Ekman number

Physical key figure
Surname	Ekman number
Formula symbol	${\displaystyle {\mathit {Ek}}}$
dimension	dimensionless
definition	${\displaystyle {\mathit {Ek}}={\frac {\mathit {Ro}}{\mathit {Re}}}}$
${\displaystyle {\mathit {Ro}}}$ Rossby number ${\displaystyle {\mathit {Re}}}$ Reynolds number
Named after	Vagn Walfrid Ekman
scope of application	geophysics

The Ekman number (according to Vagn Walfrid Ekman ) is a dimensionless number of fluid mechanics , which indicates the ratio of viscous forces in a fluid to the Coriolis force : ${\displaystyle {\mathit {Ek}}}$

${\displaystyle {\mathit {Ek}}={\frac {F_{visk}}{F_{C}}}={\frac {\nu }{2\cdot D^{2}\cdot \Omega \cdot \sin \varphi }}={\frac {\mathit {Ro}}{\mathit {Re}}}}$

With

• ${\displaystyle \nu }$: kinematic viscosity
• ${\displaystyle D}$ : characteristic magnitude of the phenomenon
• ${\displaystyle \Omega }$: Angular velocity of the earth's rotation
• ${\displaystyle \varphi }$: the latitude
• ${\displaystyle {\mathit {Ro}}}$: Rossby number
• ${\displaystyle {\mathit {Re}}}$: Reynolds number .

The Ekman number is mainly used in geophysics for oceanographic and atmospheric phenomena to describe the order of magnitude of the thickness of the Ekman layer . This is a boundary layer in which the viscous diffusion is balanced out by the Coriolis effect. For small Ekman numbers, disturbances can propagate before they dissolve due to frictional effects.