#### Abstract

What is the circulation driven by wind stress in a stratified ocean above topography? This question was answered by Sverdrup (1947) for vertically integrated transport over flat topography only. By applying the ideas and methods of Rhines and Young (1982a,b), a modified form of the Sverdrup transport relation can be derived for the case of stratification and topography in certain circumstances. This circulation equation is, in quasigeostrophic form,*J*(Ψ, *βy* + *χf*_{0}*h*′_{T}/*H*) = − *χf*_{0}^{−1}*gAH J*(*βy*, *h*′_{T}) + *z* · ∇*xτ*/*&rho*_{0},where most symbols have their usual meanings, while *χ* is a parameter no larger than 1 that depends on stratification, bottom friction and horizontal diffusivity. The effect of topography is attenuated (*χ* is reduced) by strong stratification, strong bottom friction, or weak horizontal diffusivity. The circulation equation applies strictly to uniform bottom slope or other topographies obeying ∇^{2}*h*′_{T} = 0, though it approximately holds for ∇^{2}*h*′_{T} ≃ 0, a criterion for which is that the scale of bottom topography greatly exceeds the baroclinic Rossby radius of deformation. It holds only above deep closed circulations. It is remarkable for the form of the characteristic lines for transport, *βy* + *χf*_{0}*h*′_{T}/*H* = constant, and the extra forcing term on the right, which depends on topography.Examples are given of two-layer flows driven by wind-stress curl over east-west and north-south sloping topography. The determination of the boundary of the deep gyre is an implicit nonlinear problem. The solution for the case of east-west slope illustrates the general method for solving such a problem.

#### Recommended Citation

de Szoeke, R. A..
1985.
"Wind-driven mid-ocean baroclinic gyres over topography: A circulation equation extending the Sverdrup relation."
*Journal of Marine Research*
43,
(4).
https://elischolar.library.yale.edu/journal_of_marine_research/1798