The Effect of Surface Tension on the Moore Singularity of Vortex Sheet Dynamics

We investigate the regularization of Moore's singularities by surface tension in the evolution of vortex sheets and its dependence on Weber number (which is inversely proportional to surface tension coefficient). The curvature of the vortex sheet, instead of blowing-up at finite time t0, grows exponentially fast up to a O(We) limiting value close to t0. We describe the analytic structure of the solutions and their selfsimilar features and characteristic scales in terms of Weber number in a O(We-1 ) neighborhood of the time at which, in absence of surface tension effects, Moore's singularity would appear. Our arguments rely on asymptotic techniques and are supported by full numerical simulations of the PDEs describing the evolution of vortex sheets.

• Type: Journal
• Year: 2008
• Where: JNS
• Authors: Francisco de la Hoz, M. A. Fontelos, L. Vega
• Keywords: JNS 2008, Surface Tension, Vortex Sheets, Weber Number