Geometric mechanics of the vertical slice model

Abstract

The goals of this work are to: (i) investigate the dynamics of oceanic frontogenesis by taking advantage of the geometric mechanics underlying the class of Vertical Slice Models (VSMs) of ocean dynamics and (ii) illustrate the versatility and utility of deterministic and stochastic variational approaches by deriving several variants of wave–current interaction models which describe the effects of internal waves propagating within a vertical planar slice embedded in a 3D region of constant horizontal gradient of buoyancy in the direction transverse to the vertical plane.