Modeling the East Australian Current in the Western Tasman Sea

Home , East Australian Current, Tasman Front

2956 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30

PATRICK MARCHESIELLO* AND JASON H. MIDDLETON School of Mathematics, University of New South Wales, Sydney, Australia

(Manuscript received 21 January 1998, in ®nal form 1 February 2000)

ABSTRACT The East Australian Current (EAC) is a western boundary current ¯owing southward off the east coast of Australia. Its eddy variability has been shown to be vigorous, a typical feature being the formation of a large warm core eddy in the western Tasman Sea. The dynamics controlling the development of such an eddy are the subject of this paper. The Princeton Ocean Model was tuned for conditions that prevail in the western Tasman Sea, and initialized with features based on the Royal Australian Navy weekly temperature charts. A 70-day simulation initialized with summer conditions captures the formation of a large warm core eddy that matches fairly well the observations. Analyses of the results demonstrate that the formation of these eddies is associated with a wide range of dynamical aspects observed in the region, such as oscillation and propagation of the Tasman Front, EAC separation from the coast, formation of cold-core frontal eddies, and nutrient enrichment of coastal waters.

1. Introduction man Sea and the EAC as a basin edge system for climate dynamics studies. Modeling of western boundary currents such as the Our present knowledge of the EAC system is mainly East Australian Current (EAC), the Gulf Stream, the based on the compilation of many datasets. Little has Kuroshio, and the Brazil Current is a major challenge been produced from numerical models, and there is ob- of physical oceanography. The dynamics of these ¯ows viously a need for comprehensive studies of the pro- are essentially nonlinear and unstable, and they gener- cesses. In this paper, we describe a numerical investi- ally dominate the oceanographic conditions along their gation of the EAC dynamics using the Princeton Ocean paths. The EAC in particular is driven by the input of Model (POM) developed by Blumberg and Mellor the South Equatorial Current into the Coral Sea. As it (1987). Recent studies of the Gulf Stream (Mellor and ¯ows southward along the New South Wales (NSW) Ezer 1991) have shown the practical capability of the north coast, the EAC narrows to a strong shallow surface POM to simulate such complex ¯ows. A major problem current, impinging strongly but relatively steadily on area remains the initialization of such models. We pre- the continental shelf and slope. Farther south, at around sent here a ``feature model'' developed for the EAC 33ЊS, the EAC often separates from the coast, deepening and ¯owing eastward into the Tasman Sea. At times, model, based on weekly temperature charts provided by the EAC convolutes itself to form large anticyclonic the Royal Australian Navy (RAN). Another challenge eddies. The primary objective of this paper is to further when con®guring a regional model is dealing with open elucidate the dynamics of the EAC and its interaction boundary conditions. We have applied successfully ra- with the continental shelf of the western Tasman Sea. diative boundary conditions developed in Barnier et al. The motivation is a need for an understanding of the (1998). Preliminary results of the con®guration of the physical processes that govern the cross-shelf exchanges POM for the EAC, and a comparison of model predic- of organic or inorganic materials, the circulation pat- tions with RAN charts of the same period show overall terns and thermodynamical balance of the western Tas- abilities for modeling and forecasting over a period of a few weeks (Gibbs et al. 1998). This paper presents longer simulations that capture the observed EAC variability in the western Tasman Sea, including the major * Current af®liation: IGPP, University of California, Los Angeles, feature that is the formation of a large anticyclonic Los Angeles, California. warm-core eddy. These simulations allow analyses of the physical processes involved. We present in section 2 an overview of the oceano- Corresponding author address: Dr. Patrick Marchesiello, IGPP, UCLA, 405 Hilgard Avenue, Los Angeles, CA 90095-1567. graphic conditions of the western Tasman Sea, and out- E-mail: [email protected] line the thermodynamical and dynamical characteristics

᭧ 2000 American Meteorological Society

Unauthenticated | Downloaded 09/28/21 03:07 AM UTC NOVEMBER 2000 MARCHESIELLO AND MIDDLETON 2957

FIG. 1. Schematic diagram of currents around Australia (after Church and Craig 1998). to be studied. The East Australian Current model is ment and the Tropical Ocean±Global Atmosphere Ex- described in section 3. Section 4 presents a warm-core periment are focused on basin-scale dynamics relevant eddy formation as simulated by the model. We analyze to climate variability. Synoptic mappings of the tridi- the mechanisms and compare with other studies and mensional hydrographic and dynamic structure of the observations in section 5. Section 6 is devoted to dis- western Tasman Sea are still needed, and we can expect cussion of the results. large improvements in this respect from numerical models. Figure 1 depicts the location of the EAC in relation 2. Oceanographic conditions to the large-scale circulation. The current extends south- The EAC is a major oceanographic feature of the ward from about 18ЊS at its northern extreme sometimes Tasman Sea. Since the eastern Australian shelf is nar- as far as 42ЊS near Bass Strait at its southern extreme. row, the current can be a dominant factor determining South of the Great Barrier Reef (25ЊS) the shelf is much the shelf and slope circulations. Previously, the EAC narrower and the EAC is stronger (having its maximum has been observed to display signi®cant temporal and between 25Њ and 30ЊS). As a result, the current has a spatial variability. Nilsson and Cresswell (1981) have signi®cant impact on the conditions on the shelf. It fre- presented a synoptic description of its variability, while quently crosses onto the continental shelf and moves Bennett (1983) has compiled a summary of EAC dy- close inshore, causing noticeable wakes behind head- namics, including a discussion of separation, instabili- lands (Cresswell et al. 1983). As the current moves ties, and eddy formation. More recently an overview southward, following along the shelf topography it may has been given by Church and Craig (1998). However, diverge or separate and move out to sea (Fig. 2). Cape apart from the Australia Coastal Experiment (Huyer Byron (28.43ЊS, 153.34ЊE), Smoky Cape (30.55ЊS, 1988; Louis 1989), there have been few comprehensive 153.05ЊE), and Sugarloaf Point (32.25ЊS, 152.30ЊE) are studies of the EAC dynamics. Our knowledge is mainly places generally noted for this occurrence. Sugarloaf derived from the compilation of many individual da- Point appears as a major separation point (Godfrey et tasets. It is also derived from satellite observation: sea al. 1980). Some of the separating ¯ow returns to the surface temperature (Cresswell et al. 1983) or altimetry north and some can be tracked as the Tasman Front (Wilkin and Morrow 1994), but this concerns only the across the Tasman Sea and around the northern tip of surface and is limited by cloud cover. Recent obser- New Zealand. The zonal current associated with the vations linked to the World Ocean Circulation Experi- Tasman Front is seen as the ``bridge'' linking the west-

