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Let us consider a wind blowing parallel to the surface of a sea. Due to viscosity, deeper layers of the sea will move, with the magnitude of the velocity decreasing with depth. In a rotating frame, like on a spinning planet, the velocity is also affected by the Coriolis force. The governing equations for the two components of the velocity parallel to the surface $u$, $v$ are

$-f v = D \frac{d^2 u}{d z^2}$

$f u = D \frac{d^2 v}{d z^2}$

where $D$ is the viscosity or diffusion coefficient, $f = 2 \Omega \sin \phi$ is the Coriolis parameter, $\Omega$ is the spin frequency and $\phi$ is the latitude. We can express the two components of the velocity as a single complex variable $w = u + i v$

$D \frac{d^2 w}{d z^2} = i f w \Rightarrow w = w_0 \exp \left(- z \sqrt{\frac{f}{2 D}} \right) \left(1+i \right)$

Hence the velocity rotates and declines as the depth $z$ increases. The characteristic distance over which this happens is $\sqrt{D/f}$.