Stochastic effects of waves on currents in the ocean mixed layer

TL;DR

This paper develops an energy-preserving stochastic model, SFLT, to analyze wave effects on ocean currents, demonstrating its application across various fluid dynamics scenarios and introducing an averaged version for enhanced analysis.

Contribution

It introduces the SFLT model derived from a variational principle, preserving energy and Kelvin circulation, and extends it with an Eulerian-averaged version for studying wave-current interactions.

Findings

SFLT captures stochastic wave effects on currents in different fluid models.

The Eulerian-averaged SFLT provides a new approach for analyzing fluctuations.

Model preserves energy and circulation properties in stochastic settings.

Abstract

This paper introduces an energy-preserving stochastic model for studying wave effects on currents in the ocean mixing layer. The model is called stochastic forcing by Lie transport (SFLT). The SFLT model is derived here from a stochastic constrained variational principle, so it has a Kelvin circulation theorem. The examples of SFLT given here treat 3D Euler fluid flow, rotating shallow water dynamics and the Euler-Boussinesq equations. In each example, one sees the effect of stochastic Stokes drift and material entrainment in the generation of fluid circulation. We also present an Eulerian-averaged SFLT model (EA SFLT), based on decomposing the Eulerian solutions of the energy-conserving SFLT model into sums of their expectations and fluctuations.