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


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.


Harmonic Wave Initial Disturbance Array Structure Hexagonal Array Lattice Symmetry 
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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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