Development of Rayleigh-Taylor and Richtmyer-Meshkov instabilities in three-dimensional space: topology of vortex surfaces

The evolution of the boundary of a liquid during the development of mixing instabilities is studied. The vortex filaments, which transport liquid mass es, are generators of the boundary surface. There is a fundamental differen ce between two-dimensional (2D) and three-dimensional (3D) motions. In the first case the vortices are rectilinear in planar geometry (2D(p)) and ring -shaped in axisymmetric geometry (2D(a)). In the second case the vortices a re very complicated. Spatially periodic ("single-mode") solutions, which ar e important in mixing theory, are investigated. These solutions describe on e-dimensional chains of alternating bubbles and jets in 2D(p) geometry and planar (two-dimensional) arrays or lattices of bubbles and jets in 3D geome try. An analytical description is obtained for the basic types of arrays (r ectangular, hexagonal, and triangular). The analysis agrees with the result s of numerical simulation. (C) 1999 American Institute of Physics. [S0021-3 640(99)00510-1].