Stokes's drift velocity

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Stokes's drift velocity

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
ams2001glos-Se69
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,
ams2001glos-Se70
where a is the wave amplitude, k is the wavenumber vector, k =
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, ω is the wave frequency, z is the vertical coordinate (negative below the ocean surface), and H is the depth of the ocean.