extends 500 km in the ffshre directin. t is feasible that alngshre variatins in the alngshre wind field can result in the develpment f a cmplex system f currents and cntribute t sme f the spatial seasnal variability

9 500 Jurnal f Marine Research [47,3 f the CCS. T examine the rle f alngshre variatins in the wind in the area ff Cape Mendcin, the climatlgical alngshre wind stress frm Nelsn (1977) was znally averaged ver the mdel dmain fr the summer seasn (Fig. 2) and used as the frcing in Experiments 3 and 4. The alngshre variatins in the znally averaged wind stress shw a maximum suthward stress f -1.2 dyne cm- 2 at 39.5N, which culd serve t generate eddies preferentially at this latitude. f Surface thermal frcing. Like all majr eastern bundary current systems, the CCS is a regin f net annual heat gain (Nelsn and Husby, 1983). This heat gain ccurs because f relatively lw clud cver (cmpared with farther ffshre), reduced latent heat flux, and dwnward sensible heat flux due t the presence f cld upwelled water during summer. T fcus this study n wind frcing as a pssible mechanism fr the generatin f thermal variability in the CCS, the surface thermal frcing in the mdel was highly simplified. The slar radiatin at the sea surface, S, was specified t be the summer-mean and CCS-mean value frm Nelsn and Husby (1983). On the ther hand, the sum f the net lngwave radiatin, latent and sensible heat fluxes, Qs, was cmputed during the mdel experiments frm standard bulk frmulas (Haney et al., 1978) using the summer- and CCS-mean value f alngshre wind (abve), clud cver, relative humidity, air temperature and mdel-predicted sea surface temperature. n all the experiments shwn belw, the initial sea surface temperature was chsen s that the ttal heat flux acrss the sea surface, S - Qs. was zer at the initial time. Therefre, the nly surface heat flux frcing in the experiments was that which develped in Qs as a result f (wind-frced) fluctuatins in the sea surface temperature. As discussed in Haney (1985), such a surface thermal frcing damps the sea surface temperature fluctuatins t the atmsphere n a time scale f the rder f 100 days. Cnsequently, sea surface temperature fluctuatins that develp due t wind frcing shuld be bserved lng befre they are damped by the cmputed surface heat flux. g. Bundary cnditins. The eastern bundary, representing the west cast f Nrth America, is mdeled as a straight, vertical wall. A n-slip cnditin n the tangential velcity is invked at the castline. The nrthern, suthern and western bundaries are pen using a mdified versin f the radiatin bundary cnditins f Camerleng and O'Brien (1980). Whereas n prblems were encuntered in the use f these pen bundary cnditins fr unfrced cases as in Batteen (1989), the results are nt realistic fr wind-frced cases if the frcing is applied nt nly in the interir but als n bth the nrthern and suthern pen bundaries f the mdel dmain. McCreary (1981) shwed that if a unifrm wind stress is used, a steady alngshre current will result that is t strng, t deep and directed equatrward at all depths. T generate a realistic undercurrent, he recmmended the use f wind band frcing f the frm: (10)

10 1989] Batteen et al.: A numerical study f wind frcing 501 where 'T is the actual wind stress (which may depend n y, as in Fig. 2), and Y(y) is an impsed latitudinal variatin that is needed t make 'T = 0 n the nrthern and suthern bundaries. Fllwing McCreary et al. (1987), we have als impsed a band f meridinal wind frcing in the interir f the dmain away frm bth the nrthern and suthern bundaries. The wind band functin is given by Y(y) = 1 37 <y < 42 [ therwise. (11) The use f wind band frcing Y(y), while smewhat artificial in frm, allws fr the prpagatin f castal Kelvin waves which thereby establish the alngshre pressure gradient field, with the result that a surface-trapped castal jet and a relatively realistic undercurrent are generated. n additin, we extend the results f McCreary et al. (1987) by shwing that the jet and undercurrent are unstable and as a result, eddies and jets are generated. h. nitial cnditins. The initial mean stratificatin used in all experiments was an expnential temperature prfile with a vertical length scale f h = 450 m. The exact frm was: where T B = 2 C is the temperature at great depth and!1t = l3 C is the increase in temperature between the bttm f the cean and the surface. This temperature prfile was derived frm available CCS bservatins used t supprt the Dynalysis f Princetn mdel (Blumberg and Mellr, 1987) and has been cnsidered by Blumberg and Mellr (1987) t be representative f the lng-term, mean climatlgical temperature stratificatin fr the CCS regin as a whle. (12) 3. Results n the fllwing sectins we examine the ceanic respnse t steady winds, either with r withut alngshre variability, n bth anf-plane and a {j-plane. Experiments and 2 use a band f cnstant wind stress n anf-plane and a {j-plane, respectively, while Experiments 3 and 4 use a band f alngshre-varying wind stress n anf-plane and a {j-plane, respectively. a. Experiment 1 (cnstant wind stress n an f-plane). Experiment 1 was run n an f-plane with a cnstant Crilis parameter f f = 9.3 X 10-5 S- based n the mean latitude f the dmain. The wind frcing ('T) fr this experiment was cnstant ( dyne cm- 2 ), bth in the alngshre and crss-shre directins and steady fr a 90-day perid. The mdel was frced with full magnitude winds and, as expected, inertial scillatins f near-surface cean currents develped. These scillatins were damped

