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1990-09 Modeling Studies of Eddies in the Leeuwin Current: The Role of Thermal Forcing
Batteen, Mary L.
Journal of Physical Oceanography, Vol. 20, pp. 1484-1520. http://hdl.handle.net/10945/47167 1484 JOURNAL CF PHYSICAL OCEANOGRAPHY VOLUME20
Modeling Studies of Eddies in the Leeuwin Current: The Role of Thermal Forcing
MARYL. BATTEEN AND MARTIN J. RUTHERFORD* Department ofOceanography, Naval Postgraduate School, Monterey, California (Manuscript received 29 November 1989, in final form 5 April 1990)
ABSTRACT A high resolution, multilevel, primitive equation (PE) model is used to investigate the generation and stability of the Leeuwin Current and eddies off the west coast of Australia. Two numerical experiments are conducted to investigate the roles of the Indian Ocean temperature field and the North West (NW) Shelf waters in generating both the current and eddies. In the first experiment an alongshore temperature gradient, typical of the Indian Ocean temperature field, is imposed, while in the second experiment the additional effects of the NW Shelf waters are considered. In the first experiment, the meridional Indian Ocean temperature gradient is sufficient to drive a poleward surface flow (the Leeuwin Current) and an equatorial undercurrent. The surface flow is augmented by onshore geostrophic flow and accelerates downstream. In the second experiment, the inclusion of the NW Shelf waters completely dominates in the NW Shelf equatorial source region. The effects of the NW Shelf waters weaken away from the source region but they continue to augment the Indian Ocean forcing, resulting in a stronger flow along the entire coastal boundary. The currents generated by the model agree well with the Leeuwin Current Interdisciplinary Experiment (LUCIE) current meter observations obtained during the austral fall and winter, when the Leeuwin Current is observed, and other recent modeling studies. The current is unstable and has significant mesoscale variability. The current forced only by the alongshore temperature gradient is unstable toward the poleward end of the model domain. In this region, barotropic instability tends to dominate over baroclinic instability. When the NW Shelf waters are added to force the current, eddies are generated near the source of these waters (in the equatorward end of the model domain) through barotropic instability of the current. Farther downstream, the NW Shelf waters add strong baroclinicity, which weakens poleward, to the current. Eddies are subsequently generated downstream from the NW Shelf region through both baroclinic and barotropic instability processes. Several scales of eddies are found to be dominant. The forcing by the Indian Ocean leads to eddy growth on scales around l 50 km. With the inclusion of the NW Shelf waters, the wavelength associated with mesoscale variability is around 180 km. Both of these length scales are close to the wavelength associated with a low-mode Rossby radius of deformation. The eddies generated by the model compare well with available observations. This study shows that the Leeuwin Current can be successfully modeled using a PE model forced by the mean climatology. Consistent with the findings of recent modeling studies, a shelf is not required to produce and maintain the current. The mesoscale features which have been missing from previous modeling studies are produced by the model and at scales comparable with available observations.
1. Introduction reviews of the current, see Church et al. 1989; Weaver The Leeuwin Current is a surface flow of warm, low and Middleton 1989). Off the west coast of Australia, salinity, tropical water, poleward along the west coast the maximum flow occurs along the southern portion of Australia, then eastward into the Great Australian of the North West (NW) Shelf(22°S) from February Bight. It appears to have its source in the northeast to June (Holloway and Nye 1985). Based on obser Indian Ocean and extends to Australia's southern vations from the Leeuwin Current Interdisciplinary coastal waters, having been reported as far east as 142 °E Experiment (LUCIE) reported by Boland et al. ( 1988), (Godfrey et al. 1986) and 130°E (Rochford 1986). the maximum flow occurs off Dongara (29.5°S) from The current is narrow ( < 100 km wide), shallow April to June and further south at Cape Mentelle (generally <300 m), has an underlying equatorwa.rd (34°S) from June to July (see Fig. 1 for geographical flow and is strongly seasonal in nature (for excellent locations). The flow's eastward limit south of Australia is reached in July (Rochford 1986). The Leeuwin Current differs markedly in its char • Present affiliation: Australian Joint Maritime War Centre, Naval acteristics, and hence presumably in its associated dy Air Station, New South Wales, Australia 2541. namics, from currents found in other eastern ocean regions. The other major eastern boundary currents, Corresponding author address: Dr. Mary L. Batteen, Department i.e., Peru, California, Benguela, and Canary, are char ofOceanography, Naval Postgraduate School, Monterey, CA 93943- acterized by climatologically weak ( < l 0 cm s-1) sur 5000. face flow toward the equator, cold upwelled water at SEPTEMBER 1990 MARYL. BATTEEN AND MARTIN J. RUTHERFORD 1485 the surface, shallow ( <30 m depth) thermoclines and The deployment of satellite-tracked drifting buoys high biological production (Parrish et al. 1983). In off Western Australia from 1975 to 1977 added a new contrast, the Leeuwin Current has a poleward surface dimension to the data collected on the circulation fea flow that exceeds 150 cm s - t at times (Cresswell and tures. Cresswell and Golding ( 1979) illustrated the Golding 1980; Godfrey et al. 1986), anomalously warm spatial and temporal complexity of the current in charts water, downwelling, a deep (>50 m) thermocline of buoy tracks and showed clear evidence for the ex (Thompson 1984) and low fish production. The other istence of mesoscale eddies on the western side of the currents are part of the subtropical anticyclonic gyres current. The buoys were observed to accelerate as they that are driven primarily by the anticyclonic wind entered the current and to slow again in their departure fields, and variations in current strength are highly co providing evidence of a high speed core current that herent with variations in local wind stress (Allen 1980; was measured at up to 170 cm s _, from buoy positions. Huyer 1990). With such markedly different features, High spatial resolution ( - 1 km) and temperature the Leeuwin Current may be expected to depart just discrimination ( <0. l °C) of both infrared and Ad as markedly in its generation mechanisms and dynamic vanced Very High Resolution Radiometer (A VHRR) features. imagery since the mid- l 970s have been used to reveal Within the past decade alone, there have been ex the temperature contrasts between the different cur tensive modeling and observational studies of the rents and cyclonic and anticyclonic eddies off the coast Leeuwin Current. Because the results of these as well of Western Australia. For example, the satellite image as previous investigations are pertinent to the present of Pearce and Cresswell ( 1985) shows a large wedge of study, we present a brief historical survey of observa warm water in the northeast Indian Ocean being fun tional, modeling, and theoretical studies of the Leeuwin neled into a narrow current near North West Cape, Current and its eddies. The survey will show that, de then moving south along the shelf and slope until spite extensive investigations, a complete explanation reaching Cape Leeuwin, where it abruptly swings east is missing for the Leeuwin Current, its different features ward and extends across the Great Australian Bight. (in comparison with other eastern boundary currents) Mesoscale features can be seen off Perth, and filament and its eddies. like features can be seen off the south coast. Between September 1986 and August 1987, the most a. Observational studies of the Leeuwin Current extensive current meter measurements of the Leeuwin Current to date were made as part of the LUCIE ex The earliest documentation of the characteristics of periment, coordinated by the CSIRO Division of a poleward flowing current (named the Leeuwin Cur Oceanography. The data, reported by Boland et al. rent by Cresswell and Golding 1980, in honor of the ( 1988), show that the current is weakest from Septem first Batavia-bound Dutch vessel to explore the south ber to February and strongest from February to August. west of Australia) was by Saville-Kent ( 1897) following The measurements also show the presence of an equa studies of the marine fauna of the Abrolhos Islands torward undercurrent and an acceleration of the Leeu (28.5°S). Anomalously warm water was found around win Current poleward. the Islands but not on the mainland coast 50 miles to the east where temperatures were about 7°C cooler. b. Modeling studies of the Leeuwin Current This led to a suggestion that the water must be trans ported to the region. Dakin ( 1919) noted that the tem Thompson and Veronis (1983) were the first to perature difference between the Abrolhos Islands and model the Leeuwin Current. They suggested that local the mainland was greatest in the austral winter. Roch winds on the NW Shelf could generate the current. ford ( 1969) used drift bottles to ascertain that the pole This theory was refuted by the current meter obser ward flow in the austral winter extended to the south vations of Holloway and Nye ( 1985). It was also re ofRottnest Island (32°S) and that a flow reversal oc jected by Thompson ( 1984), who proposed instead an curred in the austral summer. The reversal was also alongshore steric height gradient as the primary forcing apparent in salinity records for the southwest coast of mechanism with the winter deepening of the mixed Australia. The salinity variation was over twice that layer offsetting the effects of the equatorward wind attributable to evaporation and precipitation; hence, stress. Godfrey and Ridgway ( 1985) quantified the the salinity became an effective tracer of the flow regime contributions of the alongshore pressure gradient and in the region. Kitani ( 1977) observed low salinity water equatorward wind stress and strongly supported at 32°S in November 1975, which showed that the Thompson's ( 1984) finding. They further proposed occurrence of tropical water was not confined to the that flow from the Pacific Ocean through the Indone austral winter. The eastward continuation of the pole sian Archipelago to the northeast Indian Ocean could ward flow into the Great Australian Bight was inferred be responsible for the large steric height gradient, a by Colborn ( 1975) from temperature data, and by feature which makes the Leeuwin Current unique Markina ( 1976) from plankton data, which further among eastern boundary currents. emphasized its strong signal. McCreary et al. ( 1986) rejected the throughflow as 1486 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 20
being a primary forcing mechanism and proposed that culation model to investigate the contributions to the thermohaline gradients were responsible for the along Leeuwin Current from both the alongshore density shore pressure gradient. Their model results showed a gradient and the warmer, fresher NW Shelf waters. The poleward surface current and equatorward undercur model, which includes simple coastal geography and rent comparable in strength to observations, but no topography, produced a realistic Leeuwin Current, but mesoscale features were shown. Kundu and McCreary the current lacks mesoscale variability. Weaver and ( 1986) examined the throughflow theory separately Middleton ( 1989) concluded that the Leeuwin Current and produced a weak poleward flow. They concluded is a baroclinic current driven by the alongshore density that the throughflow was a secondary forcing mecha gradient. They also believe the current is strengthened nism. locally, by barotropic enhancement, in the vicinity of Thompson ( 1987) used an analytic model of the the source of the NW Shelf waters. Leeuwin Current to investigate why the flow is pole ward and why no upwelling occurs, despite the up c. Theories for the Leeuwin Current welling-favorable wind. He concluded that the wind mixed (or surface Ekman) layer is deep enough to re Despite extensive modeling studies throughout the duce the effects of wind forcing below the level of the 1980s, a complete explanation for the Leeuwin Current forcing due to the poleward pressure gradient. and its different features, in comparison with other Gentilli ( 1972) suggested that a seasonal (austral eastern boundary currents, remains outstanding. A autumn and winter) throughflow could be isolated in synopsis of recent theories is presented here. There is the northeast Indian Ocean during the austral summer, general agreement (e.g., by Thompson 1987; Godfrey providing a source for the subsequent Leeuwin Current and Ridgway 1985; McCreary et al. 1986; Pearce and generation. This theory is supported by the satellite Cresswell 1985; Weaver and Middleton 1989) that the image of Pearce and Cresswell ( 1985) of a large wedge Leeuwin Current is generated by a meridional pressure shaped mass of warm water off northwest Australia gradient that overwhelms the opposing equatorward funneling into a poleward current. Weaver and Mid wind stress. The wind forcing effects are diminished dleton ( 1989) used a Bryan-Cox ocean general cir- by deep mixed layers (Thompson 1987), possibly
Cape WESTERN AUSTRALIA
Islands
Island Greal Au lralLan BL ht
4o's+-~~~+-~~~-+-~~~-+-~~~-+-~~~-+~~~--; 105° E 110° E 115° E 120° E 125° E 130° E 135° E FIG. I. Study domain. The rectangle represents the primitive equation (PE) model domain. SEPTEMBER 1990 MARY L. BATTEEN AND MARTIN J. RUTHERFORD 1487
TABLE I. Initial temperature ( 0 C) for Indian Ocean.
