Stochastic effects of waves on currents in the ocean mixed layer

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.

arXiv comment33 pages, no figures, 4th version, comments welcome by email

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Cited by in corpus (5)

• Variational Principles on Geometric Rough Paths and the Lévy Area Correction
• Deterministic and Stochastic Euler-Boussinesq Convection
• Variational Stochastic Parameterisations and their Applications to Primitive Equation Models
• A structure preserving stochastic perturbation of classical water wave theory
• Stochastic multisymplectic PDEs and their structure-preserving numerical methods