11 502 Jurnal f Marine Research [47,3 42N 40N 38N 36N ~ ~ : :t ~ t~ ~r~tl--. : : : : : : : : ~ i ~ ~ t-- :!_ i ~ --~ t~ _~ t--~j- - :.., :... ;J ;~..k ~J ~ ~ ;J.~Z. : : : : :,. -<.,.:....:~,. ~ <....:-. k.j.. % ~.--~.l~ _ ~ ± r --.. j i l i i _...~.._j..~_...~..t-_.:_..l... : : : : :, '4 ""'""i"..i- '""'""1~ : : : : :._..=.._j._~----~..t... =_..j... ~... :.l~ = _±_ ~ ~...:~,. ~...,. :+...J.. ~ i ~ j ~.,.. ~. 'Of. j..... ~ ~... i"", +- l.. --.,... 1 J 1 J - i. ~ ~ ~ ~1~ 4 ~ ~ MlM ~ t : : : : : ~ + T ~j~ ~ ~ ~ ~l ~ ~ ~ +,, ' : : : : ' : : _~ :. 130W, : : ', :, : ' ' : : : : : :, : : : : : : : : : : ' 128W D8y40 126W ') 20 em/sec Figure 3. Surface current vectrs fr Experiment 1 at day W after several inertial perids, leaving quasi-steady ffshre Ekman transprt t the right f the wind stress, as shwn at day 40 in Figure 3. The subsequent ffshre prgressin f cld water (Figs. 4a and 4b) is caused by the cld, upwelled water replacing the castal waters. Surface temperature gradients near the cast are -O.031 C km- and increase slightly with time thrughut the duratin f the experiment.

12 1989] Batteen et al.: A numerical study fwindfarcing 503 T at day 20 depth 0 T at day 40 depth 0 A B ~ JB4E 384;[., C.., u c: c: 0.s iii '" B cntur interval::::: 0, cntur interval :::: 0.5 Figure 4. Surface cnturs f temperature (0C) fr Experiment at (A) day 20 and (B) day 40. Cntur interval is 0.5 C n West-east distance (km) cntur interval = ~ 2120 g t 2520 ~ Figure 5. Vertical crss-shre sectin f meridinal (v) velcity (cm S-) fr Experiment at day 40. Cntur interval is 2.0 em S-. Dashed cnturs dente equatrward velcities. The vertical crss-sectin was alngshre-averaged.

13 504 Jurnal 01 Marine Research [47,3 West-east distance (km) = ,~ 2120,!; cntur interval = R <1J Figure 6. Vertical crss-shre sectin f temperature (0C) fr Experiment at day 40. Cntur interval is.o C. The vertical crss-sectin was alngshre-averaged. The steady, equatrward wind frcing resulted in an equatrward, surface castal jet (Fig. 5) with a maximum velcity f -14 cm S- by day 40. This nearshre surface flw is gestrphic and in balance with the density field accrding t the thermal wind equatin. Gill (1982) shwed that n an [plane the castal jet shuld be cnfined t within the first internal Rssby radius f defrmatin f the cast. This radius is -30 km fr the mdel dmain, as calculated by the methd f Feliks (1985). The castal jet axis seen in Figure 5 is -16 km frm the cast, has a maximum ffshre extent f -45 km and extends t -200 m depth. This castal jet develpment agrees well with the steady wind frcing results f McCreary et a/. (1987). A weak, pleward current f -2 cm S-1 is als seen in Figure 5 belw the surface current at a depth f m. The ffshre extent f the undercurrent is cnfined t -10 km f the cast. McCreary (1981) fund that a pleward undercurrent can develp as a result f an alngshre pressure gradient established via an alngshre variatin in the wind stress and the pleward prpagatin f Kelvin waves. Vertical mixing f heat and mmentum was als necessary. McCreary (1981) described the sequence f events n ani-plane with suddenly impsed winds. First, ffshre Ekman transprt ccurred in the area f the applied wind. Next, an upwelling signal prpagated rapidly pleward as a castal Kelvin wave. As the Kelvin wave passed, a castal jet was set up and prvided a surce f water fr the ffshre Ekman transprt.

14 1989] Batteen et al.: A numerical study f wind frcing 505 U at day 45 depth 0 r ,--rr J ' ', _,,,... \, \ '\ ~ '....' \ : :.'\. \ \, ~' '... : ", ~ \.. \ /\ \ , 364, '..' ),,,.,,.. -'-' " ,,'... _', " /. \ \. \ l-_ t /...,, ' '17\ \ \. \,,,. ~- J ~ ',,,,/) / \ ~,..,...},ff/ E.:L '--' OJ 320 u ca +-' Ul r' , cntur interval = 2.0 Figure 7. Surface znal (u) velcity (cm g-) fr Experiment 2.0 cm S-. Dashed cnturs dente ffshre velcities. 1 at day 45. Cntur interval is Philander and Yn (1982) fund that Kelvin waves als intrduced an undercurrent which reduced the intensity f castal upwelling, but did nt mdify the znal velcity perpendicular t the cast. The vertical and ffshre extent f the clder, upwelled waters is depicted in the vertical crss-shre sectin f temperature (Fig. 6). The initial cnditins f a hrizntally unifrm temperature field have been changed by the presence f clder, upwelled water near the cast. Cnsequently, a rise f istherms, cnsistent with upwelling, abve -200 m can be seen. The near-surface upwelled water extends - 70 km ffshre. These results are cnsistent with McCreary (1981), wh fund that upwelling did nt reach deep depths, but was cnfined t abve the cre f the undercurrent. At arund day 45 f the experiment, the first evidence f develping cean eddies can be seen (Fig. 7) as perturbatins in the znal current near the cast at

