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Coriolis–Stokes force - Wikipedia

  • ️Tue Aug 08 2017

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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]

{\displaystyle \rho {\boldsymbol {f}}\times {\boldsymbol {u}}_{S},}

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

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

  1. ^ a b c d Polton, J.A.; Lewis, D.M.; Belcher, S.E. (2005), "The role of wave-induced Coriolis–Stokes forcing on the wind-driven mixed layer" (PDF), Journal of Physical Oceanography, 35 (4): 444–457, Bibcode:2005JPO....35..444P, CiteSeerX 10.1.1.482.7543, doi:10.1175/JPO2701.1, archived from the original (PDF) on 2017-08-08, retrieved 2009-03-31