A Form of Potential Vorticity Equation for Depth-Integrated Flow with a Free Surface

Chris W. Hughes Proudman Oceanographic Laboratory, Liverpool, United Kingdom

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Abstract

A form of linear, barotropic potential vorticity equation is derived for an ocean with a free surface, in which only one scalar variable appears (ocean bottom pressure, or subsurface pressure). Unlike quasigeostrophic or rigid-lid derivations, the only approximation made (apart from linearization) is that changes in the circulation must be slow compared with the inertial frequency. Effects of stratification are included, but only parametrically in the sense that density is treated as a given quantity or forcing term rather than a variable.

Corresponding author address: Chris W. Hughes, Proudman Oceanographic Laboratory, 6 Brownlow St., Liverpool L3 5DA, United Kingdom. Email: cwh@pol.ac.uk

Abstract

A form of linear, barotropic potential vorticity equation is derived for an ocean with a free surface, in which only one scalar variable appears (ocean bottom pressure, or subsurface pressure). Unlike quasigeostrophic or rigid-lid derivations, the only approximation made (apart from linearization) is that changes in the circulation must be slow compared with the inertial frequency. Effects of stratification are included, but only parametrically in the sense that density is treated as a given quantity or forcing term rather than a variable.

Corresponding author address: Chris W. Hughes, Proudman Oceanographic Laboratory, 6 Brownlow St., Liverpool L3 5DA, United Kingdom. Email: cwh@pol.ac.uk

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