THREE-DIMENSIONAL, NONLINEAR, INSTABILITY OF THE BURGERS VORTEX

Burgers' vortex is one of the few analytically known, three-dimensional, vortical solutions to the Navier-Stokes equations. It relies on vortex stretching, thought to be one of the sustaining mechanisms of turbulence. Remarkably, this solution has been shown to be linearly stable. At the same time, there are theoretical indications that families of less symmetric solutions and more realistic equilibrium vortical flows exist near Burgers' solution. We explore the phase space around Burgers' flow by direct numerical simulations of finite-sized perturbations for low and intermediate Reynolds numbers, relying on the finite element code OOMPH-LIB for time-stepping as well as for the computation and continuation of equilibria and their spectra.