Ekman number#

Named after: Vagn Walfrid Ekman (1874-1954).

$$\text{Ek} \stackrel{\text{def}}{=} \frac{\nu}{\Omega L^{2}} \sim \frac{\text{viscous diffusion}}{\text{rotation}}$$

Measures viscous diffusion relative to rotational effects. It indicates the importance of viscous boundary layers in rotating flows.

Name	Symbol	SI units	Dimension
kinematic viscosity	$\nu$	$\mathrm{m}^{2}\,\mathrm{s}^{-1}$	$\text L^{2}\,\text T^{-1}$
angular velocity	$\Omega$	$\mathrm{Hz}$	$\text T^{-1}$
characteristic length	$L$	$\mathrm{m}$	$\text L$

Rotating flow

Range	Regime	Description
0 – 0.01	rotation dominated	Rotation is strong compared with viscous diffusion. Thin Ekman layers control boundary adjustment.
0.01 – 1	mixed viscous-rotating	Viscous diffusion and rotation both influence the flow over the characteristic length.
1 – ∞	viscous dominated	Viscous diffusion acts faster than rotational adjustment. Rotation has a weak dynamical effect.

Name	Symbol	SI units	Dimension
kinematic viscosity	\(\nu\)	\(\mathrm{m}^{2}\,\mathrm{s}^{-1}\)	\(\text L^{2}\,\text T^{-1}\)
angular velocity	\(\Omega\)	\(\mathrm{Hz}\)	\(\text T^{-1}\)
characteristic length	\(L\)	\(\mathrm{m}\)	\(\text L\)