An exact, stratified model of a meddy

An exact model to describe submesoscale, coherent vortices in a uniformly stratified fluid is presented. The model allows for stratification of the eddy interior, so as to agree with observations. The closed set of equations governing the evolution of the eddy on the F-plane is derived. In the case that the interior isopycnal surfaces remain horizontal the stratified analogue of the ‘rodon’, a special solution of the ‘lens equations’ that govern the evolution of uniform-density, warm-core surface eddies, is obtained.