Stokes's drift velocity
From Glossary of Meteorology
The average velocity of a fluid particle in wave motion of infinitesimal amplitude.
To the order of the square of the wave amplitude, it is 
, ω is the wave frequency, z is the vertical coordinate (negative below the ocean surface), and H is the depth of the ocean.
where <·> represents the average over a wave period, t is time, u is the local (Eulerian) velocity of the wave motion, and x is the position of the fluid particle at t = t0. As an example, for surface gravity waves of a homogeneous ocean with a flat bottom,
where a is the wave amplitude, k is the wavenumber vector, k =
, ω is the wave frequency, z is the vertical coordinate (negative below the ocean surface), and H is the depth of the ocean.
