Physics:Coriolis–Stokes force

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Short description: Concept in fluid dynamics

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), (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]

[math]\displaystyle{ \rho\boldsymbol{f}\times\boldsymbol{u}_S, }[/math]

to be added to the common Coriolis forcing [math]\displaystyle{ \rho\boldsymbol{f}\times\boldsymbol{u}. }[/math] Here [math]\displaystyle{ \boldsymbol{u} }[/math] is the mean flow velocity in an Eulerian reference frame and [math]\displaystyle{ \boldsymbol{u}_S }[/math] is the Stokes drift velocity – provided both are horizontal velocities (perpendicular to [math]\displaystyle{ \hat{\boldsymbol{z}} }[/math]). Further [math]\displaystyle{ \rho }[/math] is the fluid density, [math]\displaystyle{ \times }[/math] is the cross product operator, [math]\displaystyle{ \boldsymbol{f}=f\hat{\boldsymbol{z}} }[/math] where [math]\displaystyle{ f=2\Omega\sin\phi }[/math] is the Coriolis parameter (with [math]\displaystyle{ \Omega }[/math] the Earth's rotation angular speed and [math]\displaystyle{ \sin\phi }[/math] the sine of the latitude) and [math]\displaystyle{ \hat{\boldsymbol{z}} }[/math] is the unit vector in the vertical upward direction (opposing the Earth's gravity).

Since the Stokes drift velocity [math]\displaystyle{ \boldsymbol{u}_S }[/math] is in the wave propagation direction, and [math]\displaystyle{ \boldsymbol{f} }[/math] 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 [math]\displaystyle{ \boldsymbol{u}_S=\boldsymbol{c}\,(ka)^2\exp(2kz) }[/math] with [math]\displaystyle{ \boldsymbol{c} }[/math] the wave's phase velocity, [math]\displaystyle{ k }[/math] the wavenumber, [math]\displaystyle{ a }[/math] the wave amplitude and [math]\displaystyle{ z }[/math] the vertical coordinate (positive in the upward direction opposing the gravitational acceleration).[1]

See also


  1. 1.0 1.1 1.2 1.3 Polton, J.A.; Lewis, D.M.; Belcher, S.E. (2005), "The role of wave-induced Coriolis–Stokes forcing on the wind-driven mixed layer", Journal of Physical Oceanography 35 (4): 444–457, doi:10.1175/JPO2701.1, Bibcode2005JPO....35..444P,, retrieved 2009-03-31