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.

Mathematical description

looked for a solution for the Navier-Stokes equations in cylindrical coordinates with velocity components of the form
where is the circulation of the vortex core. This lead Navier-Stokes equations to reduce to
which when is subjected to the conditions that is regular at and becomes unity as, leads to
where is the kinematic viscosity of the fluid. At, 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

Generalized Oseen vortex

The generalized Oseen vortex may obtained by looking for solutions of the form
that leads to the equation
Self-similar solution exists for the coordinate, provided, where is a constant, in which case. The solution for may be written according to Rott as
where is an arbitrary constant. For, the classical Lamb-Oseen vortex is recovered. The case corresponds to the axisymmetric stagnation point flow, where is a constant. When,, a Burgers vortex is a obtained. For arbitrary, the solution becomes , where is an arbitrary constant. As, Burgers vortex is recovered.