Geometric Mechanics of the Vertical Slice Model

TL;DR

This paper explores the geometric mechanics of Vertical Slice Models to understand oceanic frontogenesis and derives wave-current interaction models using variational approaches, highlighting their versatility in ocean dynamics analysis.

Contribution

It introduces a geometric mechanics framework for VSMs and develops new deterministic and stochastic models for wave-current interactions in oceanography.

Findings

Derived multiple variants of wave-current interaction models.

Demonstrated the utility of variational approaches in ocean dynamics.

Provided insights into the dynamics of oceanic front formation.

Abstract

The goals of the present 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.