Layer Latitude (oS) 2 3 4 5 6 7 8 9 10
22 24.0 22.9 21.6 19.2 14.5 9.4 5.9 3.5 2.0 1.0 24 23.3 22.3 20.9 18.6 14.3 9.4 5.9 3.5 2.0 1.0 26 22.6 21.7 20.3 18.0 14.1 9.3 5.9 3.5 2.0 1.0 28 22.0 21.0 19.7 17.4 13.9 9.3 5.9 3.5 2.0 1.0 30 21.3 20.4 19.0 16.7 13.6 9.2 5.8 3.5 2.0 1.0 32 20.6 19.8 18.4 16.1 13.4 9.2 5.8 3.5 2.0 1.0 34 19.9 19.1 17.7 15.5 13.2 9.1 5.8 3.5 2.0 1.0
formed in response to a strong heat flux out of the The existence of eddies in the eastern Indian Ocean ocean, which is a feature unique to the Leeuwin Cur was first postulated by Wyrtki ( 1962). Using dynamic rent among eastern boundary currents (Hsiung 1985; height calculations relative to 1750 decibars, he showed Godfrey and Weaver 1990; Weaver and Middleton a strong semipermanent eddy present near 32 °S, 110°£ 1990). The source of the Leeuwin Current water is with cyclonic circulation above the reference level and predominantly geostrophic inflow from the west anticyclonic below. Analysis by Hamon ( 1965) sug (McCreary et al. 1986; Thompson 1987) and is aug gested a double eddy structure in the region 30°-32°S, mented by a source from the NW Shelf ( Kundu and east of 107°£ during the austral winter period of late McCreary 1986; Weaver and Middleton 1989), pos April to November. In a subsequent study, Hamon sibly having its origin in the Pacific Ocean (Godfrey ( 1972) found little seasonal variation in dynamic height and Ridgway 1985 ). The inflow of the NW Shelf waters anomalies in the same area, although a tendency to is consistent with the warm, low-salinity signature of ward greater variability during the months from August the Leeuwin Current surface waters. The results of to November was noted. Weaver and Middleton ( 1989) suggest that poleward Andrews ( 1977) investigated mesoscale features in gradients of both temperature and salinity are sufficient the region and observed nearly zonal planetary Rossby to establish a pressure gradient strong enough to sup waves in the West Australian Current and nearly me port the observed flow. Godfrey and Weaver ( 1990) ridional coastal waves in the coastal current south of propose enhancement of this pressure gradient by the 15 °S, where zonal inflow occurred. The interaction of buildup of warm, fresh water near Indonesia due to the two wave types, particularly in the vicinity of a the action of zonal winds in the equatorial Pacific. In large trough, resulted in meandering in both currents. particular, they argue that channels through the In No clear ringlike features (i.e., closed isopleths of ve donesian Archipelago are crucial for the existence of locity and temperature at several depths) were apparent the Leeuwin Current by allowing the continuity of to Andrews in his study, although some mixed layer warm, fresh waters from the western equatorial Pacific and surface temperature rings were analyzed. Andrews coast through to the northwest tip of Australia. Internal ( 1983) attempted to reconcile the apparently contra Kelvin waves propagate along the coast of Western dictory findings of Hamon and Cresswell ( 1972) and Australia radiating internal Rossby waves westward, Golding and Symonds ( 1978), who reported mesoscale trying to maintain the specific volume anomaly profile structures with length scales of 200-300 km and 140 off Western Australia equal to that at the northwest tip km, respectively. He concluded that both length scales of Australia. Convective surface cooling then occurs can be present with the shorter wavelength (A. = 157 poleward of about 20°S, and the deep Indian Ocean ± 25 km) associated with Rossby deformation-scale alongshore density gradient is set up. eddy structures in the strong poleward flow over the slope and the longer (A. = 309 ± 28 km) associated d. Mesoscale variability with the weaker, large-scale, West Australian Current One of the major gaps in Leeuwin Current research is in the area of the complex eddy fields found in the current. While observational (e.g., Hamon and Cres TABLE 2. Initial temperature for North West Shelf. swell 1972; Golding and Symonds 1978; Cresswell and Golding 1979, 1980; Andrews 1977, 1983; Griffiths Layer Temperature ( 0 C) and Pearce 1985) and laboratory (e.g., Condie and Ivey I 29.5 1988) studies reveal the nature and characteristics of 2 28.5 the mesoscale features, no modeling studies have suc 3 26.0 cessfully produced eddy fields which would allow anal 4 20.5 ysis of their generation mechanisms. 5 15.7 1488 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 20
T at day 0 depth 0 . P at day 0 depth 0 T at day 0 depth 350 1280 1280 1280
20- 1024 i-1024 - 1024 ------·-10- -
21-,_ 768 -768 I- 768 E' _::£. '---"' 23-1-256 -256 I- 256 a c e I I 0 ...... -...~~,---.-...-~,-.--.-...-+-o I I 0 576 384 192 0 576 384 192 0 576 384 192 0 Distance (km) Distance (km) Distance (km) contour interval = 0.5 contour interval = 0.5 T at day 0 depth 0 P at day 0 depth 0 T at day 0 depth 350 1280 1280 1280 1024 1024 1024 ,--. t------21 - 768 E 768 768 .:Y. ~ 256 256 - 256 - b d f rr= 0 I 576 384 192 576 384 192 576 384 192 0 Distance (km) Distance (km) Distance (km) contour interval = 1.5 contour interval = 0.5 FIG. 2. The initialized fields of surface temperature ( T) for Case I (a) and Case 2 (b); of surface dynamic height (p) (referenced to 2000 m depth) for Case I ( c) and Case 2 ( d); and of the 350 m depth temperature ( T) for Case I ( e) and Case 2 ( f). The model results shown here, and in subsequent plots, have been plotted with a Northern Hemisphere interpretation so that the equatorward (poleward) end of the domain is at 0 km ( 1280 km) in the alongshore direction. The contour interval is 0.5°C for (a), (e) and (f), l.5°C for (b ), 5 cm for (c), and 10 cm for (d). Jn all the temperature plots (a,b,e, f), the temperature increases equatorwards. SEPTEMBER 1990 MARYL. BATTEEN AND MARTIN J. RUTHERFORD 1489 a b c U at day 10 depth 0 V at day 10 depth 0 C at day 10 .-~~~~~~~~~..-1280 .-~~~~~~~..... '"fffi~1280 ---~~~~~~~..... """""rhl-1280 -1152 1024 1024 -1024 0 896 0 768 "'0 768 >7777777777~~~~~~A 512 ~>>>>>>>>>>77?r~{A~ -512 ~~~~~~~~~~~>>>77~~ t 4 256 256 256 0 128 ._,.....,.....,....,.....,....,,_.,...,...... ,..+o ,....,_,,_.,..,...... ,....,,..,,_...... ,.....,,_._o p...,,...."""""_,.._....___.,,,_.....,....,..,.._ o 576 384 192 0 576 384 192 0 576 384 192 0 Distance (km) Distance (km) Distance (km) contour interval = 2.0 contour interval = 10. 200cm/s ___~ FIG. 3. Time sequence for Case 1 for days 10, 40, 80, 120 and 160 for the surface (a) zonal velocity, (b) meridional velocity, and (c) velocity vector fields superimposed on the temperature fields. The contour interval is 2 cm s-1 at days 10, 40, 80, and 5 cm s-1 at days 120 and 160 for (a), 10 cm s-1 for (b), and 0.5°C for (c). Solid contours denote onshore velocities in (a) and poleward velocities in (b). In all the velocity vector fields presented (Figs. 3c, 5b, I le and 12b), to avoid clutter, velocity vectors are plotted at every fifth gridpoint in both the cross-shore and alongshore directions, and velocities less than 2 cm s-1 for the surface and I cm s-1 for 350 m depth are not plotted. offshore. While Andrews ( 1983) suggested baroclinic Initializations of the Indian Ocean temperature field instability in the poleward current as a likely generation and the NW Shelf waters will be similar to those used mechanism, no explanation was offered for the larger by Weaver and Middleton ( 1989). The use ofa straight offshore scale. meridional vertical wall for the coastline and the ab senoe of shelf and bottom topography should not se e. Objective ofthe study verely limit this process-oriented study as the coast is generally straight over the domain ( 22 ° to 34 °S) and, Because no modeling studies have successfully pro as Weaver and Middleton note, their modeled current duced eddy fields which would allow analysis of their is centered near the shelf break. This study should con generation mechanisms, the objective of this study is firm and extend previous modeling studies and provide to use a full primitive equation (PE) numerical model a firm basis for further research. to investigate the generation and stability of the Leeu For each thermal forcing mechanism proposed for win Current and eddies. In particular, the roles of the the Leeuwin Current, we will present the simulated Indian Ocean temperature field and the NW Shelf wa characteristics of the Leeuwin Current and its asso ters in generating both the current and the eddies will ciated eddy fields and will analyze the results. A com be investigated. In a subsequent study by Batteen and parison of model results with available observations Rutherford ( 1990), the additional effects of wind forc will also be made to assess whether the simulated fea ing on the Leeuwin Current will be considered. The tures of the current and eddies are consistent with those use of a multilevel PE model with active thermody observed. In addition, because no previous studies have namics and appropriate choices for diffusion param focussed on the dynamical reasons for the generation eters should result in the first modeling study of the and growth of eddies in and around the Leeuwin Cur Leeuwin Current and its associated eddy fields. rent, we will make an extensive analysis of the gener- 1490 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 20 a b c U at day 40 depth 0 V at day 40 depth 0 C at day 40 ...... ~~ ...... ~...... 1280 ~~...... ,.._,.~1280 1152 1024 1024 1024 -896 768 768 -768 640 512 512 384 256 256 >>>>>>>>777777771~~A_ 256 >> 7~~77~~~A ---o 128 1-.....,._,....,....,_.,....,,....,...... ,....,...~o ,_,._,...,._,....,....,....,...,...... ,,....,._,__Q ,_,"""""...,....,.....,....,.....,...,.....,.....,,._,.-+ 0 576 384 192 0 576 384 192 0 576 384 192 0 Distance (km) Distance (km) Distance (km) contour interval= 2.0 contour interval = 10. U at day 80 depth 0 V at day 80 depth 0 ----~~~...... ~ ...... 1280 ....,...... -..-..-1280 1152 1024 1024 1024 ,,---.__ E 768 .:x. -768 '--"' (lJ u 640 c 0 -+-' -512 VJ 512 512 0 -256 256 256 128 0 ,_,....,....,....,.....,._.,.-,....,_,....,....,...+ 6 i-._...... _.._,_...,....,_....,...... ,_.__o ,_,._,.....,....,....,...... ,....,....,_.,.....,.....,..-+o 576 384 192 0 576 384 192 0 576 384 192 0 Distance (km) Distance (km) Distance (km) contour interval= 2.0 contour interval = 10. 