SELF-GRAVITATING INSTABILITY OF TRIPLE SUPERPOSED FLUIDS OF DIFFERENTDENSITIES WITH PLANE INTERFACES

The problem of two superposed fluids is formulated and the self-gravit ating hydrodynamic basic equations are solved. Upon appropriate bounda ry conditions, a general eigenvalue relation is derived and discussed The stability states are identified as rho' < rho, rho' = rho and rho' > rho where rho' and rho are the densities of the self-gravitating su perposed fluids. The analytical results are confirmed numerically and it is found that rho'/rho is stabilizing according to restrictions. A physical interpretation has been declared to some new parameters. In p art B the governed equations of the perturbed and unperturbed states a re solved. Their solutions satisfy certain conditions across the fluid s plane interfaces. A cumbersome stability criterion is derived based on the linear perturbation technique of normal mode analysis. Several limiting cases could be recovered with some simplifications. The (in-) stability restrictions are identified for several different values of the densities ratios of the three superposed fluid layers.