The breakdown of a line vortex
Abstract
The conditions giving rise to a singularity in solutions to quasicylindrical approximation equations for a line vortex are investigated. The breakdown of the vortex is treated as a transition from the supercritical state to the subcritical state at lengths of the order of the vortex radius. The conditions under which the singularity and the criticality criteria are the same are determined. A classification of possible singularities is proposed, and it is shown that in the general case, with a given longitudinal external pressure gradient, the solution in the vicinity of the singularity cannot be continued beyond the singular point.
 Publication:

Prikladnaia Matematika i Mekhanika
 Pub Date:
 April 1985
 Bibcode:
 1985PriMM..49..220T
 Keywords:

 Computational Fluid Dynamics;
 Singularity (Mathematics);
 Supercritical Flow;
 Vortex Breakdown;
 Vortex Filaments;
 Vorticity Equations;
 Flow Velocity;
 Pipe Flow;
 Pressure Gradients;
 Subcritical Flow;
 Fluid Mechanics and Heat Transfer