Unauthenticated | Downloaded 09/28/21 03:07 AM UTC 2958 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30

the Tasman Sea. Characteristic values for the salinity of Coral Sea water are found to be 35.4±35.6 psu in the 20Њ±26ЊC temperature band. Over the central Tasman Sea a core of high salinity water (Ͼ35.7) is found to extend from 160ЊE, but along the coast of Autralia, Tas- man Sea salinity drops due to advection of tropical waters. In the western Tasman Sea, the vertical structure is composed of three main water masses. The water in the upper 1000 m consists of various central, equatorial, or subtropical water masses. Antarctic Intermediate Wa- ter is below, characterized by a salinity minimum of 34.4 psu and 5.5ЊC. Deep water has a salinity maximum of 34.7 psu and 2ЊC. The Tasman Sea is bound at its southern limit by the subtropical convergence zone located near 42ЊS. The EAC is present at all times of the year, but there is a marked seasonal cycle, with strongest ¯ow between December and April, the austral summer (Ridgway and Godfrey 1997). In the western Tasman Sea, the EAC is a narrow (40±50 km), shallow (300±500 m), and strong (1±2 m sϪ1) surface current, decreasing to approximately half this magnitude at 250 m. Below this depth, the EAC decreases more gradually and there is evidence from density structure that the EAC extends down to at least 2000-m depth. Along the sea¯oor beneath the EAC a compensating northward ¯owing current has been observed. The mean EAC volume transport has been estimated at 27 Sv (Sv ϵ 106 m3 sϪ1) by Ridgway and Godfrey (1994). FIG. 2. Grayscale image of sea surface temperature in the western Tasman Sea. The EAC clearly separates around Sugarloaf Point and Meanders and instabilities may develop along the presents energetic turbulence at different scales. coast of New South Wales. A U-shaped meander is formed between 152Њ and 158ЊE and may extend as far south as 35ЊS. At its southernmost tip the meander may ern boundary currents of Australia and New Zealand, become unstable. As instabilities in the current develop, which would explain its location. The process actually the meander pinches off to form eddies at a rate of once involves westward propagation of Rossby waves (God- or twice per year. The pinch-off process is controlled frey et al. 1980). by westward propagation of the Tasman Front according The Tasman Front forms the interface between the to Nilsson and Cresswell (1981); see Fig. 3. Large warm waters of the Coral Sea and the cooler waters of warm-core anticyclonic eddies of Coral Sea water are

FIG. 3. An illustration of how the westward propagation of the Tasman Front might control the ¯ow of the EAC and cause warm-core eddies to pinch off (after Nilsson and Cresswell 1981).

Unauthenticated | Downloaded 09/28/21 03:07 AM UTC NOVEMBER 2000 MARCHESIELLO AND MIDDLETON 2959

typically formed, and south of approximately 33ЊS they EAC and its eddies. Data analyses (Gibbs et al. 1997) are the dominant feature of the EAC system. On oc- and numerical studies (Marchesiello et al. 2000) using casion however contrasting cold-core cyclonic eddies a two-dimensional (vertical cross section) version of are also observed. The warm core eddies range in size POM have con®rmed the primary role of local wind from 150 to 250 km in diameter. They seem to maintain stress in near-shore upwelling processes. Even when the their water mass identities for many months. These ed- EAC is responsible for uplifting nutrient-rich water onto dies have a well-mixed layer, sometimes down to a depth the shelf, upwelling favorable winds seem to be re- of 400 m, and may affect the thermal structure down sponsible for bringing this water to the surface. These to 1300-m depth. Mainly the eddies meander along com- studies have shown that a bottom Ekman layer driven plex paths and propagate southwestward as a distinct by the EAC is unlikely to upwell cold plumes, as sug- single oceanographic feature, but alternatively may be gested by Blackburn and Cresswell (1993). Another nu- reabsorbed into the general Tasman Sea circulation. merical study (Gibbs et al. 1998) using preliminary re- Within the warm core eddies temperatures in excess of sults of the model presented in this paper, reveals a 25ЊC have been observed at the sea surface during sum- plausible mechanism for nutrient enrichment on the mer. During the winter months the eddies can bring NSW shelf involving small cold-core frontal eddies gen- unseasonable ®shing conditions due to the entrapment erated by the EAC. The present paper will discuss this of Coral Sea marine life. The warm water creatures are point further in the general context of EAC physical frequently caught in a layer of warm Coral Sea water processes. overlying the southwestern Tasman Sea water. As the eddies migrate on and off shore, their deep features 3. The model interact with the continental shelf and induce complex surface currents near to the coast. Louis (1989) observes The numerical simulations were performed using the the interaction between the EAC and the continental Princeton Ocean Model, a three-dimensional fully non- shelf of NSW, and reveals the presence of short coastal- linear primitive equation model (Blumberg and Mellor trapped waves generated by these interactions. Accord- 1987). The model incorporates a free surface and a ter- ing to Louis, the scales of these oscillations are also rain-following coordinate ␴ in the vertical direction. As such that ampli®cation resulting from topographic in- opposed to the geopotential coordinate, the ␴ coordinate stability in the wave ®eld is also possible. is thought to better capture interactions between bottom The shoreward migration of the EAC and its eddies topography and ocean dynamics (Marchesiello et al. seems to be correlated with occasional upwelling, which 1998). Vertical diffusivities and viscosities are derived entrains water from the bottom of the continental shelf from the Mellor±Yamada turbulent closure submodel, drawing it upward toward the shore. This puts the water which yields realistic surface and bottom Ekman layers. that is usually found at the shelf break close to the coast, Horizontal diffusivities and viscosities are parameter- attracting winter ®sh such as barracuda, trevally, and ized by the Smagorinsky relation to horizontal resolu- pilchard. Nutrient-rich subsurface water may also sup- tion and dynamics. The POM has been succesfully used ply the formation of large plankton blooms in bay areas for similar coastal and regional modeling applications like Jervis Bay or Port Stephens. The mechanism re- (Mellor and Ezer 1991; Miller and Lee 1995) and hence sponsible for upwelling of subsurface water is unclear. was appropiate for this application. Part of the major upwelling events is correlated with The model is based on the hydrostatic primitive equa- local wind stress, the remaining is correlated with the tions in ␴ coordinates:

␦␩ ␦(uD) ␦(␷D) ␦␻ ϩϩϩϭ0 (1) ␦t ␦x ␦y ␦␴

␦(uD) ␦(uD2 ) ␦(u␷D) ␦(u␻) ␦␩ gD2 0 ␦␳Ј ␴Ј ␦D ␦␳Ј ␦ K ␦u ϩϩϩϪf␷D ϭϪgD ϪϪd␴Јϩ M ␦t ␦x ␦y ␦␴ ␦x ␳␦0 ͵ xD␦x ␦␴Ј ␦␴ D ␦␴ ␴ ΂΃΂΃

