Overturned internal capillary-gravity waves
نویسندگان
چکیده
A vortex sheet formulation of irrotational, incompressible Euler flow is used to compute periodic traveling waves at the interface between two constant-density, two-dimensional fluids, including waves with overturned crests. Branches of traveling waves are computed via numerical continuation, which are jointly continuous in the physical parameters: Bond number, Atwood number and mean shear. Global branches are computed, for various choices of parameters, illustrating the termination criteria of the global bifurcation theorem of [1]. Small amplitude asymptotics of traveling waves are calculated. The role of the wave’s second harmonic in determining crest/trough shape is discussed. Waves of extremal displacement and those approaching self-intersection are computed. Surfaces in parameter space indicating where traveling waves exist are computed; these surfaces themselves have both overturned and self-intersecting boundaries.
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