Coriolis–Stokes force

In fluid dynamics, the Coriolis–Stokes force is a forcing of the mean flow in a rotating fluid due to interaction of the Coriolis effect and wave-induced Stokes drift.

This force acts on water independently of the wind stress.

[1] This force is named after Gaspard-Gustave Coriolis and George Gabriel Stokes, two nineteenth-century scientists.

Important initial studies into the effects of the Earth's rotation on the wave motion – and the resulting forcing effects on the mean ocean circulation – were done by Ursell & Deacon (1950), Hasselmann (1970) and Pollard (1970).

[1] The Coriolis–Stokes forcing on the mean circulation in an Eulerian reference frame was first given by Hasselmann (1970):[1] to be added to the common Coriolis forcing

is the mean flow velocity in an Eulerian reference frame and

is the cross product operator,

the Earth's rotation angular speed and

is the unit vector in the vertical upward direction (opposing the Earth's gravity).

Since the Stokes drift velocity

is in the wave propagation direction, and

is in the vertical direction, the Coriolis–Stokes forcing is perpendicular to the wave propagation direction (i.e. in the direction parallel to the wave crests).

In deep water the Stokes drift velocity is

the wave's phase velocity,

the vertical coordinate (positive in the upward direction opposing the gravitational acceleration).