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.

The mathematical model for the flow velocity in the circumferential ${\displaystyle \theta }$–direction in the Lamb–Oseen vortex is:

with

The radial velocity is equal to zero.

The associated vorticity distribution in the vortex-filament-direction (here ${\displaystyle {\hat {z}}}$) can be found with the curl:

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

where ${\displaystyle r_{\max }(t)={\sqrt {\alpha }}r_{c}(t)}$ is the radius at which ${\displaystyle v_{\max }}$ is attained, and the number α = 1.25643, see Devenport et al.

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