A unified geostrophic equation with application to a cold core ring

Abstract

The present paper considers a possible extension of previous work on intermediate geostrophic (IG) dynamics and an application to the Gulf Stream cyclonic ring. We generalize the IG equation to the degree at which either total energy or potential enstrophy of a reduced-gravity shallow water fluid system is conserved in time. Some progress is made in this respect and an evolution equation is derived via a perturbation approach using a high-order expansion in the Rossby number. The energy integral expression contains an ageostrophic term which is cubic in the geopotential function and suggests an asymmetric evolution of positive and negative IG vortices. We attempt to model the satellite-observed motions of a cyclonic Gulf Stream ring by using our approximate equation. The result for this example shows the present model to be superior to the quasi-geostrophic model.