␦␦u ␦␦u ␦␦␷ ϩ 2AD ϩ AD ϩ AD (2) ␦x MMM΂΃␦x ␦y ΂΃␦y ␦y ΂΃␦x ␦(␷D) ␦(u␷D) ␦(␷ 22D) ␦(␷␻) ␦␩ gD 0 ␦␳Ј ␴Ј ␦D ␦␳Ј ␦ K ␦␷ ϩϩϩϪfuD ϭϪgD ϪϪd␴Јϩ M ␦t ␦x ␦y ␦␴ ␦y ␳␦0 ͵ yD␦y ␦␴Ј ␦␴ D ␦␴ ␴ ΂΃΂΃

␦␦␷␦␦u ␦␦␷ ϩ 2AD ϩ AD ϩ AD (3) ␦y MMM΂΃␦y ␦x ΂΃␦y ␦x ΂΃␦x

Unauthenticated | Downloaded 09/28/21 03:07 AM UTC 2960 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30

␦(TD) ␦(TuD) ␦(T␷D) ␦(T␻) ␦ K ␦T ␦␦T ␦␦T ϩϩϩϭH ϩAD ϩ AD (4) ␦t ␦x ␦y ␦␴ ␦␴΂D ␦␴ ΃ ␦x HH ΂΃␦x ␦y ΂΃␦y ␦(SD) ␦(SuD) ␦(S␷D) ␦(S␻) ␦ K ␦S ␦␦S ␦␦S ϩϩϩϭH ϩAD ϩ AD , (5) ␦t ␦x ␦y ␦␴ ␦␴΂D ␦␴ ΃ ␦x HH ΂΃␦x ␦y ΂΃␦y

and the UNESCO equation of state ␳ ϭ ␳(T, S, P)to ing strati®cation'' experiments (Barnier et al. 1998) in close the system. which the model is integrated with no forcing applied. Here t is the time, ␴ is the vertical coordinate [␴ ϭ The velocities produced in this experiment result from (z Ϫ ␩)/D, z Cartesian coordinate], (x, y) the horizontal pressure gradient errors. The topography is then Cartesian coordinates, ␩ the free-surface elevation, smoothed so that the error is not signi®cant compared (u, ␷) the horizontal velocity components in the (x, y) to the magnitude of currents to be simulated. Model grid directions, ␻ a velocity component normal to ␴ surfaces, and bathymetry are plotted in Fig. 4. D is the water depth, T is the potential temperature, S The initial temperature ®eld is constructed from the the salinity, ␳ the in situ density, ␳Ј the density pertur- sea surface temperature and the temperature at a depth bation [␳Јϭ␳ Ϫ ␳(z), ␳(z) is a reference vertical pro®le of 250 m (T250), which are obtained from the RAN of density extracted to ␳ in order to limit numerical weekly temperature charts. These data come from a wide range of sources including infrared satellite imagery, errors induced by the pressure gradient term], ␳ 0 is a constant reference density, f the Coriolis parameter, g satellite tracked buoys, expendable bathythermographs (XBT, AXBT), and general shipping SST observations. the acceleration of gravity, AM and AH horizontal eddy viscosity and eddy diffusivity given by the Smagorinsky They are plotted onto the weekly analysis charts using an optimal interpolation scheme. The model domain is (1963) scheme, KM and KH vertical eddy viscosity and eddy diffusivity given by the Mellor and Yamada (1982) slightly larger than the domain used by RAN, and level 2.5 turbulent closure scheme. NOAA-11 satellite-derived SST images are used here to Further details describing the core of the model are extrapolate the temperature ®eld over the whole domain. not included here since they are well documented else- Feature models provide a means to supplement the where (Blumberg and Mellor 1987). The numerical limited in situ observations with a knowledge of the techniques may be summarized as follows. A ®nite- typical structure of mesoscale ocean fronts and eddies. difference scheme is applied on the Arakawa C grid for These models are used to infer the subsurface thermal spatial derivatives. An explicit leapfrog scheme is used structure from the surface location and are particularly for time derivatives except for vertical diffusion terms, accurate in areas of simple water mass mixing, like the Tasman Sea area [see Bennett et al. (1992) for a dis- which are treated with an implicit scheme, and a weak cussion of these models]. We constructed a feature mod- Asselin ®lter is applied to remove numerical modes. A el based on the Levitus (1982) climatological temper- mode-splitting technique allows the separation of the ature pro®les and RAN charts to project the surface barotropic and baroclinic components within the model, information into the deep layers, which produced three- which result in internal (⌬t ϭ 300 s) and external (⌬t i e dimensional synthetic temperature ®elds. In water depth ϭ 10 s) time steps. less than 250 m, we assume a uniform mixed layer of The model domain extends from 37.5ЊS to 28.5ЊS, 50 m and spline ®t the temperature between 50 m and 150ЊE to 157.5ЊE. A stretched grid was constructed us- 250 m d. In water depths greater than 250 m, we pro- ing the method developed for the Semi-Spectral Prim- duced a vertical pro®le corresponding to each T250 val- itive Equation Model (SPEM: Haidvogel et al. 1991), ue by blending two climatological pro®les, one of warm- which creates an orthogonal-curvilinear grid following er water from the Coral Sea (TW) and the second from the coast. This allows re®nements of the grid over the colder water from the southern Tasman Sea (T ): shelf and slope region, with a minimum spacing of 5 C km, increasing to a maximum of 30 km near the offshore T(z) ϭ TC(z) ϩ ␣[TC(z) Ϫ TW(z)], (6) boundary. The vertical grid spacing varies over the do- where ␣ is the mixing ration at 250 m, de®ned as main with 20 elements covering the water column. Ba- T Ϫ T (250) thymetry with a resolution of 5 minutes of latitude is ␣ ϭ 250 W . (7) obtained from the ETOPO5 (NOAA 1988) dataset, in- [TCW(250) Ϫ T (250)] terpolated onto the grid. A 50-m minimum depth has Temperature±salinity relationships for the Tasman been set to avoid numerical instability on the shelf zone. Sea are then used to calculate the salinity ®eld and hence To estimate the pressure gradient truncation errors and the three-dimensional density ®eld. The initial ¯ow ®eld hydrostatic inconsistency related to the ␴ coordinate in geostrophic balance with the density ®eld is derived (Haney 1991; Barnier et al. 1998), we conducted ``rest- from the thermal wind relation, assuming the level of

