Abstract
A model of the spiral wind-up of a vortex sheet by the flow induced by a perpendicular vortex is developed, first in the Euler limit of zero viscosity, then taking account of viscous diffusion. The wind-up of a vortex sheet by a propagating vortex pair is also considered; in this case, the vorticity grows exponentially near the two saddle points of the flow in the moving frame of the vortex pair. Estimates are obtained for the maximum vorticity ω m and maximum enstrophy Ω m attained through this process in terms of the wind-up Reynolds number Re and the initial dimensionless sheet thickness δ 0 . This paper is dedicated to Andrew Soward, whose sustained research in Dynamo Theory and Fluid Mechanics has been brilliantly inspiring for more than 50 years. Happy 80th, Andrew!
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