15 506 Jurnal f Marine Research [47,3 U at day 90 depth 0 V at day 90 depth B., '-' cntur intervl =: 5.0 cntur interval = 5.0 c P at day 90 depth 0 T at day 90 depth itl ' 640 j ~ j \ 576 fi ~ 512 Q ",;':::,,' QJ, 320 u " c,': 0 ", - -< 0'\: 256 Ci ",:<:' 192,. "'. j:) 128 D E C., 320 (J c iii -256 Ci : \ cntur interval = 2.0 cntur interval = 0.5 Figure 8. Surface ispleths fr Experiment at day 90 f (A) znal (u) velcity (em S-), (B) meridinal (v) velcity (em S-), (C) dynamic height (cm) relative t 2400 m and (D) temperature (0C), Cntur interval is 5.0 cm S- fr (A) and (B), 2.0 em fr (C) and 0.5 C fr (D). Dashed lines dente ffshre velcities in (A), equatrward velcities in (B) and negative (relative t 2400 m) values in (C).

16 1989] Batteen et 01.: A numerical study f wind frcing West-east distance (km) ~ 2120 g : ~ cntur interval = 2.0 Figure 9. Same as Figure 5 except at day 90. y km. As will be seen in Sectin 4, these eddies develp due t the presence f the castal jet, which becmes unstable. These messcale features cntinued t develp near the center f the mdel dmain alng the cast (between y km). The instantaneus znal velcity field at day 90 (Fig. 8a) shws that the alngshre wavelength fr these eddies is - 75 km with maximum znal velcities -15 cm S-. The maximum instantaneus velcity f the castal jet at day 90 (Fig. 8b) is greater than 20 cm S- with the cre at abut 30 km ffshre, and the maximum ffshre extent -64 km. The crss-shre sectin f the meridinal velcity at day 90 (Fig. 9) shws that the pleward undercurrent extends t km ffshre, frm -150 m t 600 m depth, and has a maximum cre velcity f -2 cm S-. The surface castal jet axis is shwn t extend t -32 km ffshre, and extends t -350 m depth ffshre f the undercurrent. The surface pressure field, shwn in Figure 8c at day 90, was calculated as the hydrstatic pressure field relative t 2400 m depth. The dynamic height slpes dwnward tward the cast, as expected. n additin, there is an anticyclnic eddy 50 km ffshre at y km. A cmparisn f Figure 8c with Figure 8d, which shws the sea surface temperature field at day 90, shws that the istherm perturbatins align with the ffshre/nshre gestrphic flw f the eddies. These results are cnsistent with CCS bservatins f cld, seaward flws, called squirts (Davis, 1985).

17 508 Jurnal f Marine Research [47,3 b. Experiment 2 {unifrm wind stress n a (3-plane). Experiment 2 used the same parameters and frcing mechanisms as in Experiment 1, but used a {3-plane rather than an.f-plane. The Beta effect allws the existence f freely prpagating planetary waves, i.e., Rssby waves (Gill, 1982). Due t the Beta effect, the surface castal jet des nt necessarily have t be cnfined t within a Rssby radius f defrmatin f the cast (McCreary et al., 1987). The ffshre radiatin f Rssby waves, accrding t McCreary (1981), can cntribute t the generatin f an alngshre pressure gradient field, which can cause a pleward undercurrent t develp. f n vertical mixing is allwed, the Beta effect can als intensify the undercurrent and advect the castal currents ffshre. n Experiment 2, the first evidence f develping eddies was seen in the znal velcity field (Fig. 10) at -day 40. The perturbatins were generated a little farther t the nrth in the {3-plane experiment than in the f-plane experiment. Surface cntur plts f instantaneus velcity, temperature and dynamic height at day 90 are shwn in Figure 11. The maximum znal velcity (Fig. la) reached is -15 cm s- 1 cinciding with the generatin f an anticyclnic eddy at y km (Fig. c). The 13.5 C temperature pl in the same area (Fig. ld) is assciated with the warm cre f this anticyclne. The surface equatrward castal jet (Fig. b) has maximum velcities f cm S- which are lcated ffshre at -56 km. This is apprximately 5 cm S-1 weaker and 25 km farther ffshre than the results f Experiment 1. A cmparisn f the castal jet and undercurrent regin in this experiment (Fig. 12) at day 90 and that in Experiment (Fig. 9) shwed that in this experiment the castal jet was weaker and shallwer ffshre and the undercurrent wider and strnger. The maximum ffshre extent f the undercurrent was -30 km, which was -15 km farther ffshre than in Experiment. The intensificatin and widening f the undercurrent must be due t the Beta effect. The detensificatin and shallwing f the castal jet ffshre cmpared t the jet in Experiment must als be due t the Beta effect. These results are cnsistent with Hurlburt and Thmpsn (1973) and McCreary et al. (1987). c. Experiment 3 (alngshre-varying wind stress n an j-plane). Experiment 3 was similar t Experiment 1 with the exceptin f an impsed meridinal variatin in the alngshre wind stress (T) with maximum at y km, as shwn in Figure 2 and discussed in Sectin 2. The initial results f Experiment 3 were quite similar t Experiment 1. After further evlutin f the eddy field, as seen in Figure 13, the cre f the equatrward castal jet (Fig. 13b) is centered -32 km ffshre with a maximum velcity f -20 cm S-. A ntable difference frm Experiment was that n eddies develped nrth f -385 km in Experiment 3 (cmpare Figs. 8a and 8c with Figs. 13a and 13c). This was prbably due t the maximum wind stress ccurring suth f this regin. The znal (u) velcities

