ANALYTICAL AND NUMERICAL STUDY OF RALEIGH-TAYLOR INSTABILITY FOR A THIN LIQUID LAYER

S.M. Bakhrakh, G.P. Simonov
VANT. Ser.: Mat. Mod. Fiz. Proc 1997. Вып.1. С. 42.

      Using the Lagrangian representation for equations of dynamics of an accelerated thin liquid layer the analytic solutions are found for the problem of Raleigh-Taylor instability at the process stage non-linear in the observer’s space. Evolution of various perturbation types in layer shape and component velocities is considered. It is shown that there are both exponentially growing and limited, oscillating solutions.
      This analysis is also important at consideration of Raleigh-Taylor instability regarding a relatively thick layer. This is substantiated with the results of numerical studies of compressible ideal fluid semi-space interface perturbation evolution. It is noted that there are qualitative differences between the cases when perturbations are given in semi-space interface shape and initial velocity form.
      The work was carried out under the auspices of International Science and Technology Center (grant NM-4000) and Russian Fundamental Research Foundation (project N 96-01-00043).

      Analytical solutions of the problem of Raleigh-Taylor instability for a thin liquid layer in 3-D formulation at the stage non-linear in the space of the observer are obtained. Lagrangian representation is used for the equations of accelerated layer dynamics. Evolution of perturbations both in the layer shape and in velocities of layer elements is studied, Solutions depending on initial perturbation shape and amplitude are found. Existence of both exponentially growing and limited solutions is shown.