SELF-GRAVITATING INSTABILITY OF 2 SEMIINFINITE STREAMING SUPERPOSED FLUIDS ENDOWED WITH SURFACE-TENSION

The capillary instability of self-gravitating superposed streaming flu ids of different densities with plane intel face has been developed. S ome reported works are recovered as limiting cases. The streaming has a strong stabilizing influence. The influence of the surface tension i s found here as was obtained by (Hydrodynamic and Hydromagnetic Stabil ity, (Oxford University Press) 1961) in the absence of the self-gravit ating force. The latter is stabilizing or destabilizing according to s ome restrictions on the ratio of the densities rho and rho' of the sup erposed fluids. As rho' = rho, it was found that there is no dispersio n and the resulting homogeneous self-gravitating system is marginally stable. The analytical (in)stability results are confirmed numerically for different values of rho'/rho.