Adiabatic Eastern Boundary Currents
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JUNE 2013 C E S S I A N D W O L F E 1127 Adiabatic Eastern Boundary Currents PAOLA CESSI AND CHRISTOPHER L. WOLFE Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California (Manuscript received 22 October 2012, in final form 3 February 2013) ABSTRACT The dynamics of the eastern boundary current of a high-resolution, idealized model of oceanic circulation are analyzed and interpreted in terms of residual mean theory. In this framework, it is clear that the eastern boundary current is adiabatic and inviscid. Nevertheless, the time-averaged potential vorticity is not con- served along averaged streamlines because of the divergence of Eliassen–Palm fluxes, associated with buoyancy and momentum eddy fluxes. In particular, eddy fluxes of buoyancy completely cancel the mean downwelling or upwelling, so that there is no net diapycnal residual transport. The eddy momentum flux acts like a drag on the mean velocity, opposing the acceleration from the eddy buoyancy flux: in the potential vorticity budget this results in a balance between the divergences of eddy relative vorticity and buoyancy fluxes, which leads to a baroclinic eastern boundary current whose horizontal scale is the Rossby deformation radius and whose vertical extent depends on the eddy buoyancy transport, the Coriolis parameter, and the mean surface buoyancy distribution. 1. Introduction induced by the upwelling-favorable winds, as is the case for the Leeuwin Current (Smith et al. 1991). Near the eastern boundaries of the oceans, the wind In this study we show that the poleward current, ac- stress is partially constrained by encounter with conti- companied by a deeper equatorward current, is the nents (Rienecker and Ehret 1988), where the wind ac- eastern boundary expression of the large-scale wind- quires a meridional component that generates zonal driven circulation in the subtropical and subpolar re- Ekman transport, accompanied by upwelling (or down- gions. Without a near-shore meridional component of welling). In addition, the deceleration of wind stress as the wind stress there is no surface equatorward current the coast is approached, together with the aforemen- near the eastern boundary that rides over the poleward tioned wind steering, produces a pattern of increased component of the EBC. Ekman suction (or pumping), which can also lead to Other studies have reached the same conclusion. In upwelling (or downwelling). Because of the important particular, with a series of idealized numerical experi- implications to fisheries, much of the focus on coastal ments, Godfrey and Weaver (1991) have shown that circulation has been on near-surface upwelling and the an important element for a substantial poleward EBC associated equatorward currents, which we believe arise (overlying a deeper equatorward undercurrent) is the because of the local wind stress effect. However, all of existence of a large-scale latitudinal buoyancy gradient, the eastern boundary current (EBC) systems also have which, if strong enough, can overwhelm the local wind poleward undercurrents—usually faster than the surface stress effects all the way to the surface. However, these equatorward flow—overlying a deeper equatorward numerical experiments are at a coarse resolution, which current (Barton 1998; Pierce et al. 2000; Penven et al. does not allow the development of mesoscale eddies. 2005). In some regions the poleward EBC is found at the Observations (Todd et al. 2011) and high-resolution surface, overwhelming the surface equatorward current model experiments (Marchesiello et al. 2003) have dem- onstrated that EBCs are embedded in a vigorous eddy field and clearly emerge only after an appropriate time Corresponding author address: Paola Cessi, Scripps Institution of Oceanography, University of California, San Diego, 9500 Gilman average. Regional eddy-resolving simulations include Dr., Mail Code 0213, La Jolla, CA 92093-0213. forcing and geometry (e.g., coastline and bottom relief) E-mail: [email protected] that are as realistic as possible and do not permit teasing DOI: 10.1175/JPO-D-12-0211.1 Ó 2013 American Meteorological Society Unauthenticated | Downloaded 09/27/21 07:43 AM UTC 1128 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 43 apart what aspects of the currents are extrinsically in- currents obtained in the eddy-resolving context are of duced and which are from intrinsic dynamics. For ex- larger amplitude than those obtained in laminar, viscous ample, is the cross-shore scale of the EBC set by the theories, and that their scale is much larger than the scale of the alongshore wind, by the width of the shelf, or thickness of the lateral Ekman layer. by internal dynamics? Is it necessary to have alongshore Laminar theories that account for the alongshore winds to have an EBC? In the following, it is shown that pressure gradient have to relax some of the idealized EBCs are part of the general circulation of the ocean: assumptions, for example