Ekman number

The Ekman number (Ek) is a

.

When the Ekman number is small, disturbances are able to propagate before decaying owing to low frictional effects. The Ekman number also describes the order of magnitude for the thickness of an Ekman layer, a boundary layer in which viscous diffusion is balanced by Coriolis effects, rather than the usual convective inertia.

Definitions

It is defined as:

${\displaystyle \mathrm {Ek} ={\frac {\nu }{2D^{2}\Omega \sin \varphi }}}$

- where D is a characteristic (usually vertical) length scale of a phenomenon; ν, the kinematic

. It is given in terms of the kinematic viscosity, ν; the angular velocity, Ω; and a characteristic length scale, L.

There do appear to be some differing conventions in the literature.

Tritton gives:

${\displaystyle \mathrm {Ek} ={\frac {\nu }{\Omega L^{2}}}.}$

In contrast, the NRL Plasma Formulary^[1] gives:

${\displaystyle \mathrm {Ek} ={\sqrt {\frac {\nu }{2\Omega L^{2}}}}={\sqrt {\frac {\mathrm {Ro} }{\mathrm {Re} }}}.}$

where Ro is the Rossby number and Re is the Reynolds number.

These equations can generally not be used in oceanography. An estimation of the viscous terms of Navier-Stokes equation (with eventually the

) and of the Coriolis terms needs to be done.

References