18 -O '" - ' 1989] Batteen et al.: A numerical study f wind frcing U at day 40 depth 0 U at day 50 depth 0 '1A Jr-T V --..T ? ( ;.~--. --_._ '..."'....' ~~, _ j< :::) '" t " , ' (---,-..J, _~~,',.~~':--~:,'-. -'.'~----:::.-::.-.- -~ ~~~~~~~: j... -"? _4 - --:i "-" ,:...- t ,-...,.-...,.-..., ,...-"'t""4..~~=l_ Oistance (km) J64E '" (.) c:. Ul '26 6, B _ , ~~ ~ ~ ~ ~ ~,..:,.:.~_:.. ~~-_~ -4- ~_.--. ' -----~~ ~ ~' :~:' :> - ~ ~~ ~. ~ _4_ '~, ~ "~-'.-.-_.~--.._--- -,, '92 '26 64 cntur interval'" 2.0 cntur interval = 2.0 -:.-}.-~:t:~.':) E '" (.) c: a Ui '28 6 U at day 60 depth 0 U at day 70 depth 0 C _ _ '2 4, E '" (.) C. Ul E ~::::.. --_..-.._--), '-' ' Oistance (km) cntur interval'" 2.0 cntur interval::: 2.0 Figure 10. Surface ispleths f znal (u) velcity (cm S-) fr Experiment 2 at (A) day 40, (B) day 50, (C) day 60 and (D) day 70. Cntur interval is 2.0 cm S-. Dashed cnturs dente ffshre velcities.

19 510 Jurnal f Marine Research [47,3 U at day 90 depth 0 V at day 90 depth 0 A 576 B ,, E 3 OJ 320 u c:.s Ul 256 i ' a 0 5' ' a cntur interval = 5.0 cntur interval ::;;l 5.0 P at day 90 depth 0 T at day 90 depth 0 C 6'0 6.0 D, " 576 ' " 576 ", r'" l/; all :, 38'E 38'E 3 3 " OJ OJ ~\. 320 u 320 u ",, c: c: (::',~.s.s Ul Ul ,...~:/' " ' , ,, 64 64, a J '92 '28 64 a J '28 64 cntur interval = 2.0 cntur interval = 0.5 Figure. Surface ispleths f (A) znal (u) velcity (cm S-), (B) meridinal (v) velcity (em S-), (C) dynamic height (cm) relative t 2400 m and (D) temperature (0C) fr Experiment 2 at day 90, Cntur interval is 5.0 cm S- fr (A) and (B), 2.0 cm fr (C), and O.SOCfr (D). Dashed cnturs dente ffshre velcities in (A), equatrward velcities in (B) and negative values relative t 2400 m in (C).

20 1989] Batteen et al.: A numerical study f wind frcing 511 West-east distance (km) =--=> = 2120 S.<:: 2320 g n cntur interval = 2.0 Figure 12. Same as Figure 9 except fr Experiment (Fig. 13a) f -5 cm S- well seaward f the cast are assciated with strnger Ekman transprt in respnse t the strnger alngshre varying wind stress at that latitude (see Fig. 2), as expected. Temperature perturbatins (Fig. 13d) assciated with the meandering features als ccurred farther t the suth. This experiment shwed that the alngshre variatin in the mean alngshre wind stress can mdify the lcatin f the eddy develpment regin. n particular, eddies tend t be generated preferentially in, and dwnstream f, the regin f maximum alngshre wind stress. d. Experiment 4 (alngshre-varying wind stress n a (3-plane).This experiment used the same frcing parameters as Experiment 3, but used a {3-plane rather than an f-plane. As in the previus experiments, eddies initially develped between days 40 t 50. The lcatin f the frmatin f these eddies (nt shwn), as in Experiment 2, extended a little farther nrth in this {3-plane experiment than in the f-plane Experiments and 3. Surface cntur plts f instantaneus velcity, temperature and dynamic height fr day 90 are shwn in Figure 14. The znal (Fig. 14a) and meridinal (Fig. 14b) velcities vary between -5 and 15 cm S-. A cmparisn f the dynamic height field (Fig. 14c) and the sea surface temperature field (Fig. 14d) shws, as in previus experiments, that the istherm perturbatins align with the ffshre/nshre (gestrphic) flw f the eddies, cnsistent with CCS bservatins f squirts (Davis, 1985).

