ON GRAVITATIONAL INSTABILITY OF A TWO-LAYER MODEL FOR VISCOUS INCOMPRESSIBLE FLUID WITH STOCHASTIC CHANGES IN DENSITYB. M. Naimark and A. T. Ismail-zadeh
The fine structure of the crust and the upper mantle is not known in much detail. Only some average values, say, of density or wave velocity can be specified in various models. We study gravitational instability in a two-layer nondeterministic model with Newtonian rheology. The density in the upper layer is random, and the density in the lower layer (half-space) is deterministic. We take the density depending on depth only. An inversion in the mean density is assumed. An integro-differential equation is derived for mean velocities, and the boundary conditions are usual for a Newtonian fluid. Using the Laplace transform techniques, this problem is reduced to the calculation of roots of an analytic function. To compute the roots a program was used based on the principle of the argument. Variations of eigenvalues were computed for several sets of parameters. The existence of oscillatory instability is shown for some ranges of stochastic parameters.