Calculations of the stability of some axisymmetric flows proposed as a model of vortex breakdown
We investigate the stability of some axisymmetric wavy flows, which model vortex breakdown, to three-dimensional disturbances viewing the amplitude of the wave as a bifurcation parameter. We will also look at the stability of a set of related, columnar vortex flows which are constructed by taking the two-dimensional flow at a single axial location and extending it throughout the domain without variation. The method of our investigation will be to expand the perturbation velocity in a series of divergence free vectors which ensures that the continuity equation for the incompressible fluid is satisfied exactly by the computed velocity field. Projections of the stability equation onto the space of inviscid vector fields eliminates the pressure term from the equation and reduces the differential eigen problem to a generalized matrix eigen problem. Results are presented both for the one-dimensional, columnar vortex flows and also for the wavy 'bubble' flows.
scientific article; zbMATH DE number 3988953
scientific article