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.

[1][2] Oseen looked for a solution for the Navier–Stokes equations in cylindrical coordinates

with velocity components

is the circulation of the vortex core.

Navier-Stokes equations lead to which, subject to the conditions that it is regular at

is the kinematic viscosity of the fluid.

, we have a potential vortex with concentrated vorticity at the

axis; and this vorticity diffuses away as time passes.

The only non-zero vorticity component is in the

direction, given by The pressure field simply ensures the vortex rotates in the circumferential direction, providing the centripetal force where ρ is the constant density[4] The generalized Oseen vortex may be obtained by looking for solutions of the form that leads to the equation Self-similar solution exists for the coordinate

φ ( t )

φ

φ ′

φ

is a constant, in which case

may be written according to Rott (1958)[5] as where

is an arbitrary constant.

, the classical Lamb–Oseen vortex is recovered.

corresponds to the axisymmetric stagnation point flow, where

, a Burgers vortex is a obtained.

is an arbitrary constant.

, Burgers vortex is recovered.