 Stokes drift

Stokes drift is the difference between the mean velocity of moving fluid particles and the mean velocity measured at fixed spatial positions. An oscillating particle samples a slightly different part of the velocity field during each part of its cycle. Correlation between its displacement and the spatial variation of the field can therefore produce a net drift even when the first-order Eulerian coordinate velocity average is zero.

For a small-amplitude deep-water gravity wave with surface elevation $\eta =a\cos (kx-\omega t)$, no imposed mean current and mean particle height $z\le 0$, the leading drift isIt follows the propagation direction and decreases with depth. Its being quadratic in wave amplitude explains why the linear particle orbits nearly close but do not close exactly.^[ref]

A marked fluid particle and a fixed velocity probe measure different averages, so a wave-tank comparison must also account for any compensating return current. Surface float motion can include additional effects from wind or the float's own response. Stokes drift is consequently a precise difference of averages, rather than the name for every observed motion of floating debris.

Stokes drift refers to the phenomenon in fluid dynamics where particles or fluid elements move in a direction slightly different from that of the wave propagation itself due to the non-linear nature of surface waves. This effect is most commonly observed in ocean waves. In a simplified explanation, as a wave travels through the water, it creates circular or elliptical orbital motions of water particles.