Multiple oscillating layers of a double-perturbed interface with self-gravitate.

Abstract

The multiple oscillating layers of a double perturbed interface under self-gravitating has been investigated for all the perturbation modes. This type of research may be found to examine oscillating on multiple layers with self-gravitating force. The stability criterion is constructed analytically explained and confirmed these results with the numerical computations. The governing equations (equation of motion and equation of continuous) are obtained, providing that the boundary conditions are appropriate. the fundamental equations are resolved, non-singular solutions are found using the proper boundary circumstances, also, derived the total second order differential equation. The difference between these two states, stable and unstable, relies on the value of densities. In this point, the gravitational instability of the current model, which forms the basis of this work, will be decreased, The streaming is unstable. The gravitationally stable and unstable zones are discovered and graphically displayed. The triple fluid layers' weight force and densities ratios contribute significantly to the unstable nature of the current model.