Stokes' drift: a rocking ratchet

TL;DR

This paper derives an explicit formula for Stokes' drift under dichotomic Markov forcing, revealing how amplitude and frequency influence drift enhancement, reduction, or reversal in a one-dimensional system.

Contribution

It provides the first explicit analytic expression for Stokes' drift with dichotomic Markov forcing, analyzing the effects of amplitude and frequency on drift behavior.

Findings

Small forcing amplitudes enhance drift.

Increasing forcing frequency reduces drift enhancement.

Large amplitudes can cause drift reduction or flux reversal.

Abstract

We derive the explicit analytic expression for the Stokes' drift in one dimension in the presence of a dichotomic Markov forcing. For small amplitudes of the forcing, the drift is enhanced, but the enhancement is reduced with increasing frequency of the forcing. On the other hand, a reduction of the drift or even a flux reversal can be induced at larger amplitudes, while the flux is now found to be an increasing function of the perturbation frequency.