Unauthenticated | Downloaded 09/28/21 03:07 AM UTC NOVEMBER 2000 MARCHESIELLO AND MIDDLETON 2961

FIG. 4. Model grid and bathymetry. no motion at 2000 m. The barotropic component of the ␦␾ ␦␾ ϩ c ϭ 0, (8) ¯ow is then constrained to the conservation of volume ␦t x ␦x transport. In order to avoid initialization problems related to imbalanced mass and baroclinic ¯ow ®elds where cx is the normal phase velocity calculated from (Temperton 1973), the model is run in robust diagnostic the ␾ ®eld surrounding the boundary point as mode. Temperature and salinity ®elds are strongly constrained to the observations, while the ¯ow ®eld adjusts ␦␾ ␦␾ to the mass ®eld. The solution obtained is used as the new initial state in the prognostic mode. All initial ®elds ␦x ␦t cx ϭ . (9) supply boundary values, used throughout the simulation ␦␾22 ␦␾ to force the model. ϩ ␦x ␦y As usual in regional modeling, open boundary con- ΂΃ ΂΃ ditions need special considerations. The variables are Note that the relation for c differs from Orlanski (1976) speci®ed at the northern boundary, which is sensitive x where tangential derivatives are neglected. We then to the strong southward currents and northward prop- avoid erronous strong values of c in case of propagation agating waves. To avoid re¯ections of these waves, a x sponge layer is added for surface elevation, temperature, along the boundary (␦␾/␦x small), a classical problem and salinity. Radiative conditions are used for all var- of one-dimensional radiation schemes (Raymond and iables at the southward and seaward boundaries. The Kuo 1984). Radiative conditions are passive, that is, radiation boundary scheme is described in details and effective when features are propagating outward but in- validated in Barnier et al. (1998), then used in Mar- operative when they are propagating inward. Hence, a chesiello et al. (1998) to achieve long-term simulations relaxation term to initial values is applied in case of of the South Atlantic circulation with three open bound- inward wave propagation, as in one-way nesting meth- aries. The radiation scheme estimates a two-component, ods (Miyakoda and Rosati 1977). This will allow further horizontal phase velocity near the open boundaries re®nements such as coupling with time-varying data or (Raymond and Kuo 1984). However, unlike in Raymond large-scale models. and Kuo, only the normal phase velocity is eventually The model was forced only at the boundaries, in par- retained because of greater numerical stability. This can ticular an in¯owing EAC jet at the northern boundary. be written for a prognostic model variable ␾ at an east- No heat ¯ux, freshwater ¯ux, or wind stress terms were ern boundary as imposed.

Unauthenticated | Downloaded 09/28/21 03:07 AM UTC 2962 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30

4. Simulation of warm-core eddy formation Time series of a temperature section crossing the eddy are shown in Fig. 6 and are compared to an observed We choose to present here a 70-day simulation start- eddy section (Nilsson and Cresswell 1981). Clearly, the ing from an analysis of the ocean on 23 November 1992. observed and simulated eddies are very similar, al- A preliminary study (Gibbs et al. 1998) has already though the frontal features are sharper in reality. In both shown that the model is close to observations for up to cases, the eddies are deep (more than 500 m) and about 3 weeks when compared to weekly RAN charts of the 250 km wide, asymmetric with a deeper mixed layer on same period. The period is obviously re¯ecting the sit- the inner edge, and important outcropping on the outer uation of an energy growing EAC, which is favorable edge [inner (outer) are referred to here as inshore (off- to the formation of a warm core eddy. In particular, the shore) branches of the meander that previously existed]. formation of a large meander previous to the eddy is By looking at the evolution of the model temperature, clearly con®rmed by the observations of November± it appears that coastal dynamics may be partly respon- December 1992 and is not a result of the model spinup. sible for the eddy features. At day 10, the EAC trans- We are focusing here on the model ability to capture ports warm Coral Sea water above the slope of NSW. the mechanisms involved in the formation of the eddy, As the meander develops, a large trough appears with as opposed to its forecasting ability over a 2-month a deep mixed layer, while a cold dome forms on the period. outer shelf edge of Jervis Bay, which drives the inner Six frames on Fig. 5 present the surface velocities branch offshore (day 30). Since no coastal dynamics representative of the whole period of simulation. The in¯uence the other edge of the meander/eddy, it is able initial state of the model presents a smooth but classical to spread (day 50). In the following section, the physical feature of the western Tasman Sea: a Tasman Front mechanisms involved in the warm-core eddy formation slightly meandering from the coast at around 33 S and Њ are analyzed more precisely. an anticyclonic warm-core eddy located south of Jervis Bay. We have estimated a volume transport of 22 Sv and currents of about 1 m sϪ1 in the northern part of 5. Analyses NSW (Fig. 5a). a. Pinch-off process During the ®rst 2 weeks, the EAC energy is growing in the northern part and being advected southward. The The aforementioned simulation is consistent with the southward branch of the current increases and develops scenario proposed by Nilsson and Cresswell (1981), rep- a large U-shaped meander between 152Њ and 154ЊE, resented in Fig. 3. The main aspect is the southward extending southward to Jervis Bay (Fig. 5b). As the propagation of a large meander and its pinch-off re- energy of the EAC is propagating past Sugarloaf Point, sulting in an eddy. Nilsson and Cresswell relate the a perturbation appears between the coast and the current pinch-off process to westward propagation of baroclinic (visible on Fig. 7 around day 10), propagating south- Rossby waves along the Tasman Front. Based on their ward and developing as a cyclonic circulation. While observations, they proposed a phase speed of 2 cm sϪ1, propagating, the cyclonic circulation grows in scale and that is, sligthly above the value of 1.5 cm sϪ1 suggested strength, bringing cold water toward the surface. The by linear baroclinic waves theory. This discrepency has southward drift of the cold-core eddy stops near Jervis been attributed to nonlinear effects. In order to verify Bay, and the eddy starts migrating offshore, resulting the validity of the Rossby wave effect theory on the in the separation of the current from the coast (Fig. 5c). pinch-off process, we ®rst analyzed the wave speed of Meanwhile, the eastern branch of the meander prop- the Tasman Front. Figure 7a shows the contours of agates shoreward, resulting in a pinch-off of the me- alongshore velocity along a cross-shore line starting at ander (Fig. 5c). After the pinch-off, a northward ¯ow Sugarloaf Point and roughly following the Tasman appears around 33ЊS, forming a small cyclonic circu- Front. We note the westward propagation of the outer lation (Fig. 5d). This feature grows, pumping up cold branch with an average speed estimated over the pinch- subsurface water and pushing the EAC eastward. The off process of 2 cm sϪ1. Around day 35, a reversal in anticyclonic warm core circulation transforms into an the phase is initiated with northward ¯owing coastal eddy. The separation between the eddy and the main- currents. The phase speed estimated for the model is stream current is ®nally realized when cold waters are then similar to the value proposed by Nilsson and Cress- upwelled within the cyclonic perturbation near Sugar- well (1981). Note that the instantaneous phase speed loaf Point. Then the cold-core eddy migrates south- can reach higher values. This is acceptable for baroclinic westward (Fig. 5e), leaving the EAC to the north and rossby waves, considering the important effect of non- an anticyclonic eddy fully formed off Jervis Bay (Fig. linearity as demonstrated by Andrews et al. (1980). Fur- 5f). ther simulations in the f plane (Fig. 7b) con®rm the

→

FIG. 5. Time series of surface velocity vectors illustrating the 70-day simulation of a warm-core eddy formation.

