Three-dimensional array structures associated with Richtmyer-Meshkov and Rayleigh-Taylor instability

A boundary separating adjacent gas or liquid media is frequently unstable. Richtmyer-Meshkov and Rayleigh-Taylor instability cause the growth of intri cate structures on such boundaries. All the lattice symmetries [rectangular (pmm2), square (p4mm), hexagonal (p6mm), and triangular (p3m1) lattices] w hich are of interest in connection with the instability of the surface of a fluid are studied for the first time. They are obtained from initial distu rbances consisting of one (planar case, two-dimensional flow), two (rectang ular cells), or three (hexagons and triangles) harmonic waves. It is shown that the dynamic system undergoes a transition during development from an i nitial, weakly disturbed state to a limiting or asymptotic stationary state (stationary point). The stability of these points (stationary states) is i nvestigated. It is shown that the stationary states are stable toward large -scale disturbances both in the case of Richtmyer-Meshkov instability and i n the case of Rayleigh-Taylor instability. It is discovered that the symmet ry increases as the system evolves in certain cases. In one example the ini tial Richtmyer-Meshkov or Rayleigh-Taylor disturbance is a sum of two waves perpendicular to one another with equal wave numbers, but unequal amplitud es: a(1)(t=0)not equal a(2)(t=0). Then, during evolution, the flow has p2 s ymmetry (rotation relative to the vertical axis by 180 degrees), which goes over to p4 symmetry (rotation by 90 degrees) at t -->infinity, since the a mplitudes equalize in the stationary state: a(1)(t=infinity)=a(2)(t=infinit y). It is shown that the hexagonal and triangular arrays are complementary. Upon time inversion (t -->-t), "rephasing" occurs, and the bubbles of a he xagonal array transform into jets of a triangular array and vice versa. (C) 1999 American Institute of Physics. [S1063-7761(99)01209-3].