200 cm/s ____ FIG. 3. (Continued) SEPTEMBER 1990 MARYL. BATTEEN AND MARTIN J. RUTHERFORD 1491 a b c U at day 120 depth 0 V at day 120 depth 0 .--~~~~~....-~...-~~1280 ' 1280 1024 0 768 -768 512 -512 512 384 256 256 ~')_) c:::;,. - 128 0 0 0 576 384 192 0 576 384 192 0 576 384 192 0 Distance (km) Distance (km) Distance (km) contour interval = 5.0 contour interval= 10. u at day 160 depth 0 v at day 160 depth 0 c at day160 1280 1280 1280 1024 1024 ,,--.. ,,--.. ,,--.. 768 E 768 E E ..__,..Y ..Y .:x '-" '-" (j) (j) (!) () () 640 () c c c 0 0 0 ...... +-' -512 UJ -512 UJ 512 UJ 0 0 0 256 256 -128 1=-.....-...-...=;-..-....,....,...... 0 576 384 192 576 384 192 576 384 192 0 Distance (km) Distance (km) Distance (km) contour interval = 5.0 contour interval = 10. 200 cm/s _____.. FIG. 3. (Continued) 1492 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 20 ation mechanisms for the eddies in the Leeuwin Cur of coastline features and bottom topography, and an rent, using the energy, spectral, and stability techniques examination of their effects on the current and eddies, described in the Appendix. are considered a separate study. The constant depth The organization of this study is as follows. In section used in the model is 4500 m. 2- we describe the numerical model and the specific Unlike previous Leeuwin Current modeling studies experimental conditions. The results of the numerical (e.g., McCreary et al. 1986; Weaver and Middleton experiments are presented in section 3 along with a 1989), which used Laplacian lateral heat and momen comparison with observations and an analysis of the tum diffusion, the model uses biharmonic lateral heat generation mechanisms for the Leeuwin Current eddy and momentum diffusion with the same choice of coef fields. A summary is presented in section 4. ficients, i.e., 2.0 X 10 17 cm4 s-1 as in Batteen et al. ( 1989). Holland ( 1978) showed that the highly scale 2. Model description and specific experimental con selective biharmonic diffusion acts predominantly on ditions sub-mesoscales, while Holland and Batteen ( 1986) found that baroclinic mesoscale processes can be a. Model description damped by Laplacian lateral heat diffusion. As a result, the use of biharmonic lateral diffusion should allow The numerical model used in this study is an ad mesoscale eddy generation via barotropic and/ or aptation of the model used by Batteen et al. ( 1989). baroclinic instability mechanisms. As in Batteen et al. 2 1 It is a ten-level PE model for a baroclinic ocean on a (1989), weak (0.5 cm s- ) vertical eddy viscosities {j-plane, based on the hydrostatic, Boussinesq, and rigid and conductivities are used. Bottom stress is parame lid approximations. The governing equations are de terized by a simplified quadratic drag law (Weatherly fined in Batteen et al. ( 1989). Unlike Batteen et al. 1972). ( 1989), there is no wind forcing used in this study. As described in the next section, the model is initialized b. Specific experimental conditions with thermal forcing. For the finite differencing, a space-staggered B-scheme (Arakawa and Lamb 1977; The model is initialized with climatological thermal Batteen and Han 1981) is used in the horizontal. In forcing. The ocean is then allowed to geostrophically the vertical, the ten layers are separated by constant z adjust in the absence of external forcing. The ocean levels at depths of 13, 46, 98, 182, 316, 529, 870, 1416, temperature structure used to initialize the experiments 2283 and 3656 m. is considered in two parts with the warmer, less saline The eastern boundary of the model domain repre NW Shelf waters separated from the Indian Ocean wa sents a straight idealization of the continental shelf off ters. Climatological mean temperatures for both the Western Australia (Fig. 1 ). A no-slip condition on the Indian Ocean and the NW Shelf are used and zonal alongshore velocity is invoked. The northern, southern, homogeneity is assumed in the Indian Ocean. These and western borders are open boundaries that use a specific experimental conditions are similar to those modified version of the radiation boundary conditions used by Weaver and Middleton ( 1989). of Camerlengo and O'Brien (1980). The model do The initial temperature data used for the Indian main is a rectangular area 1280 km alongshore covering Ocean are presented in Table 1 for each layer of the latitudes 22° to 34 °S, extending 576 km offshore. Hor model. The temperature data were derived from Lev izontal resolution of the model is 20 km alongshore itus ( 1982). After interpolating between data points, and 9 km cross-shore. Comparisons with numerical a vertically integrated temperature for each layer was simulations made by a higher resolution model ( 10 calculated and applied to the constant z levels. For km by 9 km) with half the latitudinal extent showed computational ease, the data were further smoothed no significant degradation in the resolution of meso and a linear gradient fitted to each layer over its me scale features in the coarse grid model; hence, the pres ridional extent. Zonal homogeneity was assumed at all ent grid resolution was adopted to enable coverage of levels as the data show little variability, apart from in the larger geographical region off Western Australia. the region of the Leeuwin Current. Slight differences Because the model is an adaption of a Northern Hemi between the final values used for the Indian Ocean sphere model, model results will be discussed in terms forcing in this study (Table 1) and those of Weaver of alongshore (poleward or equatorward) and cross and Middleton ( 1989) (the same Levitus data source shore (onshore or offshore) flows (as in McCreary et was used) could be due to slightly different vertical al. 1986, who also adapted a Northern Hemisphere integration and smoothing techniques and/ or to the model). This use of terminology should facilitate com additional data sources of Rochford ( 1962, 1969) used parison with other eastern boundary currents. by Weaver and Middleton ( 1989). In order to isolate the role of thermal forcing in the Salinity values from Levitus ( 1982) have a range of generation and stability of the Leeuwin Current and only 35.6 ± 0.2 ppt over most of the domain in the eddies, both coastline features and topography are upper five layers. This range is considered narrow omitted from this process-oriented study. The inclusion enough to discount salinity variability, so that no com- SEPTEMBER 1990 MARY L. BATTEEN AND MARTIN J. RUTHERFORD 1493 P at day10 depth 0 Pat day 20 depth 0 Pat day 30 depth 0 1280 1280 1280 I I I I I I I I I I I I I I I I I I I I I : I I I I / / I I , I I , I / I I , J I I I I J I I I J I I I I I I ,c !7 I I 1024 I 1024 / 1024 ,'c / I J I / / I , / , , ------I ------I ,..---- ,.---.... / / 768 E 768 E , 768 E ------..:£. ..:£. ..:£...... __,. ------'-" ....__,. Q) Q) Q) () () () c c c 0 0 0 -+-' ...... 512 Ul 512 Ul 512 Ul 0 Ci 0 ,<:> ,<:> 256 256 256 .....,_..,.....,.. __.._,_.,.....,....,.-+-, 0 ,o I 0 576 384 192 0 576 384 192 0 576 384 192 0 Distance (km) Distance (km) Distance (km) P at day 40 depth 0 1280 I I I I I I J I I I I I I c J " I _I I 1024 I I I I I / 768 --- Q) () FIG. 4. Time sequence for Case I at 10-day intervals for the surface dynamic height c field (p). The contour interval is 5 cm. Closed solid contours denote anticyclones, ...... 0 while dashed contours denote cyclones . 512 Ul 0 256 ------.-.-...-...- ...., 0 576 384 192 0 Distance (km) pensation is made for the assumption that density is a arately from the Indian Ocean, the NW Shelf waters function of temperature alone. are initialized separately in this model. As for the Indian To investigate the impact of NW Shelf waters sep- Ocean, the data were again derived from Levitus ( 1982) 1494 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME20 Pat day 50 depth 0 P at day 60 depth 0 P at day 70 depth 0 1280 1280 1280 I' I I I , I 1024 1024 1024 I I I , , I ,,..... ~ ~ I I 768 E 768 E 768 E , , ..Y. ..Y. ..Y. , '-- '-' '-' ----- Q) Q) Q) 0 (.) (.) c c c 0 0 0 +-' +-' +-' 512 (/) 512 (/) (/) 0 0 0 ,o ,o 256 256 256 0 0 ,o ' 576 .384 192' 0 576 .384 192 0 576 384 192 0 Distance (km) Distance (km) Distance (km) P at day 80 depth 0 Pat day 90 depth 0 Pat day 100 depth 0 1280 1280 1280 I ' , I , I , I' I , I I I I :: J J f: I I I I I I I I 1024 , I I I I 1024 1024 , I I I I I , I I I , I I , , I I I I I I I I I , I ,,..... I ,--.... I ,--.... , I I , , 768 E I 768 E I 768 E ..Y. I .::£. .::£. I , '-- I I I Q) ----- I -----(!) , I (!) 0 , (.) (.) c c c 0 0 0 +-' +-' +-' 512 (/) 512 UJ 512 (/) 0 0 0 256 256 256 i-.-.--...... - ...... -+-o ~...... --....-----.-..------4-0 1--,_.,-,----,----..i..., 0 576 384 192 0 576 384 192 0 576 384 192 0 Distance (km) Distance (km) Distance (km) FIG. 4. (Continued) and vertically integrated and smoothed. Due to the waters are given an equivalent temperature that com marked contrast in salinity between the water masses pensates for variations from a mean salinity of of the Indian Ocean and the NW Shelf, the NW Shelf 35.6 ppt. SEPTEMBER 1990 MARY L. BATTEEN AND MAR TIN J. RUTHERFORD 1495 Pat day 110 depth 0 Pat day 120 depth 0 P at day 130 depth 0 1280 1280 1280 I I I I I I :2 I I 0 :2 I I I I I I I I I I I I I I , , I 1024 , 1024 , , 1024 I I I I I I I I , I I I I I I I I I I , I I I , I I I I I I I , I ,.,...... , ,-..._ , ,-..._ I , I I () I 0 I 768 E 768 E I 768 E , ...... _~ I ~ I ~ , , ,I '-' QJ I Q) Q) (.) (.) (.) c c c ...... 0 ...... 0 ..,...,0 512 (/) 512 (/) 512 (/) 0 0 0 ' 256 256 256 1--...... _-1- 0 ip..~.,....,....,...... _....,,...... ,....,..-1-, 0 1--..-..-.....,...... -1-0 576 384 192 0 576 384 192 0 576 384 192 0 Distance (km) Distance (km) Distance (km) P at day 140 depth 0 P at day 150 depth 0 P at day 160 depth 0 .-~-.~...... ~~~ ...... 1280 r-~-:-~~~~~~~~:o:r-1280 I I 0 I j I I I ,'~ I I , I I I , I I I I I I I I I I I , , I I 1024 I 1024 I I I I I , I I 1024 I I I I I , I I I I , I I I I I I I I I I I I i I -~ I ,.,...... () 768 E E' 768 ~ 768 ~ ...... _ '-' QJ Q) Cl.l (.) (.) u c c c 0 0 0 +-' +-' ..,..... 512 (/) 512 (/) 512 (/) 0 0 0 256 256 256 1--...... -,...., ...... '"""-0 ,...... ~..-~...... ""l"'" ...... '4-, 0 ,....