Unauthenticated | Downloaded 09/28/21 03:07 AM UTC NOVEMBER 2000 MARCHESIELLO AND MIDDLETON 2963

Unauthenticated | Downloaded 09/28/21 03:07 AM UTC 2964 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30

FIG. 6. Comparison between model and observations of temperature sections crossing a warm-core eddy. The bottom right panel shows an XBT temperature section south of Jervis Bay for the period 8±9 Oct 1976 (after Nilsson and Cresswell 1981). The other panels show the simulated time evolution of temperature section at Jervis Bay latitude. importance of the ␤ effect. Without the ␤ effect, the short wave has a rapid decay, and is subject to nonlinear outer branch of the meander does not propagate west- instability. This description matches the model solution. ward, and no pinch-off occurs. Although signi®cant var- In the model, a long baroclinic wave is initiated by the iability is still notable, the commonly observed large formation of a large meander (wavelength ϳ400 km warm-core eddy is not able to form in the f plane, nor compared to 30±40 km for the local ®rst baroclinic is the EAC able to separate. Rossby radius of deformation estimated by Chelton et The EAC and Tasman Front are analogous to the al. 1998). After westward propagation of the meander Brazil Current and con¯uence region of the southwest outer branch, a phase reversal occurs, evident on both Atlantic Ocean. Matano and Philander (1994) have Fig. 5 and Fig. 7a. The re¯ected wave results in a small shown the importance of the westward propagation of energetic cyclonic circulation (ϳ100 km) in¯uenced by baroclinic Rossby waves on large meanders of eastern nonlinear processes. It is interesting to point out here currents like the Brazil Current. Nilsson and Cresswell that this cyclonic eddy induces an upwelling of cold (1981) suggested that a westward propagation of Rossby subsurface water, frequently observed at the separation waves should be followed by a phase reversal, with point of the EAC from the coast. Note that upwelling reverse currents close to the coastal region. They support of nutrient-rich water around the separation point may this assertion with the observation of northerly currents be responsible for the blooms occasionally observed in occasionally reported along the shelf edge. In inviscid Port Stephens. shallow water theory, the conditions for re¯ection of Rossby waves at western boundaries are well docu- b. Separation process mented in Longuet-Higgins (1966) and Pedlosky (1987). It is shown that a long incident wave propa- In this section we focus more closely on the mech- gating toward a western boundary may be re¯ected. The anisms of separation of the EAC from the coast. Con- outgoing wave conserves ``elastically'' the incident en- sidering the basin-scale dynamics, westward propa- ergy, but is short (relative to the internal Rossby radius) gation of Rossby waves from New Zealand may de- with high energy density and an increased meridional termine the general location of the Tasman Front. As velocity directed northward at the coast. The re¯ected we have discussed, the location and oscillations of the

Unauthenticated | Downloaded 09/28/21 03:07 AM UTC NOVEMBER 2000 MARCHESIELLO AND MIDDLETON 2965

FIG. 7. Time evolution of the simulated alongshore surface velocity off Sugarloaf Point (upper-left panel indicates the zonal location) for A: the standard case, B: the f plane case, and C: the smooth bathymetry case. Solid and dash lines indicate respectively northward and southward velocity; ␦␷ ϭ 0.3 m sϪ1.

Tasman Front near the NSW coast may determine the and, in particular, the bend in the the coastline at Sug- general location of current separation. However, we arloaf Point. observe that the EAC separates from the coast near The observed separation points are also found to be speci®c spots like Smoky Cape, Sugarloaf Point, and separation points in the present model. The Jervis Bay Jervis Bay. Godfrey et al. (1980) had proposed that location appears more related to the meander than the the exact location is dependent on bottom topography mainstream, unlike Sugaloaf Point, and this will be dis-

Unauthenticated | Downloaded 09/28/21 03:07 AM UTC 2966 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30 cussed in the next section. To analyze the mechanisms ating to eliminate the surface pressure terms. Then, the involved, a vorticity balance has been computed. A continuity equation (1) yields an equation for the rate depth-averaged vorticity equation can be obtain by of change of the vorticity of the depth-averaged ¯ow depth averaging (2) and (3) and then cross differenti- given by

␦␦␷␦uf␦D ␦D ϪϭϪ␤␷ ϩ u ϩ ␷ ␦t΂΃␦x ␦yD ΂␦x ␦y ΃ g 00␦␳Ј ␦D ␦␳Ј 00 ␦␳Ј ␦D ␦␳Ј Ϫ curlz D Ϫ ␴Ј d␴Ј d␴, D Ϫ ␴Ј d␴Ј d␴ ␳␦0 ͵͵x ␦x ␦␴Ј ͵͵ ␦y ␦y ␦␴Ј [ Ϫ1 ␴ ΂΃΂΃Ϫ1 ␴ ] CC ␦(uD22) ␦(u␷ D) ␦(␷ D) ␦(u␷ D) Ϫ curlDD (u2ϩ ␷ 2) 1/2u ,(u2ϩ ␷ 2) 1/2␷ Ϫ curl ϩ , ϩ . (10) zbbbbbbz[][]DD ␦x ␦y ␦y ␦x

