On the Role of Bottom Pressure Torques in Wind-Driven Gyres

Abstract

Previous studies have concluded that the wind-input vorticity in ocean gyres is balanced by bottom pressure torques (BPT), when integrated over latitude bands. However, the BPT must vanish when integrated over any area enclosed by an isobath. This constraint raises ambiguities regarding the regions over which BPT should close the vorticity budget, and implies that BPT generated to balance a local wind stress curl necessitates the generation of a compensating, non-local BPT and thus non-local circulation. This study aims to clarify the role of BPT in wind-driven gyres using an idealized isopycnal model. Experiments performed with a single-signed wind stress curl in an enclosed, sloped basin reveal that BPT balances the winds only when integrated over latitude bands. Integrating over other, dynamically-motivated definitions of the gyre, such as barotropic streamlines, yields a balance between wind stress curl and bottom frictional torques. This implies that bottom friction plays a non-negligible role in structuring the gyre circulation. Non-local bottom pressure torques manifest in the form of along-slope pressure gradients associated with a weak basin-scale circulation, and are associated with a transition to a balance between wind stress and bottom friction around the coasts. Finally, a suite of perturbation experiments is used to investigate the dynamics of BPT. To predict the BPT, the authors extend previous theory that describes propagation of surface pressure signals from the gyre interior toward the coast along planetary potential vorticity contours. This theory is shown to agree closely with the diagnosed contributions to the vorticity budget across the suite of model experiments.

Spurious Forces Can Dominate the Vorticity Budget of Ocean Gyres on the C‐Grid

“…This formulation is practical as topographic interactions emerge from pressure gradients in the form of the bottom pressure torque and beta effects emerge from the curl of the Coriolis acceleration; the Coriolis acceleration is responsible for one physically meaningful term in the analytic vorticity budget. Equation 2 is also used in Stewart et al (2021). Jackson et al (2006) conclude that the leading order balance between bottom pressure torques and the planetary vorticity term in Equation 2 is crucial for steering jets and western boundary currents over bottom topography.…”

“…Terrain-following coordinates (or σ-coordinates) are an alternative form of vertical coordinate where the vertical resolution adjusts with the bottom topography so that the same number of model levels are present in all fluid columns (Song & Haidvogel, 1994). σ-coordinates are used in Stewart et al (2021), Schoonover et al (2016), and Jackson et al (2006 and have the advantage of removing spurious terms that emerge from model level steps. The forms of the EEN, ENE, and ENS vorticity schemes are unchanged when using terrain-following coordinates so the horizontal variations in cell thicknesses could still cause a spurious signal.…”

“…Stewart et al. (2021) discuss how the integrating area affects the resultant vorticity balances and in their model the wind stress curl is only balanced by bottom pressure torques when integrated over latitude bands. Jackson et al.…”

“…The recent article by Stewart et al. (2021) also studied the impact of bottom topography on vorticity budgets. However, the model used by Stewart et al.…”

“…However, the model used by Stewart et al. (2021) is a two layer isopycnal model where the bottom topography is completely contained in the lower density layer. In this article we consider models that have a higher vertical resolution and a step‐like bathymetry.…”