~...... ~...... _, 0 576 384 192 0 576 384 192 0 576 384 192 0 Distance (km) Distance (km) Distance (km) FIG. 4. (Continued) The NW Shelf waters are restricted to the upper five ments, the NW Shelf waters are treated as a raft of layers only, so that the lower layers are initialized as warm water in the inshore equatorward end of the for the Indian Ocean. When included in the experi- model, in the upper 500 m and are linearly smoothed 1496 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 20 a b V at day 40 depth 350 C at day 40 --~~~~~~~~~...-...-1280 fl/\/\A AA A /\ /\/\/\ /\ A fl 1152 1\111111 A A /\ -1024 1024 896 ol I '-768 768 -512 v., 11 v-354 Vy 256 lly 256 vv vv v 128 v ,_.,....,....,....,....,....,_~,...... -1~-i--o ,_.,...... _,....,._,....,...... -.,...., ...... -+-0 576 384 192 0 576 384 192 0 Distance (km) Distance (km) contour interval = 10. V at day 80 depth 350 C at day 80 .-~~~~~~~~..... ,..,.....1280 I I I I I I I I 1152 I I I I I 1024 1024 I, ,I , , ,, 896 0 ,, I 768 768 512 512 v J, v '1'111111\/\ -384 II /\ "" J, v -256 "" v 256 J-vvv J,yy v 128 v ,...... ,,_..,...,.....,.._,....,....,.....,..-.....,....,.-+- 0 0 576 384 192 0 576 384 192 0 Distance (km) Distance (km) contour interval = 10. 100 cm/s FIG. 5. Time sequence for Case I at 40-day intervals at 350 m depth for(a) meridional velocity and (b) velocity vector fields superimposed on the temperature fields. The contour interval is 10 cm s-1 for (a), and 0.5°C for (b). SEPTEMBER 1990 MARYL. BATTEEN AND MARTIN J. RUTHERFORD 1497 a b V at day 120 depth 350 Cat day120 p=~~~~~~--,,~~....--1280 896 -768 768 y)l)I " vvv "... 640 t-vvv I Vy t-vv -512 ~A A A A vv -512 ,\AA t-t-v v Vy " t-J.-/,y vv -384 " " t-t-t-v Vy "" ,L.t-t-J.-J.-t- v 256 256 J.-t- 128 ...... , ...... ~...... _ ...... ,.+o 0 576 384 192 0 576 384 192 0 Distance (km) Distance (km) contour interval = 10. V at day 160 depth 350 c at day160 r-~~~~...,.~~~~rr-1280 1280 """ """" 1152 ,\/\A""" """" ,', -1024 1024 '• a I'• O' "E " -768 _y_ 768 E ....._,, ....._,,_y_ ([) Q) u 640 u c c 0 vv 0 +-' +-' -512 (/) vv 512 (/) 0 "!-" t-t-t-J.-y/,J,yy vv 0 ;_,t..t-t-t-J.-J.-J.- vv 384 t-t-t-;_t-J-J.- vv 1-.1-.1-.1-.1-J.. v 256 256 ,t..J-.J....1-~ J.-J.-J.- -128 ~...... -...... -.-9"""-.--JL=.=.l;F"T-'l-0 0 576 384 192 0 576 384 192 0 Distance (km) Distance (km) contour interval = 10. 100 cm/s FIG. 5. (Continued) 1498 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 20 into the surrounding Indian Ocean waters. The values speed of 20 cm s-1 is reached by day SO, and is main used to initialize the NW Shelf waters are presented in tained through day 80 (Fig. 3b). Table 2. The 10-day time sequence of the dynamic height The first of the forcing mechanisms to be investigated field (Figs. 2c and 4) for this time period shows that, is the Indian Ocean thermal gradient. In this experi as expected, by day 10 there is an increase in dynamic ment, hereafter referred to as Case 1, the model is in height near the coast, which is maintained throughout itialized with the temperature data from Table 1 and the experiment. Also at day 10, due to the strong pole allowed to run for 160 days. This time period was cho ward velocity, there is a tight dynamic height gradient sen to include both the generation of the current and at the poleward end of the domain. From days 20-70, any eddies which may form in the flow. the gradient widens with time, consistent with the In the second experiment, hereafter referred to as weakening of the poleward current. Likewise, due to Case 2, the role of the NW Shelf waters is investigated. the slowing down of the geostrophic process with time, The background Indian Ocean thermal field is retained the initially strong onshore flow is seen to dissipate to maintain the large-scale forcing as in Case 1. The westward. warmer water, as detailed in Table 2, is then added to The v and c fields for 350 m depth, corresponding the inshore, equatorward corner of the model to sim to the average core depth of the undercurrent (see Fig. ulate the influx of NW Shelf waters. The model is then 1Ob), are presented for this time period in Figs. Sa and run for 160 days. Sb, respectively. The initial thermal field is shown in Fig. 2e. By day 40 (Figs. Sa,b), the pressure gradient in the Indian Ocean due to the thermal gradient is 3. Results of the numerical experiments sufficient to establish an equatorward flow. The stron 1 gest equatorward flow ( 10 cm s- ) is in the poleward a. Case 1. Forcing by Indian Ocean density field end of the domain and is maintained throughout. 1 ) GENERATION OF THE CURRENTS AND EDDIES (ii) Eddy generation period (days 80-160) The initialized surface thermal and dynamic height fields are shown in Figs. 2a and c, respectively. A time The pressure gradient in the Indian Ocean due to sequence of the fields of surface cross-shore ( u) and the thermal gradient is sufficient to establish an unstable alongshore ( v) velocity components and of the velocity poleward flow. The u velocity fields (Fig. 3a) are gen vectors ( c) superimposed on the temperature field is erally the best indicators of eddy formation. By day shown in Fig. 3, and of the surface dynamic height (p) 80, instability has led to the generation of an eddy at field (calculated from a reference level of 2000 m) in the poleward end of the domain. The eddy growth is Fig. 4. seen at day 120 (Figs. 3a,c) and by day 160, the eddies have started to move offshore (Figs. 3a,c) advecting ( i) Pre-eddy period (days 0-80) the warm surface temperatures (Fig. 3c) with them. The 10-day time sequence of the dynamic height As expected, when the temperature decreases pole field for this time period (Fig. 4) illustrates the evo ward (Fig. 2a), the pressure gradient due to the tem lution of the eddy fields. By day 90 an anticyclonic perature gradient establishes an onshore geostrophic meander develops at the poleward end of the model inflow in the interior ocean (Figs. 3a,c). Because the domain (y ~ 1024 km) on the offshore side of the initialized alongshore temperature field is not constant, current. This anticyclonic eddy intensifies and prop agates westward with time. From days 130 to 160, other the onshore flow varies between 2 and S cm s - l . On approaching the eastern boundary, the onshore flow eddies develop equatorward of this eddy, and subse turns and forms a poleward flowing boundary current quently intensify and propagate westward with time. (Figs. 3b,c), which advects warm water from the equa The fields of velocity vectors ( c) superimposed on torial end of the domain (Fig. 3c). Because it is con the temperature fields at the surface (Fig. 3c) and at tinually augmented downstream by additional onshore 3SO m depth (Fig. Sb) illustrate that, away from the flow, the poleward current increases in magnitude to eddy generation region, the flow is predominantly par ward the pole, so that by day 10 maximum velocities allel to the isotherms, as expected. In the eddy gener ation region-i.e., in the poleward end of the domain of the order of 70 cm s -l are observed near the poleward end of the domain (Fig. 3b). As time progresses, the there is significant advection of warm water offshore onshore geostrophic flow weakens slightly in magnitude by the anticyclonic eddies. to between 2 and 3 cm s - t (Fig. 3a) so the geostrophic process slows down. The poleward boundary current (iii) Comparisons with other studies significantly weakens as time progresses so that max imum speeds decrease from SO cm s-1 at day 20 (not Overall, the magnitudes of the model poleward ( S- 1 1 1 shown) to 30 cm s- at day 40 (Fig. 3b). A minimum 40 cm s- ) and equatorward (5-10 cm s- ) currents SEPTEMBER 1990 MARYL. BATTEEN AND MARTIN J. RUTHERFORD 1499 180 160 140 120 100 \:'.' eo 60 40 20 o-i-~...... ~-.-~-.-~-.-~--~....,...~-.-~-.-~...... ~.....,..~.....,..~"""'T~"""'T~__,~__,~--1 O 10 20 30 '40 50 60 70 BO 90 100 110 120 130 1'40 150 160 Time (days) FIG. 6. Energy time series for Case I summed over all layers and over 2 2 the entire domain for total kinetic energy in units of cm s- • compare favorably with observations taken near the zontal shear zone on the offshore side of the current. poleward end of the current during the austral winter. The anticyclonic, westward-propagating eddy at the In particular, the current magnitudes are consistent poleward end of the model domain (y - 1024 km) is with the current meter data obtained at Cape Mentelle reminiscent of observations by Cresswell and Golding (34°S) in LUCIE (Boland et al. 1988), which show ( 1979) and Godfrey et al. ( 1979) of a semipermanent mean alongshore poleward velocities of28.8 cm s-1 at anticyclonic eddy located west of Cape Naturaliste 43 m depth, decreasing to 3.2 cm s-1 at 230 m depth, (33.5°S). [According to Godfrey (personal commu with evidence of an undercurrent at 320 m depth. nication, 1990), since it is primarily the anticyclonic, However, comparisons with the LUCIE current meter warm core eddies that have been observed to move observations at the equatorward end of the domain offshore, this could result in a selective way of weak show that the alongshore velocities produced by the ening both temperature and steric height gradients off model may be too weak. For example, the current me Western Australia.] ter data obtained at Camarvon (25°S) show mean The model results are also consistent with those of poleward velocities of 5. 7 cm s - l , while the model re previous modeling studies, e.g., McCreary et al. ( 1986) sults show mean velocities of 1.5 cm s _, at the same and Weaver and Middleton ( 1989). In particular, the location and depth. Since the current meter data at general structure of the Leeuwin Current is portrayed, Camarvon are located on a sloping shelf, it may well with a poleward surface current overlying an equator be that the model underestimates the alongshore ve ward undercurrent (see Fig. 1Ob). The undercurrent locities in this region, since the inclusion of a sloping rises as it flows equatorward and weakens in intensity shelf in a model can increase the magnitude of the (Fig. 5). The surface current is augmented by onshore alongshore current (Weaver and Middleton 1989). geostrophic inflow and accelerates downstream. Con However, as Case 2 will show, the NW Shelf waters sistent with Weaver and Middleton ( 1989), after the augment the poleward velocities in the equatorward surface current reaches its largest velocity, it subse end of the domain, so that a sloping shelf may not be quently broadens and drifts westward through baro required to obtain comparable alongshore velocities. clinic Rossby wave propagation. After about 80 days Consistent with the buoy observations of Cresswell the surface current at the poleward end of the domain and Golding ( 1979, 1980), eddies form in the hori- intensifies again (Fig. 3b), which, consistent with 1500 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME20 1280- 1280 1260 a b c ;'\ 1' 1152 1152- . 