A Compact Eulerian Representation of Axisymmetric Inviscid Vortex Sheet Dynamics
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Abstract
A classical problem in fluid mechanics is the motion of an axisymmetric
vortex sheet evolving under the action of surface tension, surrounded by an
inviscid fluid. Lagrangian descriptions of these dynamics are well-known,
involving complex nonlocal expressions for the radial and longitudinal
velocities in terms of elliptic integrals. Here we use these prior results to
arrive at a remarkably compact and exact Eulerian evolution equation for the
sheet radius
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1097-0312
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Engineering and Physical Sciences Research Council (EP/I036060/1)