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Journal of Experimental and Theoretical Physics

, Volume 89, Issue 3, pp 481–499 | Cite as

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

  • N. A. Inogamov
  • A. M. Oparin
Fluids

Abstract

A boundary separating adjacent gas or liquid media is frequently unstable. Richtmyer-Meshkov and Rayleigh-Taylor instability cause the growth of intricate structures on such boundaries. All the lattice symmetries [rectangular (pmm2), square (p4mm), hexagonal (p6mm), and triangular (p3m1) lattices] which 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 disturbances consisting of one (planar case, two-dimensional flow), two (rectangular cells), or three (hexagons and triangles) harmonic waves. It is shown that the dynamic system undergoes a transition during development from an initial, weakly disturbed state to a limiting or asymptotic stationary state (stationary point). The stability of these points (stationary states) is investigated. It is shown that the stationary states are stable toward large-scale disturbances both in the case of Richtmyer-Meshkov instability and in the case of Rayleigh-Taylor instability. It is discovered that the symmetry increases as the system evolves in certain cases. In one example the initial Richtmyer-Meshkov or Rayleigh-Taylor disturbance is a sum of two waves perpendicular to one another with equal wave numbers, but unequal amplitudes: a1(t=0)≠a2(t=0). Then, during evolution, the flow has p2 symmetry (rotation relative to the vertical axis by 180°), which goes over to p4 symmetry (rotation by 90°) at t→∞, since the amplitudes equalize in the stationary state: a1(t=∞)=a2(t=∞). It is shown that the hexagonal and triangular arrays are complementary. Upon time inversion (t→−t), “rephasing” occurs, and the bubbles of a hexagonal array transform into jets of a triangular array and vice versa.

Keywords

Harmonic Wave Initial Disturbance Array Structure Hexagonal Array Lattice Symmetry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© American Institute of Physics 1999

Authors and Affiliations

  • N. A. Inogamov
    • 1
  • A. M. Oparin
    • 2
  1. 1.L. D. Landau Institute of Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow RegionRussia
  2. 2.Institute of Computer-Aided DesignRussian Academy of SciencesMoscowRussia

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