21 512 Jurnal f Marine Research [47,3 U al day 90 depth 0 V at day 90 deplh 0 A J can lur interval = 5.0 cntur interval = 5.0 c P al day 90 depth 0 T al day 90 deplh a 640 D " ::: (j \t\ 4<8 :,.;.lb4e ::\.6 :': 2, 1J // ~.}20 u 0':>: 255iS 448 JB4E ;;;.. (..""1 192 " ', ' ~, ~ 128,1: \ M (.4 Dislance (km) cntur interval = 2.0 cnlur interval = 0.5 Figure 13. Same as Figure 8 except fr Experiment 3. Of particular interest is the nrth-suth extent f the perturbatin fields. A cmparisn f the znal velcity fields at day 90 fr this experiment (Fig. 14a) and Experiment 3 (Fig. 13a) shws that bth the Beta effect and the variatin in alngshre wind stress can affect the lcatin f the eddy develpment regin. On an f-plane, when the variatin in alngshre wind stress is included, eddies are preferen-

22 \989] Batteen et al.: A numerical study f wind frcing 5\3, A U at day 90 depth 0 V at day 90 depth 0 }\../, '. \....,.:: r', '::(.':."., y',. ' '" u c: 0 U; '26 B,,,,,, : ~.~,,,'-.jj;:~::: 0\:' :: ~ \\/:,.;: ~ ~ ;);~:::".' :; ''' B B 64 cntur interval::::: 5.0 cntur interval = 5.0 c P at day 90 depth 0 T at day 90 depth '? 6 <U.320 U c: ~ 256 Ci B B cntur interval = 2.0 cntur interval = 0.5 Figure 14. Same as Figure 8 except fr Experiment 4. tially generated in and t the suth f the area f maximum alngshre wind stress (cmpare Fig. 8a with Fig. 13a). With the additin f the Beta effect, eddies als appear t the nrth f this area (Fig. 14a). Because f the inclusin f bth alngshre-varying wind stress and the {3-plane, the results f this experiment shuld be mre representative f the bserved flw in the CCS than the ther experiments.

23 514 Jurnal f Marine Research [47,3 4. Stability analysis The dynamical reasns fr the generatin f the eddy and jet patterns in the abve experiments will be investigated here. First, we examine the necessary cnditins t determine the ptential fr the flw field t becme unstable and generate eddies and jets. t is knwn that bartrpic instability can ccur in an.fplane jet if the curvature f the velcity prfile changes sign (Haltiner and Williams, 1980). n additin t bartrpic instability, barclinic instability culd als be significant due t the available energy frm the vertical shear f the castal jet and undercurrent. Watts (1983) and Watts and Jhns (1982) examined the distributin f ptential vrticity in the Gulf Stream as a signature f instability. A necessary cnditin fr barclinic instability t ccur is that the crss-stream derivative f ptential vrticity change sign smewhere within the dmain. n additin, the prduct f the crss-stream derivative and the basic current is required t be psitive. Finally, the castal jet must meet the requirement fr linearizatin f a basic state current that is slwly changing in space and time (Rbinsn, 1983); this requirement is met by the structure f the castal jet in this study. Watts (1983) examined the ptential vrticity (q) signature in the Gulf Stream using the fllwing expressin: at az q-(f.+s)---- atav ax az (13) where av ax f=---. au ay (14) Fllwing Watts, we similarly studied the castal jet t determine its ptential fr instability. A crss-sectin plt f the time-averaged (days 30-40) ptential vrticity (Fig. 15a) fr Experiment 1 shwed the tendency fr ptential vrticity t be unifrm alng isthermal surfaces and t change vertically, cnsistent with the ffshre temperature stratificatin. The time-average ver days 30 t 40 was chsen because it was the perid during which the instability ccurred. The range f the ptential vrticity was between x 10-6 C m- S- ffshre f the castal jet. A relative minimum existed in the surface layer f the ffshre regin due t weak stratificatin frm turbulent vertical mixing. Strng upwelling in the nearshre regin caused weak stratificatin and deeper minimum values there. A relative maximum f ptential vrticity was lcated at a depth f -100 m, and at distances greater than 63 km ffshre, which crrespnded t the "seasnal" thermcline in the mdel. All experiments in this study, where instability ccurred, shwed similar ptential vrticity patterns, and s will nt be shwn here. The crss-stream derivative f ptential vrticity was pltted (Fig. Sb) by first calculating the hrizntal derivative (aqlax) and then multiplying by ne grid length

24 1989] Batteen et 01.: A numerical study f wind frcing 515 West-east distance (km) J20 280, '-"_c ~~..'" 1.6./J / ~ J ~ :5 a. Q) A cntur intervl = 0.2 lj J West-east distance (km) J !i.2 :g: : " B cntur interval = 0.1 lj Figure 15. Vertical crss-sectin f (A) ptential vrticity (OC m - S-) scaled by 10 6, and (B) the crss-stream derivative f ptential vrticity multiplied by the grid size (OC m- S-) als scaled by J06, fr the time-averaged days f Experiment. Cntur interval is 0.2 C m- S- in (A) and 0.1 C m- S- in (B). Dashed cnturs in (B) dente negative values. The vertical crss-sectins were alngshre-averaged.