Hence, the tendency for depth-averaged vorticity is rection for STRETCHING. The idea is that the com- determined by planetary vorticity, topographic stretch- ponent of the ¯ow responsible for topographic stretching ing, joint effect of baroclinicity and relief (JEBAR), is not the depth-averaged ¯ow, but the bottom current. bottom friction (we neglected here the interior viscos- Since STRETCHING is written as a function of the ity), and advection: depth-averaged ¯ow in Eq. (10), a correction is needed to account for the real topographic effect. This correc- TENDENCY ϭ BETA ϩ STRETCHING ϩ JEBAR tion is related to baroclinicity, which tends to decrease ϩ FRICTION ϩ ADVECTION. (11) the bottom current by inverting the pressure gradient toward the bottom. Thus, baroclinicity inhibits the Figure 8 shows contours of the different vorticity stretching effect induced by oscillations over a sloping terms (apart from BETA and TENDENCY) at day 10 topography. This interpretation is compatible with our for the northern part of the domain. In very local areas result where JEBAR appears to inhibit STRETCHING discussed below, BETA is two orders of magnitude (opposite signs and comparable magnitude). This would smaller than the biggest individual term. Although, integrated values of BETA are signi®cant in the vorticity result in offshore excursion of the EAC when ADVEC- budget. TENDENCY is also an order of magnitude TION is signi®cant. smaller locally than the biggest term, and ¯uctuates Our proposition is that the EAC is accelerated at greatly with small changes of the big terms. Smoky Cape where the slope width narrows, while the The results are generally representative of the whole local bottom friction balances the advection of vorticity. simulation. Positive values tend to drive the current off- At Crowdy Head, the strong current is advected offshore shore, while negative values tend to keep the current on as the isobaths alignment bends eastward. When the the continental slope. It appears that all terms are im- bottom friction does not completely balance the advec- portant in localized positions on the continental slope. tion, the bottom stretching is enhanced. But, the strong These positions correspond to the commonly cited sep- baroclinicity of the current inhibits the stretching effect, aration points. Yet, rather than Sugarloaf Point, Crowdy enabling the EAC to cross the slope. Note that a sim- Head is identi®ed as a position of signi®cant vorticity ulation performed without bottom friction emphasizes variability (located sligthly north of Sugarloaf Point). further the role played by the other terms as described Jervis Bay (not shown) is also identi®ed but to a lesser here. extent. ADVECTION and FRICTION are shown to be Myers et al. (1996) concluded that the JEBAR term signi®cant (up to 3.5 ϫ 10Ϫ9 sϪ2) and appear to balance was primarily responsible for the separation of the Gulf each other well. ADVECTION forces the EAC offshore Stream from the coast. Our conclusion is similar for the while FRICTION tends to maintain its paths along the EAC in that bottom topography indeed determines the isobaths. Similarly STRETCHING and JEBAR terms exact location of separation. However, unlike the Gulf are of the same order (up to 1.5 ϫ 10Ϫ9 sϪ2), and again Stream, which seems to separate ``naturally'' from Cape appear to be balanced. Hatteras, the EAC separation requires added forcing. The interpretation of terms in the vorticity budget Reverse Rossby waves generated by large meanders of seems quite trivial exept for the JEBAR term. Mertz the Tasman Front near the coast may provide this forcing and Wright (1992) give a usefull interpretation for JE- by driving the EAC offshore. This is revealed by com- BAR. They suggest that JEBAR may appear as a cor- parisons of standard and f-plane simulations (Figs.

Unauthenticated | Downloaded 09/28/21 03:07 AM UTC NOVEMBER 2000 MARCHESIELLO AND MIDDLETON 2967

FIG. 8. Maps of the different terms of the depth-averaged vorticity balance. Low values have been ®ltered to emphasize local high values; CI ϭ 0.5 ϫ 10Ϫ9 sϪ2.

7a,b). On the other end, the EAC may be able to meander Rossby wave forcing is not as effective in the separation signi®cantly only on ``fragile'' positions like Crowdy process (around day 35). Hence, the combination of the Head. A sensitivity test has been performed with a very local topography effect and Tasman Front forcing may smoothed bathymetry in the alongshore direction. Fig- determine the exact location of the EAC separation. The ure 7c shows that in the absence of local topographic separation is actually completed when the lateral ex- structures, the EAC has no signi®cant natural offshore cursion of the current activates the formation of a cold- de¯ection (around day 10) that would develop into a core frontal eddy, mainly through baroclinic instabilities frontal eddy, as in the standard case. Furthermore, the of the mean ¯ow, as described by Miller and Lee (1995)

Unauthenticated | Downloaded 09/28/21 03:07 AM UTC 2968 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30

FIG. 9. Comparison between model and observations of dynamic topography and surface currents around Sugarloaf Point. Left: Model results (␩ and currents) at day 54; right: results of a Sprightly cruise for the period 30 Mar±11 Apr 1978, that is, the surface dynamic height 2 Ϫ2 ␩D relative to 1300 db and currents (after Godfrey et al. 1980); ␦␩ ϭ 0.1m, ␦␩D ϭ 0.1 m s . for the Gulf Stream cold-core frontal eddies upstream However, we can observe them more clearly from sat- of Cape Hatteras. When the eddy upwells enough sub- ellite altimetry. In the present model, they also appear surface cold water and migrates offshore, the large more clearly on sea surface elevation and subsurface warm-core eddy is isolated and the separation is com- temperature (e.g., T250). These cyclonic features seem pleted. Observations of cold-core frontal eddies near to play an important role in the offshore circulation as Sugarloaf Point, comparable to our computation (Fig. we have shown. They also interact with coastal waters. 9), tends to validate this mechanism. Nutrient enrichment in NSW coastal waters is particularly revealed by the occasional occurence of phy- c. Interactions with coastal waters toplankton blooms during the spring season. It is as- sumed that the wind plays a major role in upwelling As shown previously, one feature of the present model nutrients that supply these blooms. However the events is the formation of small cold-core eddies along the appear to be correlated with the EAC variability (Tranter outer shelf edge. Cyclonic cold-core features in the et al. 1986; Hallegraeff and Jeffrey 1993). This study western Tasman Sea have been observed, and are anal- follows a series of papers that attempted to identify the ogous to Gulf Stream frontal eddies, which have been mechanisms involved. We ®rst applied a two-dimen- the center of considerably more attention. The surface sional version of POM (vertical cross-shelf section) to temperature signal of a cold-core eddy is not as clear a cross-shelf section of the Sydney shelf, where obser- as it is for the warm-core eddies since they have smaller vations were acquired from a ®eld experiment (Gibbs scales, shorter periods, and appear in the Tasman Sea et al. 1997; Marchesiello et al. 2000). The model con- where the background temperature is relatively cold. ®rmed that the vertical displacements of water in the

Unauthenticated | Downloaded 09/28/21 03:07 AM UTC NOVEMBER 2000 MARCHESIELLO AND MIDDLETON 2969