by assuming that frictional they are found without local alongshore winds or topo- and/or diabatic effects become important as the eastern graphic features. boundary is approached. In particular, several authors Classical theories of the ocean’s general circulation have assumed that diabatic mixing is a dominant process assume that the eastern boundary is the region of weakest throughout the region of alongshore gradients (McCreary subsurface flow. Specifically, laminar thermocline the- 1981; Colin de Verdiere 1989; Sumata and Kubokawa ories confine the motion near the eastern boundary of 2001). Sumata and Kubokawa (2001) showed that the the surface, with the subsurface near-shore region at region containing the horizontal gradient near the rest: this is the ‘‘shadow-zone’’ of Luyten et al. (1983) or eastern boundary is a deep mixed layer where density is the ‘‘blocked region’’ of Rhines and Young (1982). This vertically homogenized by the strong downwelling of the region is required by the condition of no alongshore impinging eastward flow near the eastern boundary, pressure gradient at the solid boundary, so that there balanced by mixing. Schloesser et al. (2012) interpret the is no geostrophic flow into the wall. This configuration eastern boundary solution of Sumata and Kubokawa implies that the meridional buoyancy gradients are (2001) as an adiabatic process where the flow is oriented squeezed into a region whose thickness vanishes on the along the quasi-vertical isopycnals. It is not clear whether eastern boundary, creating a singularity in the buoyancy in the solution of Sumata and Kubokawa (2001) dia- field. It is thus not surprising that an energetic field of pycnal mixing is important or negligible because neither eddies spontaneously develops in response to the sin- Sumata and Kubokawa (2001) nor Schloesser et al. gular density gradient predicted by laminar theories. In (2012) present buoyancy diagnostics to clarify whether turn, the eddy fluxes of buoyancy and momentum break the mean vertical advection is primarily balanced by the geostrophic constraint in an inviscid and adiabatic mean horizontal advection (e.g., adiabatic dynamics) or fashion, driving an across-shore pressure gradient that by mixing processes (e.g., diabatic dynamics). Because supports the EBC. Here, we illustrate the resulting EBC of the neglect of eddy processes, these are the only and its connection to the general circulation of the ocean balances possible in laminar models. in a simple geometry and for idealized large-scale wind In our study we find that the region of alongshore and buoyancy forcing. buoyancy and pressure gradients next to the eastern Contrary to the assumption of classical theories, boundary is quasi-adiabatic, and that the advection from EBC have alongshore pressure and buoyancy gradients the mean downwelling is compensated by the eddy flux (Godfrey and Ridgway 1985; Chapman and Lentz 2005); of buoyancy. This balance leads to a sloping buoyancy although the alongshore velocity in EBC systems is in profile: the eddy buoyancy flux restratifies the fluid against geostrophic balance, and thus not directly related to the the action of the mean vertical velocity. This eddy flux of meridional pressure gradient, various frictional pro- buoyancy also provides an acceleration of the time-mean cesses (lateral friction, vertical friction, or bottom drag) meridional flow, which is halted by the eddy momentum have been advocated to justify the balance between the flux, resulting in a net baroclinic meridional EBC. alongshore pressure gradient and the EBC. In the fol- The constraint that the circulation remains adiabatic lowing, we will show that there is no need to invoke and inviscid all the way to the eastern boundary, while viscous processes in the EBC and that a boundary cur- relaxing the assumption of laminar flow, provides a rent can be obtained with inviscid dynamics. However, scaling for the width of the EBC and the depth through eddy processes are essential and in particular the across- which the alongshore pressure gradients act. Because of shore eddy transport of buoyancy and momentum bal- the importance of eddy fluxes, these scales depend on ances the alongshore pressure gradient, in accordance the statistics of the eddy field, which are not easily re- with observations of the Leeuwin Current (Feng et al. lated to the properties of the statistically steady flow. As 2005). Eddy fluxes of buoyancy and momentum are detailed below, this study differs from our previous at- often parameterized as downgradient diffusion and tempts to construct a theory of EBC, which includes the viscosity, respectively, and in this sense there is a con- rectified effect of eddies (Cessi and Wolfe 2009a; Cessi nection between the laminar, frictional theories, and the et al. 2010) in that the dynamics are adiabatic and eddy eddy-resolving results. We find that the mean boundary momentum flux is important. Unauthenticated | Downloaded 09/27/21 07:43 AM UTC JUNE 2013 C E S S I A N D W O L F E 1129 FIG. 1.