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. 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, and. The Coriolis–Stokes forcing on the mean circulation in an Eulerian reference frame was first given by : to be added to the common Coriolis forcing Here is the mean flow velocity in an Eulerian reference frame and is the Stokes drift velocity – provided both are horizontal velocities (perpendicular to ). Further \rho is the fluid density, \times is the cross product operator, where is the Coriolis parameter (with \Omega the Earth's rotation angular speed and \sin\phi the sine of the latitude) 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 with the wave's phase velocity, k the wavenumber, a the wave amplitude and z the vertical coordinate (positive in the upward direction opposing the gravitational acceleration).