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The Effect of Surface Tension on the Moore Singularity of Vortex Sheet Dynamics
Authors:F de la Hoz  M A Fontelos  L Vega
Institution:(1) Departamento de Matemática Aplicada, Estadística e Inv. Operativa, Universidad del País Vasco-Euskal Herriko Unibertsitatea, 48080 Bilbao, Spain;(2) Instituto de Matemáticas y Física Fundamental, Consejo Superior de Investigaciones Científicas, C/ Serrano 123, 28006 Madrid, Spain;(3) Departamento de Matemáticas, Universidad del País Vasco-Euskal Herriko Unibertsitatea, 48080 Bilbao, Spain
Abstract:We investigate the regularization of Moore’s singularities by surface tension in the evolution of vortex sheets and its dependence on the Weber number (which is inversely proportional to surface tension coefficient). The curvature of the vortex sheet, instead of blowing up at finite time t 0, grows exponentially fast up to a O(We) limiting value close to t 0. We describe the analytic structure of the solutions and their self-similar features and characteristic scales in terms of the 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.
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