Development of Rayleigh-Taylor and Richtmyer-Meshkov instabilities in three-dimensional space: Topology of vortex surfaces
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The evolution of the boundary of a liquid during the development of mixing instabilities is studied. The vortex filaments, which transport liquid masses, are generators of the boundary surface. There is a fundamental difference between two-dimensional (2D) and three-dimensional (3D) motions. In the first case the vortices are rectilinear in planar geometry (2Dp) and ring-shaped in axisymmetric geometry (2Da). In the second case the vortices are very complicated. Spatially periodic (“single-mode”) solutions, which are important in mixing theory, are investigated. These solutions describe one-dimensional chains of alternating bubbles and jets in 2Dp geometry and planar (two-dimensional) arrays or lattices of bubbles and jets in 3D geometry. An analytical description is obtained for the basic types of arrays (rectangular, hexagonal, and triangular). The analysis agrees with the results of numerical simulation.
PACS numbers47.20.−k 47.32.Cc 47.55.Dz
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