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| The '''Ekman number''' ('''Ek''') is a [[dimensionless number]] used in describing [[geophysics|geophysical]] phenomena in the [[oceans]] and [[Celestial body atmosphere|atmosphere]]. It characterises the ratio of [[viscosity|viscous]] forces in a [[fluid]] to the [[Coriolis effect|fictitious forces]] arising from [[planet]]ary [[rotation]]. It is named after the [[Sweden|Swedish]] [[oceanographer]] [[Vagn Walfrid Ekman]].
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| More generally, in any rotating flow, the Ekman number is the ratio of viscous forces to [[Coriolis force]]s. When the Ekman number is small, disturbances are able to propagate before decaying owing to frictional effects. The Ekman number 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]].
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| ==Definitions==
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| It is defined as:
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| :<math>\mathrm{Ek}=\frac{\nu}{2D^2\Omega\sin\varphi}</math>
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| - where ''D'' is a characteristic (usually vertical) length scale of a phenomenon; ''ν'', the kinematic [[eddy viscosity]]; Ω, the [[angular velocity]] of [[planet]]ary [[rotation]]; and φ, the [[latitude]]. The term 2 Ω sin φ is the [[Coriolis effect|Coriolis frequency]].
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| It is given in terms of the kinematic viscosity, ''ν''; the angular velocity, Ω; and a characteristic length scale, ''L''.
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| There do appear to be some differing conventions in the literature.
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| Tritton gives:
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| :<math> | |
| \mathrm{Ek} = \frac{\nu}{\Omega L^2}.
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| </math>
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| In contrast, the NRL Plasma Formulary<ref>http://www.ipp.mpg.de/~dpc/nrl/23.html</ref> gives:
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| :<math>
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| \mathrm{Ek} = \sqrt{\frac{\nu}{2\Omega L^2}} = \sqrt{\frac{\mathrm{Ro}}{\mathrm{Re}}}.
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| </math>
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| where Ro is the [[Rossby number]] and Re is the [[Reynolds number]].
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| ==References==
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| {{Reflist}}
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| {{NonDimFluMech}}
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| [[Category:Dimensionless numbers of fluid mechanics]]
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| [[Category:Fluid dynamics]]
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| [[Category:Geophysics]]
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| {{fluiddynamics-stub}}
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Hi several. My name is Maynard and I totally dig that details. Supervising is his day job now. One of what I love most in order to do design but I'm thinking on starting new things. California is the place he loves almost any. She's been working on her behalf website remedied time appropriate now. Check it out here: http://devolro.com/armoring