25 516 Jurnal 01 Marine Research [47,3 (~x). Frm Figure 15b, it is bvius that the crss-stream derivative meets the necessary cnditin (f a sign change) fr barclinic instability in the vicinity f the castal jet and undercurrent, and fr bartrpic instability in the vicinity f the ffshre regin f the castal jet. n additin t satisfying the necessary cnditin fr instability, it is useful t determine the sufficient cnditins fr instability. The simple quasigestrphic twlevel mdel f a unifrm barclinic jet (Hltn, 1979) predicts that all waves with an alngshre wave number k <.fix where X- = Nfl* /10 is the Rssby radius f defrmatin, N is the buyancy frequency and H* is the interfacial depth, are barclinically unstable with a grwth rate given by (S) Nte that 0 depends n A and n the vertical shear V T = 1/2 (V - V 2 ), where V and V 2 are the upper and lwer level currents, respectively. The grwth rate, 0, is als a functin f k, and is a maximum at an intermediate wavenumber smewhat smaller than = 4 cm S-1 as representative.fi X. Using H* = 150 m, N = 4.7 X 10-3 S-, and Vr f the jet in Experiment fr days 30-40, we find that X- = - 7 km, and that all waves lnger than -30 km are unstable. The mst unstable wave (cmputed frm (15» has a wavelength f -50 km and an e-flding time f -3.5 days. The shrtest e-flding time indicates that eddy develpment shuld be apparent within a week r s f mdel integratin, after this unstable state has been achieved. Nte that these values f the e-flding times and the wavelength f maximum grwth rate are nly rugh apprximatins t the true values due t the limited applicability f the tw-level analysis t the cntinuus mdel. n additin t a stability analysis f the mean flw, it is necessary t examine mdel heat and mmentum diffusin and its assciated damping (e-flding) time scale. f the damping time fr diffusin is less than the e-flding time due t barclinic instability, barc1inic instability can be suppressed. Biharmnic heat and mmentum diffusin, as described in Sectin 2, are used in the PE mdel. Fllwing the analysis f Hlland and Batteen (1986) fr a quasigestrphic (QG) mdel, the diffusive terms in the thermal vrticity equatin can be shwn t have the frm: where if; is QG "temperature" (if;. - if;3 in a tw layer mdel), A is the biharmnic eddy viscsity, K is the biharmnic eddy heat diffusin cefficient, and X- is the Rssby radius f defrmatin as befre. Assuming wave numbers (k, ), (16) becmes: (16) (17)

26 1989] Batteen et al.: A numerical study f wind frcing 517 with slutin tit = tlte--r t (18) The e-flding (damping) time f barc1inic mdes is therefre: _ (k X2) l' = A(k2 + 12)3 + X2K(k2 + 12)2 (19) f A = K, as in the PE mdel, the dependence f ')'-1 n X drps ut and (19) becmes (20) Using A = K = 2 X cm 4 S-, an alngshre wavelength f 75 km, and a crss-shre wavelength f 130 km (frm Fig. 8a), Eq. (20) yields 1'-1-65 days. Since the shrtest e-flding time due t barclinic instability was previusly shwn t be 3.5 days, diffusive damping wuld appear t be fairly negligible cmpared with the barc1inic grwth rate. Fr lnger wavelengths, which als experience sme grwth due t barc1inic instability, the diffusive damping is entirely negligible. Stability analysis f the ther experiments was als made. Experiment 3, which included the alngshre-varying wind stress n anf-plane, had similar stability results as Experiment due t the interactin f the castal jet and undercurrent. Fr a meridinal flw, as in this study, Olivier (1987) demnstrated that there is a difference in flw behavir between a nn-znal and znal flw n a l3-plane. n particular, energy can be released withut any cmpnent f 13 acting n it; therefre, any vertical shear abve the dissipatin level may prduce instability. nstability did ccur in the l3-plane Experiments 2 and 4. Bth f these experiments prduced an equatrward castal jet verlying a pleward undercurrent, with the subsequent develpment f eddies and jets. These, alng with the previus experiments, prvide evidence that the generatin f cmplex eddy and jet patterns culd be attributed t the instability created by the shear between the castal jet and the pleward undercurrent. 5. Cmparisn f mdel results with bservatins Hickey (1979) and Huyer (1983) described the classical features f the CCS as cnsisting f a barc1inic alngshre castal upwelling jet with the strngest flw at the surface ver the midshelf r uter shelf and a pleward undercurrent ver the shelf break. [n ther investigatins (Bernstein et al., 1977; Mers and Rbinsn, 1984; Rienecker et al., 1985, 1988; Davis, 1985; Ksr and Huyer, 1986; Ksr, 1987; Huyer and Ksr, 1987 and Lynn and Simpsn, 1987), the instantaneus near-surface currents ften deviated substantially frm the time-averaged, classical picture. n particular, Ksr (1987) examined synptic maps f the castal current field ff nrthern Califrnia during CODE (Castal Ocean Dynamics Experiment) and fund

