Influid dynamics, theCoriolis–Stokes force is a forcing of themean flow in a rotating fluid due to interaction of theCoriolis effect and wave-inducedStokes drift. This force acts on water independently of thewind stress.^[1]

This force is named afterGaspard-Gustave Coriolis andGeorge Gabriel Stokes, two nineteenth-century scientists. Important initial studies into the effects of theEarth's rotation on thewave motion – and the resulting forcing effects on the meanocean circulation – were done byUrsell & Deacon (1950),Hasselmann (1970) andPollard (1970).^[1]

The Coriolis–Stokes forcing on the mean circulation in anEulerian reference frame was first given byHasselmann (1970):^[1]

${\displaystyle \rho \mathit{f}\times {\mathit{u}}_S,}$

to be added to the common Coriolis forcing${\displaystyle \rho \mathit{f}\times \mathit{u}.}$ Here${\displaystyle \mathit{u}}$ is themeanflow velocity in an Eulerian reference frame and${\displaystyle {\mathit{u}}_S}$ is the Stokes drift velocity – provided both are horizontal velocities (perpendicular to${\displaystyle \hat{\mathit{z}}}$). Further${\displaystyle \rho }$ is the fluiddensity,${\displaystyle \times }$ is thecross product operator,${\displaystyle \mathit{f}=f\hat{\mathit{z}}}$ where${\displaystyle f=2\mathrm{\Omega }\sin \varphi }$ is theCoriolis parameter (with${\displaystyle \mathrm{\Omega }}$ the Earth's rotationangular speed and${\displaystyle \sin \varphi }$ thesine of thelatitude) and${\displaystyle \hat{\mathit{z}}}$ is the unit vector in the vertical upward direction (opposing theEarth's gravity).

Since the Stokes drift velocity${\displaystyle {\mathit{u}}_S}$ is in thewave propagation direction, and${\displaystyle \mathit{f}}$ is in the vertical direction, the Coriolis–Stokes forcing isperpendicular to the wave propagation direction (i.e. in the direction parallel to thewave crests). In deep water the Stokes drift velocity is${\displaystyle {\mathit{u}}_S=\mathit{c}(ka{)}^2\exp (2kz)}$ with${\displaystyle \mathit{c}}$ the wave'sphase velocity,${\displaystyle k}$ thewavenumber,${\displaystyle a}$ the waveamplitude and${\displaystyle z}$ the vertical coordinate (positive in the upward direction opposing the gravitational acceleration).^[1]

• Ekman layer
• Ekman transport

• Fluid dynamics
• Water waves

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