Ekman Layer - Mathematical Formulation

Mathematical Formulation

The mathematical formulation of the Ekman layer can be found by assuming a neutrally stratified fluid, with horizontal momentum in balance between the forces of pressure gradient, Coriolis and turbulent drag.

\begin{align} -fv &= -\frac{1}{\rho_o} \frac{\part p}{\part x}+K_m \frac{\part^2 u}{\part z^2}, \\ fu &= -\frac{1}{\rho_o} \frac{\part p}{\part y}+K_m \frac{\part^2 v}{\part z^2}, \\ 0 &= -\frac{1}{\rho_o} \frac{\part p}{\part z}, \end{align}

where and are the velocities in the and directions, respectively, is the local Coriolis parameter, and is the diffusive eddy viscosity, which can be derived using mixing length theory.

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