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# Lamb-Oseen vortex

In Fluid Mechanics, the Lamb-Oseen vortex models a line vortex that decays due to viscosity.

The mathematical model for the velocity in the θ direction in the Lamb-Oseen vortex is:

$V_\theta\ (r) = \frac{\Gamma}{2\pi} \frac{1-e^{-\left (\frac{r}{r_c} \right )^2}}{r}$

r = radius rc = Core radius of vortex Γ = Circulation contained in the vortex

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

$V_\theta\left( r \right) = V_{\theta max} \left( 1 + \frac{0.5}{\alpha} \right) \frac{r_c}{r} \left[ 1 - \exp \left( - \alpha \frac{r^2}{{r_c}^2} \right) \right]$

where α = 1.26 as used in Devenport et al in a 1996 Journal of Fluid Mechanics paper (vol 312, pp67-106).