On the Evolution of an Angle in a Vortex Patch
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The inviscid incompressible two-dimensional motion of some initially convex singular vortex patches is examined. The angles evolution of a tangent-slope discontinuity on a singular contour is studied from a numerical and theoretical point of view. Different numerical examples show that the angle shrinks for initial angle less than 90o, and the angle widens when the initial angle is greater than 90o or is “approximately” preserved for initial angle 90o for small time evolution. An asymptotic expansion of the initial velocity field near a singularity for a class of singular vortex patches is performed to reinforce this result analytically. Some initially nonconvex singular patches in which the evolution does not follow this rule are shown.
KeywordsEuler Equation Lipschitz Function Initial Angle Initial Contour Vortex Method
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