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 \(\theta\)–direction in the Lamb–Oseen vortex is:

\[V_\theta(r,t) = \frac{\Gamma}{2\pi r} \left(1-\exp\frac{-r^2}{r_c^2(t)}\right), \]

with

• \(r\) = radius,
• \(\nu\) = viscosity,
• \(r_c(t)=\sqrt{4\nu t}\) = core radius of vortex 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

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

where α = 1.25643 as used by Devenport et al.