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Lamb–Oseen vortex : ウィキペディア英語版
Lamb–Oseen vortex
In fluid dynamics, the Lamb–Oseen vortex models a line vortex that decays due to viscosity. This vortex is named after Horace Lamb and Carl Wilhelm Oseen.〔 p. 253.〕
The mathematical model for the flow velocity in the circumferential \theta–direction in the Lamb–Oseen vortex is:
:V_\theta(r,t) = \frac \left(1-\exp\left(-\frac\right)\right),
with
*r = radius,
*r_c(t)=\sqrt = core radius of vortex,
*\nu = viscosity, and
*\Gamma = circulation contained in the vortex.
The radial velocity is equal to zero.
An alternative definition is to use the peak tangential velocity of the vortex rather than the total circulation
:V_\theta\left( r \right) =
V_ \left( 1 + \frac \right)
\frac
\left(1 - \exp \left( - \alpha \frac \right)
\right
),

where r_\max (t)=\sqrt r_c(t) is the radius at which v_\max is
attained, and the number ''α'' = 1.25643, see Devenport et al.
The pressure field simply ensures the vortex rotates in the circumferential direction, providing the centripetal force
: = \rho ,

where ''ρ'' is the constant density
==References==



抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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