1152- ,·,,,:~,: ~1:.- : 0 ~: 1024 c: ~J 1024 1024- 896 696- 896- 768 76B- 768- E' E' E' c, c, c, QJ Cl> Cl> 0 640 0 640 0 640 c: c: c: 2 0 2 Ci"' i:3 Ci"' 512 "' 512 512 384 384 384 256- 256 256 128 128 128- O-i-----"'T'""~~-~~~--1 0 0 576 384 192 0 576 384 192 0 576 384 192 0 Distance (km) Distance (km) Distance (km) r-__u_a_t_da....;y_9_0_d-:ep_t_h~0~~~ 1260 d 896 FIG. 7. Energy transfers, as defined in Eqs. (8)-(10) in the Appendix, for Case I. -768 Transfers of energy from (a) P to P' (mean to eddy available potential energy), ( b) P' E' c, to K' (eddy available potential to eddy kinetic energy), and (c) Kto K' (mean to eddy Cl> kinetic energy). Transfers are averaged over days 70-90 and summed over the upper -640 0 c: five layers. Subplot ( d) is the cross-shore velocity component at day 90. The contour 2 interval is 1.6 X 10-5 erg cm-3 s-1 in (a)-(c) and 1.0 cm s-1 in (d). Solid contours i:3"' denote (a) transfer of energy from Pto P', (b) transfer of energy from P' to K' (baroclinic 512 transfer), ( c) transfer of energy from K to K' ( barotropic transfer) and ( d) onshore velocity. 384 256 128 0 576 384 192 0 Distance (km) Weaver and Middleton ( 1989), is due to a nonlinear by the initial poleward advection, generate thermal feedback mechanism which becomes important at this winds that feed back to enhance the poleward flow at time. In particular, the strong offshore fronts, caused the surface. en m [:g~ :a \0 \0 0 lOOOO>:r~~~~~~~~~~~~~~~~~~~~~~~~~~~-- 10000-.-~-r--r--r--r--r--r--r--r--r--r--r--r--r-~~-r-~~~~-r-~-r-~~~~~-r-....., a b ~ 1000 1000 > 0 0 :::ti ·-._v ·.v -<: t""' 100 100- t:l:l .T ... Q ....,> Q, ...., ',,u ... ·····- .. _O"·~·>·,,- -";,,\ t'I1 --~--- t'I1 ]:;- 10 10. ·u; '.:·-..~ -£/ z c a._, Q) £ - - {/) ·., > 0 c T . ' 0 Q) z L ···~\ 0 :.. \ ,~5! ti u '.1/ I Q) 2 ':1' 0.. u ~ VJ Q) -51,, .· ;' ·:-:,,. 0.. :_ _.:a " ,Bil > \ID VJ :::ti ·····a··"",' \ ... n, ...., ' 0.1 13:,., ···o. \:/ z- '·,._ /ff\ '-' . I ' \ l£l. I \ID '. .' '~ :'} :::ti 0.01 0.01- 0 c...., 'o.:' ·-·a :::c 0 t'I1 :::ti 'Tl o.0005 , ______0.001-J--,.--.--.-~..--r-~-r-~r-~-r-r--~r---.--...-r--..,-..-r"'---'---r-~..,..--r-~...--' 0 o.001b:;;;;ri;;;-r~~o;-~~-:;~~:::::~~~...,..~~,--,--'"-;;::-:-~~~~.--~~-0.001 op,1 0.00~ 0.001 0 p,1 :::ti Alongshore Wave Number (km - ) Alongshore Wove Number (km-) ti FIG. 8. Spectral density (cm 2 s-2 km for u, v; K 2 km for T) versus alongshore wavenumber for Case I at days 70 (a) and 100 (b). The wavenumber is an inverse wavelength. A logarithmic scale is used for the spectral density. Vt 0 1502 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME20 q 0 FIG. 9. Time series of spectral density (cm 2 s-2 km) for u of Case I from days 60-160 for the domain extending to 90 km offshore. The amplitude of the spectral energy has been plotted on a linear scale. Cross-shore distance (km) 6,0 50 •O -- 700 900 1100 l300 1500 1700 1900 2100 1: 2300 % 2500 8 oo 2700 2900 .'.3100 3300 3500 3700 3900 FIG. 10. Cross sections for Case I of the alongshore velocity and of the cross-stream derivative of potential vorticity, dq / dx, where q is the potential vorticity defined in Eq. ( 11) in the Appendix. (a) Vertical cross section of the time-averaged (days 70-90) cross-stream 1 1 8 1 1 derivative of potential vorticity, multiplied by the grid size ( °C m- s- ), and scaled by 10 • Contour interval is 0.05°C m- s- • (b) Vertical 1 cross section of the time-averaged (days 70-90) alongshore velocity component (cm s - i ) . Contour interval is 2.0 cm s - • Vertical cross sections are at I 080 km alongshore, extending to 90 km offshore. Dashed contours denote negative values. SEPTEMBER 1990 MARY L. BATTEEN AND MAR TIN J. RUTHERFORD 1503 a b c U at day 10 depth 0 V at day 10 depth 0 C at day 10 --~~~~~~~~...-...-1280 --~~~~~~~~_,,,,,~1280 --~~~~~~~..-'""'4~1280 ,111 >. >."' A>.>.+ 1------"'T + -1152 777777777777/?~~~A 777777777777/~~1~Af -1024 1024 1024 777777777777/~~A~A+ >>>> 777>777?~1~AA ~~~~~~~~~~>~77~~A~ -896 >~~~~~~~~~>>>7~t ~~ 768 768 k.=--:~'"5"5'55~7~7~7:;:;7~~>.+ -768 77>>>>>>77>777~1~A* 77777777777777~1~>.+ -640 >777777777777~11~>.~ 512 512 512 256 -256 256 128 i-.-...-...... -..-~~...... ,....,....~o 576 384 192 576 384 192 0 576 384 192 Distance (km) Distance (km) Distance (km) contour interval = 10. contour interval = 40. 300 cm/s ------+ FIG. 11. Same as Fig. 3 but for Case 2. The contour interval is IO cm s-• for (a), 40 cm s-1 for (b ), and l.5°C for ( c). 2) ANALYSES OF EDDY GENERATION MECHANISMS corresponds to the period of eddy generation, the en Because no previous studies have focussed on the ergy transfers are calculated for that period. dynamical reasons for the generation and stability of Analysis of horizontal plots of the energy transfers the eddies in and around the Leeuwin Current off can be used to find the location and magnitude of Western Australia, we will make an extensive analysis baroclinic and barotropic transfers. Figure 7 shows of the generation mechanisms in Case 1 using the en horizontal plots for (a) the transfer between mean and ergy, spectral, and stability analyses described in the eddy available potential energy, (b) baroclinic transfer, Appendix. From the energy transfer analysis, the lo and ( c) barotropic transfer for the period days 70-90. cation and magnitude of baroclinic and barotropic Also shown, in Fig. 7d, is the cross-shore velocity com transfers can be found. Those waves which are unstable ponent at day 90. The transfers are clearly strongest in and, in particular, the fastest growing wave, can be the region of the eddy development. A comparison of determined from the internal Rossby radii, and the plots 7b and 7c, which have the same contour interval, spectra can confirm whether those waves could exist. indicates that barotropic instability is more important than baroclinic instability in providing the eddy kinetic ( i) Energy analysis energy. The magnitude of the transfers was calculated for a subdomain centered on the position of the eddy The energy analysis can be used to determine the at day 90, and showed barotropic instability to be temporal mean and eddy kinetic energy and available stronger than baroclinic in the immediate vicinity of potential energy from statistics collected during periods the eddy development. of near-constant total energy. Plots of the energy trans fers during these periods give the dominant transfers (ii) Spectral analysis and the regions in which they are most active. The total kinetic energy (Fig. 6) and available potential en Figures 8a and 8b show the spectral density as a ergy (not shown) over the entire domain and for all function of alongshore wavenumber for days 70 and layers were plotted in a time series and showed that 100, respectively. A comparison of the two figures the available potential energy decreased steadily shows energy increasing at a wavelength near 150 km throughout, whereas the kinetic energy-initially large (alongshore wavenumber of -0.0065 km_,) during while the model adjusts geostrophically to the forcing this period of eddy development (i.e., days 70-100). was nearly steady from days 70 to 90. Because this Figure 9 shows the time series of spectral density from 1504 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 20 a b c U at day 40 depth 0 V at day 40 depth 0 C at day 40 .-T""'!..-..--.~~~~~~~1280 ..-~~~~~~~~--.-.-1280 .-~~~~~.,-~~"Ffl~1280 I\ 0 -1152 1024 1024 -1024 >>>>>>777~~~~~~A A! >>777?77711111~AA~ -896 >>>77>7771111_y(AAAA 768 758 >>7>>77 ~11AAAA -768 >>>>>777~~~~~~~~AA 512 512 384 256 256 •>>777771111111111 "°7777711111\ /I '!-"A 7 '!-~/\A1Af\/\AA 575 384 192 575 384 192 576 384 192 Distance (km) Distance (km) Distance (km) contour interval = 10. contour interval = 40. U at day 80 depth 0 V at day 80 depth 0 C al day 80 ..-~~~~~~~~~---1280 ..-~...... ~~~~~~-.-1280 ---~~~...... ~~~-=i ...... --1280 D 1152 0 896 640 512 384 >711111'1A /\ 7111\" '!-f\/11 <. Ar--111HA-7 L l'-...... -...... - ...... '-4- 0 575 384 192 0 576 384 192 0 576 384 192 0 Distance (km) Distance (km) Distance (km) contour interval = 10. contour interval = 40. 300 cm/s ______. FIG. 11. (Continued) SEPTEMBER 1990 MARYL. BATTEEN AND MARTIN J. RUTHERFORD 1505 a b c U at day 120 depth 0 v at day 120 depth 0 c at doy120 ---~~~~~~~~~---1280 1280 12BO VY V """""""" VY V -1152 -1024 1024 896 768 768 512 384 256 256 576 384 192 576 384 192 576 384 192 Distance (km) Distance (km) Distance (km) contour interval= 10. contour interval = 40. U at day 160 depth 0 V at day 160 depth 0 c at day160 --~~~~~~~~~----1280 r-t'~~~...... -.....,...... ,..__1280 1280 1152 1024 1024 -1024 896 ,.----._ ,,----.. ,...... , 768 E 768 E -768 E ..._,_y_ _:x ,..'1 1-1>'-! ~ ~ l;k,LJ-V7 _,,'1 ~ ~ _:x '-"' "~~~~~~_.,._,...,...,..,.4 ,,_ '-"' ()) ()) ()) u u ,..-1/\M t-""•v"""""'"'-7 t--'i-l:-/\ -640 u c c c 0 0 >7~~~7>~~~>~~~~~ 0 +-' +-' -+--' .(/) 512 Ul -512 Ul 0 0 0 -384 256 256 256 -128 vv~v.:. 1 /)>" "7 vv ~ ,, A,,. i;- ,_,...... ,....,...... '""'"'",....,_,.~...,....,_o 0 576 384 192 576 384 192 0 576 384 192 0 Distance (km) Distance (km) Distance (km) contour interval= 10. contour interval = 40. 300 cm/s ---~ FIG. 11. (Continued) 1506 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME20 a b V at day 40 depth 350 c at day 40 --~~~~~~~~--...-1280 1280 II /\/\f\fl/\/\ A/IV II If /\/\fl/I/I/I A /IV II -1152 II A y II II II II 1024 1024 II II II If 896 II cl II :: -768 768 II II II II If 11, II I -512 I I I I 1,' '1 '1 :: 256 256 '1" 1,II I I 128 I I '1 I l 1--..-...... _...... l.!.4·-0 576 384 192 0 576 384 192 Distance (km) Distance (km) contour interval= 10. V at day 80 depth 350 C at day 80 .-..~~~~~~~--...... ·-1280 512 384 256 256 4/t/\/I/\ /I /\/I l /1/1/1/\/\/1/\ -128 /\f\/\/\/\f\M'1 lt/\/\/\/1/\/\/\4 1-...... -..-.- ...... J-....- ...... -.J..114-Q 576 384 192 576 384 192 0 Distance (km) Distance (km) contour interval = 10. 