The dynamics of stretched vortices

Abstract

The dynamics of vortices subject to stretching by a uniform plane straining flow is studied asymptotically and by means of a new class of exact solutions. The asymptotic analysis treats the stretched Burger's vortex sheet for strain rates much greater than the gradient of the sheet strength. It is found that portions of the sheet where the strength density is sufficiently large compared to (viscosity x strain rate)½ will collapse to form concentrated vortices. The exact solutions describe uniform vortices of elliptical cross-section in inviscid fluid subject to stretching parallel to their axes. These solutions complement the description of vortex collapse found by asymptotic methods. The relevance of these results stems from the prevalence of vortex structures subject to strain in turbulent flows.