FIG. 10. Simulated surface temperatures and currents off the coast of New South Wales, Australia, for 14 Dec 1992 (Day 21). Gray area represents relatively cold water (Ͻ21.5ЊC). Note the cold, uplifted water associated with a small cyclonic eddy between the coast at Jervis Bay and the separating EAC farther offshore. nearshore zone respond principally to the local wind small intense cold-core eddies on the ¯ank of much stress and indicated that the presence of cold-core fea- larger and more stable warm-core eddies. tures are correlated with higher upwelling events. Ap- Although this is a relatively new concept for NSW plication of the three-dimensional EAC model (Gibbs coastal waters, it has been recognized as an extremely et al. 1998) to study a bloom event observed in Jervis ef®cient process on the southeastern U.S. continental Bay during spring 1992 validated this suggestion. The shelf (Miller and Lee 1995). As it ¯ows along the outer mechanism by which the EAC may enrich coastal waters edge of the continental shelf, the Gulf Stream meanders is through baroclinic instabilities, which often appear as on and off shore, creating frontal eddies that in¯uence

Unauthenticated | Downloaded 09/28/21 03:07 AM UTC 2970 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30 the exchange of water between the shelf and the adjacent From these critical positions where they are formed, Atlantic Ocean on weekly timescales. The analyses pre- instabilities may be advected southward by the EAC, sented in this section enlighten somewhat the charac- but for the local separation to occur a forcing event is teristics of cold-core eddies associated with the EAC. needed, like a Rossby wave re¯ection. Crowdy Head Instabilities appear to originate from oscillations of the appears in the analyses as a separation point rather than EAC near Sugarloaf Point (Fig. 7a, around day 10), in Sugarloaf Point, implying that a bend in the coastline a process described by Louis (1989). They develop as might not be a determinant factor. Crowdy Head pre- small cyclonic eddies being advected southward by the sents a bend in the continental slope, downstream of an current. Parcels of slope water uplifted within the eddy acceleration favorable zone where the slope width nar- are advected downstream, consistent with observations rows signi®cantly. Cold-core frontal eddies, developed of Cresswell (1994). The cold core stops near Jervis along the outer shelf from the EAC have an active part Bay, which is another topographic feature. A cold dome in the offshore circulation pattern. They also appear to is then present as illustrated by time evolution of the ventilate signi®cantly the shelf zone with slope water, temperature section off Jervis Bay (Fig. 6). These fea- enabling the EAC to uplift cold nutrient-rich water onto tures have weekly timescales, like their analogies from the shelf, and eventually into the nearshore zone when the Gulf Stream, which would explain our dif®culty to local winds are upwelling favorable. observe them from limited physical data. The surface forcing problem was omitted in this study in order to separate out the in¯uence of the EAC alone on the western Tasman Sea. Yet, surface forcings are 6. Discussion expected to impact the oceanographic conditions. This The present model has shown its ability to simulate concerns surface heat and salt ¯uxes, and particularly the EAC dynamics with realistic results, allowing us to wind stress. Large-scale wind forcing should not affect propose plausible mechanisms to explain some funda- signi®cantly our regional model since the Sverdrup bal- mental aspects of the EAC variability and its interaction ance is rather introduced through the boundaries. Re- with the continental shelf of New South Wales. The gional winds should in¯uence the surface mixed layer model was able to capture the formation of a large an- and, along with the turbulent submodel, should lead to ticyclonic eddy within a scenario consistent with that more realistic results in this respect. More importantly proposed by Nilsson and Cresswell (1981). Nilsson and for the coastal circulation is the impact of local winds Cresswell established the role of baroclinic Rossby inducing surface mixing, upwelling, and downwelling. waves in pinching off the large meander, drifting south- The model can also be re®ned. Consideration of ward from the EAC mainstream. Our simulation clearly AVHRR images suggests that the dynamics of the EAC con®rms it. The Rossby wave, stimulated by the oscil- is associated with a wide range of time and length scales, lations of the Tasman Front near the coast, travels west- all scales supposedly interacting. The treatment of var- ward at a phase speed of about 2 cm sϪ1. It is re¯ected iability should bene®t from higher vertical and hori- at the coast with evidence of a phase reversal, associated zontal resolution, as well as improved numerical with a northward ¯owing currents near Sugarloaf Point. schemes. In particular, second-order discretized advec- The wave is destabilized and develops as a small cy- tion schemes are not the optimal choice (Sanderson clonic eddy, uplifting cold subsurface water. This cold- 1998). core eddy seems to be a key element in the last sepa- Interesting hints on the EAC variability are demon- ration process between the mainstream and the newly strated in our analyses of the simulation. However, the formed warm-core eddy. statistical reliability of our results are unclear. Long- The EAC separation from the coast discussed by God- term simulations with realistic forcing and improve- frey et al. (1980), also appears to be related to the in- ments of the model should then be subject of future teractions of the current with the topography. These in- research. teractions in the model are consistent with the propo- sitions of Louis (1989), that is, that short topographic Acknowledgments. This research was supported by waves are generated by oscillations of the EAC and the National Greenhouse Advisory Committee and the amplify as a result of instability processes involving the Australian Research Council. Our thanks go to Robert interaction with the current. Eventually, well-shaped Gardiner-Garden and Tom Deniss for their contribution small cyclonic eddies may be formed. We have estab- to the development of the model. The Oceanographic lished that oscillations of the EAC and formation of Data Center for the Royal Navy supplied the authors cyclonic eddies have preferential locations related to with the Tasman Sea temperature data used to initialize changes in topographic features. Where the bathymetry the model. changes dramatically, the current tends to cross the slope but is constrained according to the vorticity balance. Baroclinicity, expressed by the JEBAR term, is then able REFERENCES to relax the topographic constraint in a way similar to Andrews, J. C., M. W. Lawrence, and C. S Nilsson, 1980: Obser- the Gulf Stream at Cape Hatteras (Myers et al. 1996). vations of the Tasman Front. J. Phys. Oceanogr., 10, 1854±1869.