150 cm/s FIG. 12. Same as Fig. 5 but for Case 2. The contour interval is lO cm s-1 for (a) and 0.5°C for (b). SEPTEMBER 1990 MARY L. BATTEEN AND MAR TIN J. RUTHERFORD 1507 a b V at day 120 depth 350 C at day 120 --~~~_.;,~~--~-..-..-1250 .-~~--.~~~--~..,.,...12so I I I I VVVy I I 1 I vvv l/ 1 • 1152 JI I'· ', ~ -1024 I II 1024 , ,' / 896 768 512 -128 J.. ,__,...._,~,...,,.J.,..-.-.--+-..~-0 575 384 192 0 576 384 192 0 Distance (km) Distance (km) contour interval== 10. V at -1152 0 024- ,,...... E ...._,,.:.:: \l) Q) \) u c: c: 1, ...... 0 .....0 - 512 VJ (/) 0 0 'I:1 1'' q 1'11 'I vvvv v ,111 1'11 'IVVVVV 'IJ.. 111 0 575 384 192 0 576 384 192 Distance (km) Distance (km) contour interval= 10. 150 cm/s FIG. 12. (Continued) 1508 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 20 days 60 to 160. Note that, because the amplitude of perimposed on the temperature ( T) field are presented the spectral energy is on a linear scale, the aspect of in Fig. 11. Figures 2b and 2d show the initialization of this type of plot makes it possible for peaks to "hide" the NW Shelf waters (at the inshore equatorward cor other features; i.e., the linear amplitude scale can sup ner), which has been added to the same alongshore press all but the dominant wavenumbers. While the temperature gradient of the Indian Ocean used in initial development is not apparent in the 160 day Case l. spectral time series for Case l (Fig. 9), the peak energy at the end of the experiment is also at a wavelength ( i) Generation of the currents near 150 km. Hence, both development and subse quent growth of eddies appear to be at the same wave As seen in the v and c fields at day l 0 (Figs. 11 b and length scale. 11 c), the inclusion of the NW Shelf waters dominates in the NW Shelf equatorial source region, as expected. (iii) Instability analysis Although the effects of the NW Shelf waters weaken Finally, the necessary and sufficient conditions for away from the source region, they are sufficient to es the sources of instability are investigated. Figure l Oa tablish a stronger poleward flow than in Case l, not shows the alongshore and time-averaged horizontal only in the poleward end of the model domain, where gradient of potential vorticity and Fig. l Ob the along velocities exceed 140 cm s - I (Fig. 11 b) but along the shore and time-averaged alongshore velocity. Both are entire coastal boundary. The advection of the warmer averaged over the model's entire meridional extent and NW Shelf waters can be seen in the T and c fields (Fig. over days 70-90. The cross-stream derivative of po 11 c) with a narrow core of warm water evident along tential vorticity changes sign at several locations and the coastal boundary. As in Case l, the poleward its product with the alongshore mean flow is positive boundary current, due to a slowdown of the geostrophic in the domain, satisfying the necessary conditions for adjustment process and to westward Rossby wave baroclinic instability. The necessary conditions for an propagation, significantly broadens and weakens as energy source for instability are satisfied by both the time progresses so that maximum speeds in the pole vertical and horizontal shears in the flow. ward end of the domain decrease from l 00 cm s - 1 at The internal Rossby radius of deformation, Rd, was day 20 (not shown) to a minimum of 40 cm s-1 at calculated for the region of initial instability as 27.6 day 40 (Fig. 11 b). This minimum is maintained until km. As baroclinic instability favors wave growth at - day 80, when the current reintensifies to values of 1 21rRd and barotropic growth at a shorter scale (Ka 80 cm s- or greater, which are maintained for the menkovich et al. 1986), the dominant wavelength scale duration of the experiment. As in Case 1, the reinten of - 150 km is consistent with the mixed instability sification is consistent with a nonlinear feedback observed in this case. mechanism that becomes important at this time, i.e., strong thermal fronts, caused by the initial poleward (iv) Conclusions advection, generate thermal winds that feed back to The poleward surface flow and equatorward under enhance the poleward flow at the surface. current driven by the Indian Ocean climatological The v and c fields for 350 m depth, corresponding temperature field are unstable and generate mesoscale to the average core depth of the undercurrent (see Fig. eddies at the poleward end of the domain. In this re 18b) are presented in Figs. 12a,b. The initialization of gion, instability is mixed, with barotropic dominant. the NW Shelf waters is seen at the inshore equatorward The primarily anticyclonic eddies form in the hori corner in Fig. 2f. The addition of the NW Shelf waters is sufficient to establish a stronger equatorward flow zontal shear zone on the offshore side of the core of 1 the current, consistent with the buoy observations of ( 10-50 cm s- ) than was observed in Case l. Cresswell and Golding ( 1979, 1980). The eddies have a dominant wavelength of around 150 km, a scale con (ii) Generation of the eddies sistent with the Rossby radius of deformation of 27 .6 km and the mixed instability mechanism. This wave The addition of the NW Shelf waters creates a far length falls within the range of the Rossby deformation more energetic and unstable current than in Case l and leads to a much earlier generation of eddies. The length scale of eddies (wavelength "A = 157 ± 25 km) noted in the strong poleward flow over the slope by NW Shelf waters locally increase the barotropic insta bility near the source region, so that by day l 0 (Fig. Andrews (1983), and is close to the 140 km length scale of eddies observed by Golding and Symonds 11 a) an eddy forms on the boundary of the NW Shelf (1978). waters. The NW Shelf waters also increase the vertical shear b. Case 2. Forcing by Indian Ocean and NW Shelf by strengthening the surface poleward flow (Fig. 11 b) and the equatorward undercurrent (Fig. 12a). As 1 ) GENERATION OF THE CURRENTS AND EDDIES shown in the analysis section below, this vertical shear The fields of surface cross-shore ( u) and alongshore adds to the baroclinicity of the currents so that eddies ( v) velocity components, and current velocity ( c) su- are subsequently generated downstream from the SEPTEMBER 1990 MARY L. BATTEEN AND MARTIN J. RUTHERFORD 1509 P at day 10 depth 0 Pat day 20 depth 0 Pat day 30 depth 0 1280 1280 1280 I , I I I I I I I I I I I 1024 1024 I 1024 I I , I I I , , I I r--... ,,-.. r--... 768 E 768 E 768 E ,._,,...:.:'. .::£. ...:.:'. '--- Q) Q) 256 256 256 1-....,.._,...... ,.....,...... ,...... ,..i...,i...,.,...._o "----..L~----"---~---1--0 ...... _...... ,.....,...... ,....,....._o 576 384 192 0 576 384 192 0 576 384 192 0 Distance (km) Distance (km) Distance (km) P at day 40 depth 0 1280 I I I I ------I 1024 768 Q) u c FIG. 13. Same as Fig. 4 but for Case 2. The contour interval is 10 cm. 0 +-' 512 en 0 256 "---...... --~..... ,..__,1,..i,.....,_.,__o 576 384 192 0 Distance (km) source region through both baroclinic and barotropic shows the generation of eddies first in the equatorward instability processes. source region, and then, as time progresses, down The generation of the eddies is illustrated by the time stream from the source region. By day 80 eddies extend evolution of the dynamic height fields (Fig. 13 ), which throughout the entire coastal domain and show growth 1510 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 20 Pat day 50 depth 0 Pat day 60 depth 0 P at day 70 depth 0 1280 1280 1280 I J I J f , I I I ' I I ' I I 1024 1024 , , 1024 I I J I J I I / ,---- ,---... I ,---... , I / , 768 E E I E ..:.:: 768 ..:.:: , 768 ..:.:: '-- '-' , I '-' Q) llJ ' llJ (.) (.) u c c c 0 0 0 -+-' -+-' -+-' 512 (/) 512 (.I) 512 (.I) 0 0 0 256 256 0 0 576 384 192 0 576 384 192 0 576 384 192 Distance (km) Distance (km) Distance (km) Pat day 80 depth 0 P at day 90 depth 0 P at day 100 depth 0 1280 1280 . 1280 I I I f I I f I I I I I I I 1024 / I 1024 1024 I / I I I I , I I I I I I I J J I ,---- J ,,--__ ~ I I I I E E 768 E I 768 768 I ..:.:: ..:.:: I ..:.:: I I I '-' I I I (l) (l) Q) ' u u u c c c 0 0 0 -+-' -+-' -+-' 512 (.I) 512 UJ 512 (/) 0 0 0 256 256 256 1-...... ,...... -_,_ 0 .....,,....,.....,.....,.....,...,._....,.._....,.....,_~o ...... "1--0 576 384 192 0 576 384 192 0 576 384 192 0 Distance (km) Distance (km) Distance (km) FIG. 13. (Continued) and movement offshore. Generation of the eddies at the same alongshore temperature gradient, which was the poleward end of the domain occurs at around the shown to be unstable toward the poleward end of the same time (days 70-90) as in Case I, as expected, since model domain, is retained in Case 2. The closed con- SEPTEMBER 1990 MARYL. BATTEEN AND MARTIN J. RUTHERFORD 1511 P at day 110 depth 0 P at day 120 depth 0 P at day 130 depth 0 1280 I 1280 I I I I I I I I , I , I I , I I I , 1024 I 1024 1024 I I I I I I I I I I I //~~>.~I I I I I I I I I I I I I I I I I I ' ,_, I I I I I I I 768 ..::£.E I 768 'E..::£. 768 - I -...__, '"- I I Q) (J) (J) u u u c c c a 0 0 _. +-' ..., 512 (/) 512 (/) 512 (/) 0 0 0 0 256 256 0 ,...... ,....,....,._.,...,...... ,....,_..,...,._~o ...... ~ ...... "t-0 ....,,...... ,....,....,...... ,...,....,r-1 ...... ""'t-O 576 384 192 0 576 384 192 0 576 384 192 0 Distance (km) Distance (km) Distance (km) P at day 140 depth 0 P at day 150 depth 0 P at day 160 depth 0 1280 I I , 1280 . 1280 I I I I I , I I I I I I I I 1024 _, I 1024 1024 I I I _, I I I I I I I I I I I I I I 768 768 I 768 I J 'E..::£. ' 'E..::£. ' ' I '"- -- - - ...,,.,... '--' Q) 'O (J) Q) u u () c c c a 0 0 +' +-' ..., 512 (/J 512 (/) 512 (/) 0 0 0 256 256 256 ..-...... _....,....,..._.,.....,...,....,._o .....,.....,....,....,.....,....,.....,.....,....,....,....,...