Abstract
Motion of a fluid interface in Richtmyer-Meshkov instability is examined as a vortex sheet with the use of Birkhoff-Rott equation. This equation coupled with an evolution equation of the strength of the vortex sheet can describe all inviscid and incompressible fluid instabilities, i.e., Kelvin-Helmholtz, Rayleigh-Taylor, and Richtmyer-Meshkov instabilities, when Atwood numbers and initial distribution of vorticities are given. With these equations, detailed motion of a vortex core in the Richtmyer-Meshkov instability is investigated. For the Kelvin-Helmholtz and Rayleigh-Taylor instabilities, it is known that the curvature of a vortex sheet diverges at a finite time t=tc. This fact indicates that the solution loses its analyticity at tc. We show that the singularity formation also occurs in the Richtmyer-Meshkov instability and at the same time, accumulation of vorticity to some points where singularities are formed develops to the roll-up of a sheet when the sheet is regularized. We investigate motion of these accumulation points, i.e., vortex cores, and present that their trajectories and the strengths depend on the Atwood numbers.
Published Version
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