Unauthenticated | Downloaded 09/28/21 03:07 AM UTC NOVEMBER 2000 MARCHESIELLO AND MIDDLETON 2971

Barnier, B., P. Marchesiello, A. P. de Miranda, J. M. Molines, and coordinate model for studying the circulation in the South At- M. Coulibaly, 1998: A sigma-coordinate primitive equation mod- lantic. Part II: Meridional transports and seasonal variability. el for studying the circulation in the South Atlantic. Part I: Model Deep-Sea Res., 45, 543±572. con®guration with error estimates. Deep-Sea Res., 45, 543±572. , M. T. Gibbs, and J. H. Middleton, 2000: Simulations of coastal Bennett, A. F., 1983: The East Australia Current. Eddies in Marine upwelling on the Sydney continental shelf. Mar. Freshw. Res., Science, A. Robinson, Ed., Springer-Verlag, 219±242. 39, 245±288. Bennett, T., Jr., J. Boyd, L. Knauer, G. Dawson, and W. Wilson, 1992: Matano, R. P., and S. G. H. Philander, 1994: On the decay of the A feature model of the Iceland±Faeroe Front. J. Mar. Technol. meanders of eastward currents. J. Phys. Oceanogr., 24, 298± Soc., 26, 44±52. 304. Blackburn, S. I., and G. R. Cresswell, 1993: A coccolithophorid Mellor, G. L., and T. Yamada, 1982: Development of a turbulence bloom in Jervis Bay, Australia. Aust. J. Mar. Freshw. Res., 44, closure model for geophysical ¯uid problems. Rev. Geophys., 253±260. 20, 851±875. Blumberg, A. F., and G. L. Mellor, 1987: A description of a three- , and T. Ezer, 1991: A Gulf Stream model and an altimetry dimensional coastal ocean circulation model. Three-Dimensional assimilation scheme. J. Geophys. Res., 96, 8779±8795. Ocean Models, Ed., N. Heaps, Amer. Geophys. Union, 208 pp. Mertz, G., and D. G. Wright, 1992: Interpretations of the JEBAR Chelton, D. B., R. A. deSzoeke, M. G. Schlax, K. E. Naggar, and N. term. J. Phys. Oceanogr., 22, 301±305. Siwertz, 1998: Geographical variability of the ®rst baroclinic Miller, J. L., and T. N. Lee, 1995: Gulf Stream meanders in the South Rossby radius of deformation. J. Phys. Oceanogr., 28, 433±238. Atlantic Bight. 1. Scaling and energetics. J. Geophys. Res., 100, Church, J. A., and P. D. Craig, 1998: Australia's shelfseas: Diversity 6687±6704. and complexity, Chapter 11, The Sea, Vol. 11: The Global Ocean Miyakoda, K., and A. Rosati, 1977: One way nested grid models: Regional Studies and Syntheses. A. R. Robinson and K. H. Brink, The interface condition and numerical accuracy. Mon. Wea. Rev., Eds., Wiley and Sons. 105, 1108±1118. Cresswell, G. R., 1994: Nutrient enrichment of the Sydney continental Myers, P. G., A. F. Fanning, and A. J. Weaver, 1996: JEBAR, bottom shelf. Aust. J. Mar. Freshw. Res., 45, 677±691. pressure torque, and Gulf Stream separation. J. Phys. Oceanogr., , C. Ellyett, R. Legeckis, and A. F. Pearce, 1983: Nearshore 26, 671±683. features of the East Australian Current System. Aust. J. Mar. Nilsson, C. S., and G. R. Cresswell, 1981: The formation and evo- Freshw. Res., 34, 105±114. lution of East Australian Current warm-core eddies. Progress in Gibbs, M. T., J. H. Middleton, and P. Marchesiello, 1997: Baroclinic Oceanography, Vol. 9, Pergamon, 133±183. response of Sydney shelf waters to local wind and deep ocean NOAA, 1988: Digital relief of the surface of the earth. Data An- forcing. J. Phys. Oceanogr., 28, 178±190. nouncement 88-MG-02. National Geophysical Data Center, , P.Marchesiello, and J. H. Middleton, 1998: Nutrient enrichment Boulder, CO. of Jervis Bay, Australia, during the massive 1992 Coccolitho- Orlanski, I., 1976: A simple boundary condition for unbounded hy- perbolic ¯ows. J. Comput. Phys., 21, 251±269. phorid Bloom. Mar. Freshw. Res., 48, 473±478. Pedlosky, J., 1987: Geophysical Fluid Dynamics. Springer-Verlag, Godfrey, J. S., G. R. Cresswell, T. J. Golding, and A. F. Pearce, 1980: 710 pp. The separation of the East Australian Current. J. Phys. Ocean- Raymond, W. H., and H. L. Kuo, 1984: A radiation boundary con- ogr., 10, 430±439. dition for multidimensional ¯ows. Quart. J. Roy. Meteor. Soc., Haidvogel, D. B., J. L. Wilkin, and R. Young, 1991: A semi-spectral 110, 535±551. primitive equation ocean circulation model using sigma and or- Ridgway, K. R., and J. S. Godfrey, 1994: Mass and heat budgets in thogonal curvilinear horizontal coordinates. J. Comput. Phys., the East Australian Current: A direct approach. J. Geophys. Res., 94, 151±185. 99, 3231±3248. Hallegraeff, G. M., and S. W. Jeffrey, 1993: Annually recurrent di- , and , 1997: The seasonal cycle of the East Australian atom blooms in spring along the New South Wales coast of Current. J. Geophys. Res., 102, 22 921±22 936. Australia. Aust. J. Mar. Freshw. Res., 44, 325±334. Sanderson, B. G., 1998: Order and resolution for computational ocean Haney, R. L., 1991: On the pressure gradient force over steep to- dynamics. J. Phys. Oceanogr., 28, 1271±1286. pography in sigma coordinate ocean models. J. Phys. Oceanogr., Smagorinsky, J., 1963: Some experiments in dynamical initialization 21, 610±619. for a simple primitive equation model. Quart. J. Roy. Meteor. Huyer, A., 1998: Currents off south-eastern Australia: Results from Soc., 99, 303±319. the Australian Coastal Experiment. Aust. J. Mar. Freshw. Res., Temperton, C., 1973: General circulation experiment with the prim- 39, 245±288. itive equations. I: The basic experiment. Mon. Wea. Rev., 91, Levitus, S., 1982: Climatological Atlas of the World Ocean. NOAA 99±164. Prof. Paper No. 13, U.S. Govt. Printing Of®ce, 173 pp. Tranter, D. J., D. J. Carpenter, and G. S. Leech, 1986: The coastal Longuet-Higgins, M. S., 1966: Planetary waves on a rotating sphere enrichment effect of the East Australian Current eddy ®eld. bounded by meridians of longitude. Trans. Roy. Soc. London, Deep-Sea Res., 33, 1705±1721. 284A, 317±350. Wilkin, J. L., and R. A. Morrow, 1994: Eddy kinetic energy and Louis, J. P., 1989: Current±shelf interactions during the Australian momentum ¯ux in the Southern Ocean: Comparison of a global Coastal Experiment. Aust. J. Mar. Freshw. Res., 40, 571±585. eddy-resolving model with altimeter, drifter, and current-meter Marchesiello, P., B. Barnier, and A. P. De Miranda, 1998: A sigma data. J. Geophys. Res., 99, 7903±7916.

Unauthenticated | Downloaded 09/28/21 03:07 AM UTC