27 518 Jurnal f Marine Research [47,3 Table 2. Time-averaged cmparisn f mdel experiments (exp.) with bservatins (bs.) f the CCS. Obs. Exp. Exp.2 Exp.3 Exp.4 A. Maximum castal jet velcity 5-20 (1, 2, 3,4,5) (em S-) B. Offshre lcatin f castal jet (1,2) (km) C. Offshre extent f castal jet >40 (1, 2) (km) D. Depth f inshre castal jet (m) (1, 2, 3) E. Maximum vertical shear f <2.5 (1,2) castal jet (x 1O- 3 s- l ) F. Maximum undercurrent velcity 5-10 (1, 2, 3, 4) (em S-) G. Offshre lcatin f undercur- <30 (1, 2, 4) rent axis (km) H. Maximum width f undercur (1, 2) rent (km). Depth f undercurrent axis (m) >200 (1, 2, 3, 4) References: (1) Cheltn (1984) (2) Huyer and Ksr (1987) (3) Hickey (1979) (4) Lynn and Simpsn (1987) (5) Davis (1985) a qualitative crrelatin between cmplex temperature patterns in satellite imagery and intense current structures such as squirts, jets and eddies. The distance f these features frm shre and their intensity als varied greatly. Davis (1985) investigated CODE drifting buy data and cncluded that it was misleading t think f the Califrnia castal circulatin as a simple wind-driven alngshre current with crss-shelf Ekman-driven circulatin; instead, he fund that varius messcale features culd be the primary mechanisms fr crss-shelf transprt. A cmparisn f mdel results with available bservatins was carried ut t see if bth time-averaged and instantaneus mdel simulatins f the castal jet, undercurrent and eddies were cnsistent with the bserved data. The time-averaged (ver days 30 t 40) cmparisns, prir t the generatin f eddies, are shwn in Table 2, while the instantaneus cmparisns (taken at day 90) t highlight specific characteristics f the currents and eddies are shwn in Table 3. The time-averaged results frm Figure 27 (bttm) f Huyer and Ksr (1987) were btained frm a set f synptic data during CODE that included bth strng wind events and perids f wind relaxatin. These bservatins may nt be representative f lnger term average climatlgical cnditins in the CCS. Cheltn's (1984) study, which shws generally weaker mean flws, is mre representative f lng term means.

28 1989] Batteen et al.: A numerical study f wind frcing 519 Table 3. nstantaneus cmparisn f mdel experiments (exp.) with bservatins (bs.) f the CCS. Obs. Exp. Exp.2 Exp.3 Exp.4 A. Maximum castal jet velcity (,2, 3, 4) 20 S 20 S (em s 1) B. Offshre lcatin f castal jet (2,3) (km) C. Offshre extent f castal jet >40 (, 2, 3) (km) D. Depth f inshre castal jet (m) (2, 3) SO 140 SO 140 E. Maximum vertical shear f <2.9 (2, 3) castal jet (x 10-3 S-) F. Maximum undercurrent velcity 5-15(2,3) (em S-) G. Offshre lcatin f undercur (2, 3) rent axis (km) H. Maximum width f undercur (2, 3) S S rent (km). Depth f undercurrent axis (m) (2) J. Maximum znal eddy diameter (2, 5) (km) K. Maximum znal eddy velcity (,2, 3, 4) (em S-) References: () Ksr and Huyer (1986) (2) Huyer and Ksr (1987) (3) Ksr (1987) (4) Davis (1985) (5) Mers and Rbinsn (1984) As shwn by Table 2, there is very little difference in the results f the fur mdel experiments, which cmpare quite favrably with the mean cnditins in the CCS. The nly discrepancies are that the simulated castal jet is slightly deeper than in the bservatins, and the simulated pleward undercurrent is -5 em S- weaker than bservatins with its axis lcatin -10 km clser t shre. These discrepancies culd be due t the mdel chices f a flat bttm rather than a shelf/slpe tpgraphy, steady rather than transient wind frcing, neglect f salinity, and/r the particular climatlgical temperature prfile used fr the initial mean stratificatin. The presence f a shelf/slpe tpgraphy culd displace the axis lcatin f bth the castal jet and undercurrent clser t shre. n additin, transient rather than steady wind frcing culd result in a mre realistic undercurrent (McCreary et al., 1987). Mrever, ur value fr the average alngshre wind stress fr Experiment, using data frm Nelsn (1977), was -1 dyne cm- 2, which was -33% lwer than the calculated values bserved by Huyer and Ksr (1987). Our lwer value fr wind stress wuld als cntribute t a weaker undercurrent than what Huyer and Ksr (1987)

