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 Ursell & Deacon (1950), Hasselmann (1970) and Pollard (1970).
The Coriolis–Stokes forcing on the mean circulation in an Eulerian reference frame was first given by Hasselmann (1970):
ρ
f
×
u
S
,
to be added to the common Coriolis forcing
ρ
f
×
u
.
Here
u
is the mean flow velocity in an Eulerian reference frame and
u
S
is the Stokes drift velocity – provided both are horizontal velocities (perpendicular to
z
^
). Further
ρ
is the fluid density,
×
is the cross product operator,
f
=
f
z
^
where
f
=
2
Ω
sin
ϕ
is the Coriolis parameter (with
Ω
the Earth's rotation angular speed and
sin
ϕ
the sine of the latitude) and
z
^
is the unit vector in the vertical upward direction (opposing the Earth's gravity).
Since the Stokes drift velocity
u
S
is in the wave propagation direction, and
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
u
S
=
c
(
k
a
)
2
exp
(
2
k
z
)
with
c
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).
