Number of Ekman

In Mechanical of the fluids, the number of Ekman , according to Vagn Walfrid Ekman (1874-1954), is a positive parameter without unit which gives the relationship between the Viscosité and the forces fictitious (Force of Coriolis and Centrifugal force) in a reference frame in rotation. It is thus a measurement of the attenuation of the movement given to the fluid by rotation.

It is given by the equation:

N_ {Ek} = \ frac {\ naked} {2 \ Omega L^2 \ sin {\ theta '}} = \ sqrt {\ frac {Ro} {Re}}

With:

$\ nu$ kinematic viscosity;
Ω the angular vector frequency;
L the characteristic length;
θ the angle formed between Ω and the Flight Path Vector of the fluid.
Re the Reynolds number
Ro the number of Rossby

One of the uses of the number of Ekman is in the calculation of the reduction and the change of management of the winds close to the ground. Indeed, the roughness of the ground and the viscosity of the fluid are combined to what is called give the Spirale of Ekman. It is about the representation on a radial graph (Hodographe) of the winds of direction and the shifting of speed of this one between the ground and the boundary layer of friction.

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Number of Ekman

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