Lamb–Oseen vortex - Alchetron, The Free Social Encyclopedia

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.

The mathematical model for the flow velocity in the circumferential θ –direction in the Lamb–Oseen vortex is:

V θ ( r , t ) = Γ 2 π r ( 1 − exp ⁡ ( − r 2 r c 2 ( t ) ) ) ,

with

r = radius,

r c ( t ) = 4 ν t = core radius of vortex,

ν = viscosity, and

Γ = circulation contained in the vortex.

The radial velocity is equal to zero.

The associated vorticity distribution in the vortex-filament-direction (here z ^ ) can be found with the curl:

ω z ( r , t ) = Γ π r c ( t ) 2 exp ⁡ ( − r 2 r c 2 ( t ) ) ,

An alternative definition is to use the peak tangential velocity of the vortex rather than the total circulation

V θ ( r ) = V θ max ( 1 + 1 2 α ) r max r [ 1 − exp ⁡ ( − α r 2 r max 2 ) ] ,

where r max ( t ) = α 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

∂ p ∂ r = ρ v 2 r ,

where ρ is the constant density

References

Lamb–Oseen vortex Wikipedia

(Text) CC BY-SA