# Stochastic Stokes' Drift

*Physical Review Letters*
**81** 3136 (1998)

#### Kalvis M Jansons

Department of Mathematics, University College London.

Gower Street WC1E 6BT, England.
#### Grant D Lythe

GISC,
Departamento de Matemáticas

Universidad Carlos III de Madrid

Avenida de la Universidad 30

28911 Leganés, Madrid, Spain

## Abstract

Classical Stokes' drift is the small time-averaged drift
velocity of suspended non-diffusing particles in a fluid due to the
presence of a wave. We consider the effect of adding diffusion to the
motion of the particles, and show in particular that a non-zero
time-averaged drift velocity exists in general even when the classical
Stokes' drift is zero. Our results are obtained from a general
procedure for calculating ensemble-averaged Lagrangian mean velocities
for motion that is close to Brownian, and are verified by numerical
simulations in the case of sinusoidal forcing.