RAYLEIGH-TAYLOR INSTABILITY OF AN ACCELERATED THIN ELASTIC LAYER

S.M. Bakhrach, G.P. Simonov
VANT. Ser.: Mat. Mod. Fiz. Proc 1996. Вып.4. С. 77-84.

      Development of 2D and 3D perturbations of an accelerated thin elastic layer is studied analytically and numerically using the Lagrangian representation of the equation of motion.
      Approximated analytical solutions were produced for the non-linear stage of the process in the space of an observer. Ratios for the increment of the perturbation growth and critical acceleration are provided. Perturbation development as a function of non-dimensional parameters that determine the form of the initial perturbation is studied in detail for 2D perturbations. In particular it was found out that the strength changes the condition of boundedness of the solutions.
      The analytical solutions are compared with results of 2D and 3D computations using a complete system of equations of motion for an elastic medium. It is noted that the analytical solutions and the results of the numerical computations match each other.
      3D perturbations of the elastic layer (at a sufficiently high shear modulus), as opposed to a liquid one, are shown to grow not faster than its 2D perturbations.