~o ...... _....,....,..._ ...... __ o 576 384 192 0 576 384 192 0 576 384 192 0 Distance (km) Distance (km) Distance (km) FIG. 13. (Continued) tours on the temperature plot seen in Fig. 11 c from height fields, at subsequent times these rings pinch off day 80 on are associated with both cyclonic and anti the offshore meanders, trap warm NW Shelf origin wa cyclonic rings (Figs. 1 lc and 13) forming alongshore. ters, and then move offshore. The rings also show a As seen in both the surface velocity and the dynamic strong temperature structure (Fig. 11 c) as the NW Shelf 1512 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME20 1500 1400 1JOO 1200 1100 1000 900 BOO 700 ~ 600- 500 400 JOO 200 100 0 0 10 20 JO 40 50 60 70 80 90 100 110 120 130 140 150 160 Time (days) FIG. 14. Same as Fig. 6 but for Case 2. waters, advected poleward, are cut off in the rings. The kinetic energy became quasi-steady during days 30 to continued growth and offshore movement is seen at 60 before steadily growing again, days 30 to 40 were day 160. chosen for more detailed analysis. Over the same pe As in Case I, the magnitudes of the model alongshore riod, available potential energy (not shown) was quasi currents in the poleward end of the domain compare steady and then decreased. favorably with the LUCIE current meter data obtained The energy transfer plots in Fig. 15 show strong in the same vicinity, e.g., at Cape Mentelle. Unlike the transfers between the mean and eddy available poten results of Case l, the magnitudes of the alongshore tial energy (Fig. l 5a) and strong barotropic transfer currents are significantly stronger at the equatorward (Fig. l 5c), all at the equatorward end of the domain. end of the domain and along the entire coastal region. A comparison between the u velocity component fields While a comparison of the model alongshore velocities on days 30 (not shown) and 40 (Fig. 15d) shows that at the poleward and interior parts of the model domain eddy generation has occurred further poleward than with the LUCIE mean current meter data in the same shown in the transfers in Fig. 15. The transfers shown regions is favorable, the model alongshore velocities at in Fig. 15 are much stronger than those leading to eddy the equatorward end of the domain may be too strong. development farther downstream so that the down For example, the LUCIE data at 65 m depth at Car stream transfers fail to show at the contour interval narvon (25°S) show a mean poleward velocity of 5.7 used. cm s-1 compared to the mean poleward model velocity Energy transfer diagrams (not shown) calculated of 13 cm s - l . Some other factors not considered here, over the upper five layers, and extending between 520 such as wind forcing, which would generally act in the and 700 km alongshore (corresponding to the region opposite direction to the Leeuwin Current, could lead of eddy generation shown at day 40 in Fig. 11 a) showed to lower current velocities, which would be more con that for the inshore 45 km, there was baroclinic insta sistent with the current meter observations. The ad bility and a negative barotropic transfer, while over the ditional factor of wind forcing will be considered in a region extending from 45 km to 90 km offshore, the subsequent study by Batteen and Rutherford ( 1990). baroclinic contribution was weaker and barotropic in stability was apparent. 2) ANALYSES OF EDDY GENERATION MECHANISMS ( i) Energy analysis (ii) Spectral analysis Because time series of total kinetic (Fig. 14) and The spectral energy plots at days 30 and 50 are shown available potential energy (not shown) showed that the in Figs. l 6a and l 6b. The strong growth from days 30 SEPTEMBER 1990 MARY L. BATTEEN AND MARTIN J. RUTHERFORD 1513 1280- 1280 1280 a b c 1152 1152 1152 1024 1024 1024- 896 896 896 768- 768 768 'E 'E 'E c. 6 6 Q) Q) Q) u 640 u 640 u 640 c: c: c: .3 .3 0 VI VI ti Ci Ci Ci 512 512 512 , '· 384 o_,;·: 384 384- o,::.@\; ~:t' ·' ' • (> '.' 6 256 o;\• 256 256 ,, : 1 :;.,o:.. ,,,_ a:· ('\:,l l\1''. ' 128- 128 128- •'·;.;:' ' ":~ n~ ' ,..:',," O· 0 O· 576 384 192 0 576 384 192 0 576 384 192 Distance (km) Distance (km) Distance (km) ·1152 766 'E c. FIG. 15. Same as Fig. 7 but for Case 2. Transfers of energy are averaged over days Q) u c: 30-40 and summed over the upper five layers. Subplot ( d) is the cross-shore velocity 2 component at day 40. The contour interval is 4.0 X 10-3 ergs cm-3 s-• in (a)-(c), VI 0 and 5.0 cm s-• in (d). 256 128 576 384 192 Distance (km) to 50 is seen in the peak developing at a 180 km wave (alongshore wavenumber of -0.015 km -i) scales. length (alongshore wavenumber of -0.0055 km -i ). Whereas Case l had a single peak and barotropic At day 50 smaller peaks are also apparent at l 00 km growth was dominant, Case 2 has multiple spectral (alongshore wavenumber of -0.0 l km -I) and 65 km peaks during the eddy generation stage and strong ...... Vl...... """ 100001r;:;-~~~~~~~~~~~~~~~~~~~~~~~~~- 10000..---...... ,.....,.....,.....,.....,.....,.....,.....,.....,.....,.....,.....,.....,.....,.....,.....,.....,.....,.....,.....,.....,.....,.....,.....,.....,.....,.....,.~ a b o ..v 0 . v. •...... ··.. .;·>8'·"·, \ ·.. :, •\ ···-...... //' :_1 1000 1000- · .. I ·., ...... ·············o. ·.,·, u ·., 0 G---- ·.. \ ,"' c:: G-.!J_ _EJ---·~·~', • \ I I ',\' ';I::! ·.'' ·o z 100 100 o·. , ·· .. '_,EJ'·-,, T · ... Q ., > J . ' t""' ·b. "h\/ 'tJ q . ' 0 ·. ', ', fJ. 'Tl 10 10 ]':;- ·o ' ... , ]':;- ·o. \jl "I) "iii . @, "iii ::i= c c Q) Q) - Q_ Q_ t""' (/) (/) Q 0 b (') . '6 tT1 0.1 0.1 0 >z 0 0 ';I::! 0.01 0.01 > "I) ::i= - o.001..._...,...._,....,...... ,.....,...... ,...... ,...... ,...... ,...... -...,....__,...,....__,...,...... ,...... ,....__,...,....._,....,...... ,...... ,...... ,...... ,....~...,...... ,.....----1 o.001+-...... ,.....,....,._,.....,...... ,...... ,...... ,...... ,....,...... ,...._,....,....__,,..-...,...... ,..-.,...... ,...... ,....,....,...... ,...... ,...... ,....__,,..-...,...... ,.....--- o~o~ 0.001 o.p,1 0~0~ 0.001 op,1 Alongshore Wave Number (km - ) Alongshore Wave Number (km - ) FIG. 16. Same as Fig. 8 but for Case 2 at days 30 (a) and 50 (b). t!::~ tTl ~ SEPTEMBER 1990 MARY L. BATTEEN AND MAR TIN J. RUTHERFORD 1515 FIG. 17. Time series of spectral density (cm 2 s-2 km) for u of Case 2 from day 0 to 160 (a) over the entire domain; ( b) for the domain extending to 90 km offshore; and ( c) over the offshore region not covered in (b). The amplitude of the spectral energy has been plotted on a linear scale. baroclinicity is also a feature. It appears that when appears to broaden with time and a shift to larger scales baroclinicity is strong, growth at multiple wavelengths is seen. To isolate the scales of generation and growth, occurs, possibly coinciding with other internal modes. a second spectral analysis was done over the inshore The spectral density for the entire 160 days of Case 90 km of the model, coinciding with the generation 2 is shown in Fig. 17a. The dominant scale of 180 km region. The spectral time series for the inshore region, 1516 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME20 Cross-shore distance (km) 6_Q 5,0 •O 80 ',0 60 50 40 30 20 10 ~~~~~~100 E JOO 500 700 900 1100 1300 ------.-i-1soo 1700 1900 ,.--..., 2100 g_ 2300 :§_ 2500 ~ 2700 2900 3100 3300 3500 3700 3900 4100 4300 ....L4500 0 ""b ___,______ FIG. 18. Same as Fig. 10 but for Case 2. Time averaging is now over days 30-40, and the vertical cross sections are at 600 km alongshore, 1 1 1 extending to 90 km offshore. Contour intervals are (a) 0.1°C m- s- and (b) 5.0 cm s- • corresponding to the current, is shown in Fig. l 7b and occurred to the radius of deformation despite the in for the remainder of the domain in Fig. 17 c. Inshore, clusion of the NW Shelf waters. the wavelength of the dominant growth in the vicinity of the current is near 180 km (alongshore wavenumber (iv) Conclusions of -0.0055 km -l) and a secondary maximum occurs 1 at 125 km (alongshore wavenumber of -0.008 km - ). The current, driven by a combination of Indian Away from the core, Fig. 17c shows that the 180 km Ocean and NW Shelf thermal forcing, is much more wavelength is dominant and that a shift to longer vigorous and unstable than Case 1, forced by the Indian wavelengths occurs with time. Ocean alone. Barotropic instability is strong at the Comparing the results of the spectral analysis from equatorward end, near the source of the NW Shelf wa Cases l and 2, the effects of the addition of NW Shelf ters. The addition of the NW Shelf waters adds strongly waters may be determined. In the mainly barotropic to the baroclinicity of the current inshore, although the Case l, eddy generation and subsequent growth was at Rossby radius remains virtually unchanged. The baro a wavelength of approximately 150 km. With the in tropic contribution at the offshore edge of the core of clusion of the NW Shelf waters, and its strong baroclinic the current is also slightly increased by the presence of contribution toward instability, the main growth occurs the NW Shelf waters. The dominant scale of eddy gen at 180 km. The NW Shelf waters appear to increase eration in the current is 180 km. This is consistent with the scale at which the dominant eddy growth occurs the calculated Rossby radius of-28 km in the strongly by modifying the thermal structure in the inshore re baroclinic flow. This wavelength is, like Case l, con gion. sistent with the Rossby deformation length scale of ed dies found in the strong poleward flow over the slope (iii) Instability analysis by Golding and Symonds ( 1978) and Andrews ( 1983). Away from the current, a spectral shift towards longer Figure 18 is used to confirm that the necessary and wavelengths is seen, consistent with the growth of ed sufficient conditions for the observed eddy generation dies as they move offshore. are satisfied. In particular, the cross-shore derivative of potential vorticity (Fig. l 8a) changes sign inshore, and 4. Conclusions its product with the mean alongshore flow (Fig. l 8b) is clearly positive at some location in the domain, which A full primitive equation (PE) model was initialized satisfies the necessary conditions for baroclinic insta with climatological data to investigate the generation bility. The necessary conditions for an energy source and stability of the Leeuwin Current and its associated for the eddy generation are satisfied by both the vertical eddies. Initializations were done using climatological and horizontal shears in the flow. mean temperatures for the Indian Ocean and NW The Rossby radius of deformation was calculated Shelf. The ocean was then allowed to geostrophically for the region of instability as 27.9 km. Comparing this adjust in the absence of external forcing. The currents value with that of Case 1 (27.6 km), little change has generated by the model were unstable in both experi- SEPTEMBER 1990 MARYL. BATTEEN AND MARTIN J. RUTHERFORD 1517 ments and mesoscale features were observed. To ex