Stochastic effects of waves on currents in the ocean mixed layer

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