29 520 Jurnal f Marine Research [47,3 bserved. n additin, a strnger initial thermcline (including salinity effects) culd perhaps increase and narrw the castal jet structure. The instantaneus mdel results (Table 3) als shw gd agreement with CCS bservatins except that the castal jet, including the ffshre-nshre eddy flws, is t weak in the mdel. Althugh the instantaneus castal jet is als smewhat t deep, the mdel pleward undercurrent is mre cnsistent with the instantaneus bservatins. The largest difference between the mdel results and CCS bservatins is in the maximum eddy velcities. CCS bservatins frm CODE and OPTOMA shw eddy velcities f cm S- while the mdel shws maximum eddy velcities f nly -20 cm S-. This discrepancy is attributed t physical factrs nt included in the mdel. A prime candidate is the cnsiderable difference between the steady climatlgical wind stress used t frce the mdel and the strnger and transient wind stress bserved during CODE. Other factrs that are likely t be imprtant, but which have been neglected in the present fcused study, include variatins in the castline and bttm tpgraphy. 6. Summary This study used a high-reslutin, multi-level PE cean mdel t investigate wind frcing as a pssible generatin mechanism fr messcale eddies and jets in the CCS. A band f znally unifrm, steady winds, either with r withut alngshre variability, was used as frcing n either an f-plane r a ~-plane in an idealized, flat-bttmed ceanic regime alng an eastern cean bundary. The mdel results f Experiment 1, which included unifrm wind stress n an f-plane, shwed the develpment f an equatrward castal jet and pleward undercurrent. The castal jet and undercurrent became unstable after -40 t 45 days resulting in the generatin f eddies and jets. Similar results ccurred in Experiment 2, which had the same frm f wind stress as in Experiment, but used a ~-plane rather than an -plane. Hwever, a cmparisn f Experiment 2 with Experiment shwed that, due t the Beta effect, the castal jet was shallwer and weaker ffshre, and the undercurrent strnger and wider in Experiment 2. The mdel results f Experiment 3, which had an alngshre-varying wind stress (Fig. 2) n an fplane, were generally cmparable t Experiment 1. Hwever, the variatin in alngshre wind stress restricted smewhat the lcatin f eddy develpment. n particular, the eddies develped in the regin f maximum alngshre wind stress, and they were generally cnfined t the vicinity, and dwnstream f, the latitude f maximum wind stress. Experiment 4 incrprated an alngshre-varying wind stress, but used a ~-plane rather than anfplane. The fact that eddies develped farther nrth f the lcalized eddy generatin area f Experiment 3 shwed that the Beta effect can als playa rle in mdifying the lcatin f eddy generatin. Because f the inclusin f bth alngshre-varying wind stress and the ~-plane, the results f

30 1989] Batteen et al.: A numerical study f wind frcing 521 Experiment 4 shuld be mre representative f the dynamics and structure f the CCS than the ther experiments. A cmparisn f mdel results with available bservatins shwed that the time-averaged mdel castal jet and undercurrent were cnsistent with available CCS bservatins (e.g., Huyer and Ksr, 1987) and ther mdel results (McCreary et al., 1987). The time-averaged simulatins shwed a classical tw-dimensinal castal jet. The main discrepancy with bservatins is that the mdel eddies were cnsiderably weaker than bserved eddies in the CCS. The results frm these experiments strngly supprt the hypthesis that wind frcing can be a significant generatin mechanism fr eddies and jets. t shuld be nted, hwever, that this study emplyed the cnstraints f a regular, straight castline and a flat bttm in rder t islate and examine the effect f steady wind stress. Future studies will include bth an irregular castline and bttm tpgraphy. Time-dependent wind frcing, such as wind events and relaxatins, and wind stress with curl experiments are presently being systematically run and investigated t see if transient wind frcing and/r wind stress curl can als be imprtant eddy generatin mechanisms. Acknwledgments. This wrk was dne in the Departments f Oceangraphy and Meterlgy at the Naval Pstgraduate Schl (NPS) under the supprt f the NPS Research Fundatin fr Mary Batteen, the Office f Naval Research (ONR) fr Rbert Haney, and direct funding at NPS fr bth Mary Batteen and Rbert Haney with ONR as the spnsr. Cmments by Dr. J. P. McCreary, Jr. n an earlier versin f this paper, and by Dr. C. N. K. Mers, CDR Craig S. Nelsn and Ms. A. A. Bird n a later versin f this paper, are greatly appreciated. Cmputer time was prvided by the W.R. Church Cmputer Center at the Naval Pstgraduate Schl. REFERENCES Adamec, D., R. L. Elsberry, R. W. Garwd, Jr. and R. L. Haney An embedded mixed layer-cean circulatin mdel. Dyn. Atms. Oceans, Arakawa, A. and V. R. Lamb Cmputatinal design f the basic dynamical prcesses f the UCLA general circulatin mdel. Methds in Cmputatinal Physics, J. Chang, ed., Academic Press, 17, Batteen, M. L Mdel simulatins f a castal jet and undercurrent in the presence f eddies and jets in the Califrnia Current System, in Pleward Flws n Eastern Bundaries, S. Neshyba, C. N. K. Mers, R. L. Smith and R. T. Barber, eds., Lecture Ntes n Castal and Estuarine Studies, Springer-Verlag, Batteen, M. L. and Y.-J. Han On the cmputatinal nise f finite-difference schemes used in cean mdels. Tellus, Bernstein, R. L., L. C. Breaker and R. Whritner Califrnia Current eddy frmatin: ship, air and satellite results. Science, Blumberg, A. F. and G. L. Mellr A descriptin f a three-dimensinal castal cean circulatin mdel, in Three-dimensinal Castal Ocean Mdels, N. Heaps, ed., American Gephysical Unin, 4, 1-16.

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