ticyclonic, westward propagating eddy at the poleward amine the dynamical reasons for the generation and end of the model domain (y ~ l 024 km) is reminiscent stability of the eddies, a series of analysis techniques of observations by Cresswell and Golding ( 1979) and were applied to each experiment and the instability Godfrey et al. ( 1979) of a semipermanent anticyclonic mechanisms and dominant length scales determined. eddy located west of Cape Naturaliste (33.5°S). A comparison with available observations was also The addition of the NW Shelf waters (Case 2) creates made. A summary of the results from each of the two a far more energetic and unstable current. The NW phases of this study, generation and instability, is pre Shelf waters increase the vertical shear by strengthening sented below. the surface flow and the undercurrent and hence add to the baroclinicity of the current. The NW Shelf waters a. Leeuwin Current generation also locally increase the barotropic instability near the source region. The dominant wavelength associated The results of Case 1 showed that the Indian Ocean with eddies developing in the current forced by the temperature structure is sufficient to drive an unstable Indian Ocean and NW Shelf water density fields is 180 poleward surface flow (the Leeuwin Current) and an km. The NW Shelf waters appear to increase the scale equatorward undercurrent. The undercurrent rises as at which the dominant eddy growth occurs by modi it flows equatorward and weakens in intensity. The fying the thermal structure in the inshore region. The surface current is augmented by onshore geostrophic eddies have time scales of months, consistent with buoy inflow and accelerates downstream. observations (e.g., Cresswell and Golding 1979). Both The results of Case 2 showed that the inclusion of cyclonic and anticyclonic eddies are observed, consis the NW Shelf waters completely dominates in the NW tent with observations (e.g., Hamon 1965, 1972). Shelf equatorial source region. The effects of the NW In both cases, the dominant length scales of eddies Shelf waters weaken away from the source region but are close to the wavelength associated with a low-mode they continue to augment the Indian Ocean forcing, Rossby radius of deformation, consistent with obser resulting in a stronger flow along the entire coastal vations (e.g., Golding and Symonds 1978; Andrews boundary. 1983; Griffiths and Pearce 1985) and laboratory studies The results of both cases showed that, consistent with (Condie and Ivey 1988) of the Leeuwin Current. Weaver and Middleton ( 1989 ), after the surface cur This study has shown that the Leeuwin Current can rent reaches its largest velocity, it subsequently broad be successfully modeled using a PE model forced by ens and drifts westward through baroclinic Rossby the mean climatology. Consistent with the findings of wave propagation. After about 80 days the surface cur Weaver and Middleton ( 1989), a shelf is not required rent at the poleward end of the domain intensifies to produce and maintain the current. The mesoscale again, which, consistent with Weaver and Middleton features that have been missing from previous modeling ( 1989), is due to a feedback mechanism that becomes studies are produced by the model and at scales com important at this time. In particular, the strong offshore parable with available observations. fronts, caused by the initial poleward advection, gen erate thermal winds that feed back to enhance the Acknowledgments. This work was supported by the poleward flow at the surface. These strong current National Science Foundation under Grant OCE magnitudes are maintained throughout the duration 8809465 and by direct funding at the Naval Postgrad of the experiments (i.e., days 80-160). uate School (NPS) with the Office of Naval Research The currents generated by the model agree well with as the sponsor. Computer resources were provided by the Leeuwin Current Interdisciplinary Experiment the W.R. Church Computer Center at NPS. The au (LUCIE) current meter observations obtained during thors wish to thank Tim Stanton for his assistance with the austral fall and winter when the Leeuwin Current the spectral analysis techniques used in the study, and is observed, and other recent modeling studies. Craig S. Nelson, Andrew J. Weaver, and J. Stuart God frey for comments on an earlier version of the manu b. Instability and eddies script. MLB also wishes to thank Jorg Imberger for his generous hospitality at the Centre for Water Research The current driven by the Indian Ocean temperature at the University of Western Australia, where MLB gradient (Case l) is unstable at the poleward end of conducted preliminary research on the Leeuwin Cur the domain. In this region, instability is mixed, with rent in the austral summer of 1988. barotropic instability dominant. Eddy generation oc curs on the offshore side of the core of the current, consistent with the buoy observations of Cresswell and APPENDIX Golding ( 1979, 1980). The eddies have time scales of Analysis Techniques months, and wavelengths of -150 km, a scale consis tent with the Ross by radius of deformation of 27 .6 km A description of the energy, spectral and stability and the mixed instability mechanism. The dominant techniques used to analyze the generation and stability type of rotation for the eddies is anticyclonic. The an- of the Leeuwin Current and eddies is presented here. 1518 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 20 1. Energy analysis advection terms, these were recalculated in the same manner as in the model but using the stored values of An energy analysis based on that of Han ( 197 5) and u, v and T as the input data. Although the energy Semtner and Mintz ( 1977) is made to gain a better transfers are recalculated from model output, they are understanding of the energy transfers in the unstable consistent with the initial calculations of vertical ve flow. The energy calculations are presented using the locity and advection terms in the model. Semtner and Mintz ( 1977) notation: Using the energy transfers calculated above and the () time average temporal mean and eddy kinetic and available potential ( )' time deviation energy values, an energy transfer diagram may be con () horizontal space average structed for those periods in which the total energies ( )* horizontal space deviation. are nearly constant. Semtner and Mintz ( 1977) applied their energy transfer analysis to currents that had be The kinetic energy ( K) is calculated by come unstable, generated eddies and then reached a u2 + v2 quasi-steady state. In this study, the steady energetic K= 2 (1) state prior to eddy generation is examined and the en ergy transfer plots and diagrams used to argue for the and presented in a time series plot. After reaching a instability mechanism that leads to the initial eddy quasi-steady state in which the total kinetic energy is generation in each case. nearly constant, the time mean and time eddy kinetic energy are calculated by 2. Spectral analysis - u2 + v2 A spectral analysis technique is used to estimate the K=--- (2) dominant wavelengths at which eddy growth occurs. 2 The time evolution of the eddy fields can be seen on u'2 + l)'2 three-dimensional time series plots of spectral density K'=--- (3) 2 versus alongshore wavenumber. The alongshore wave number is selected based on an assumption of a me Available potential energy (P) is calculated by ridional anisotropic preference for the eddy develop 1 ment. The model configuration of 65 alongshore tem l ] perature gridpoints and 64 velocity points is ideal in p = ag [ 2 (T*)2 (af)-az (4) allowing data over the entire domain to be used to and plotted in a time series to determine when a quasi compute the discrete Fourier transform based on 64 steady state is reached and statistics can be collected. points. Leakage due to the finite length of the series is The temporal mean and eddy available potential energy reduced using a Hanning window. The loss of variance are then calculated by due to the windowing is then compensated by scaling 1 the calculated one-sided spectral density appropriately. P= ag[i(T*) 2 (:~r J (5) 3. Stability analysis 2 1 The stability analysis used in this study is based on P' =ag[i(T'*) (:~r J. (6) Batteen et al. ( 1989 ), who investigated the dynamics of the eddy generation observed in the PE model. The The transfers between the energy types are defined, potential for instability is determined by examining after Semtner and Mintz ( 1977), by the potential vorticity ( q) of the flow and also its cross {k- P} = -ag[TwJ (7) shore derivative (aq; ax). The potential vorticity is cal culated by { P' - K'} = ag[ T'w'J (8) aT aTav q-u+n---- (l l) {K--K'} = v· (V ·v'v'- + aza-) w'v' (9) az ax az where 1 av au {P-P'} =ag[T*V·v'T'*(:~r J. (10) r =ax - ay. (12) The model output consists of velocity components and For a flow that has a basic state changing slowly in temperature at daily intervals at each gridpoint; neither space and time, Kamenkovich et al. ( 1986) give the the vertical velocity nor any advection terms calculated necessary conditions for baroclinic instability as: aq / by the model are stored. As the calculation of the energy ax changes sign, and vaq I ax must be positive some transfers requires both vertical velocity and numerous where in the flow. They also give sufficient conditions SEPTEMBER 1990 MARYL. BATTEEN AND MARTIN J. RUTHERFORD 1519 for the instability mechanisms. For baroclinic insta CSIRO Australia Division of Fisheries and Oceanography Rep. bility, the source of energy is the vertical shear in the IOI. --, and --, 1980: Observations of a south-flowing current in mean flow (av/ az) and the scale of the generated dis the southeastern Indian Ocean. Deep-Sea Res., 27A, 449-466. turbances is of the order of the Rossby radius of de Dakin, W. J., 1919: The Percy Sladen Trust Expeditions to the formation. For barotropic instability, the energy source Abrolhos Islands (Indian Ocean). Rep. I. J. Linnean Soc., 34, is the horizontal shear in the mean flow (av/ ax) and 127-180. Gentilli, J., 1972: Thermal anomalies in the Eastern Indian Ocean. the disturbances grow at a scale less than the Rossby Nature (London) Phys. Sci., 238, 93-95. radius. Godfrey, J. S., and K. R. 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