Recent Development in the Asymptotic Theory of Vortex Breakdown

Abstract

Slender vortex dynamics is dominated by two very different sources of nonlinearity. There is first the nonlinearity inherent in the motion of a vortex filament due to nonlocal self-induction and local curvature effects. Secondly, there is a nonlinear core flow, which produces local axisymmetric breakdown under suitable boundary and initial conditions. Both these aspects of slender vortex dynamics have been studied in the past using tools of matched asymptotic analysis. The non-axisymmetric spiral mode of vortex breakdown appears to be due to an interaction of the core flow and the vortex centerline motion. Thus, it is a challenge to derive a unified formulation in the slender vortex limit which includes both the filament dynamics and nontrivial core structures.