Effect of general rotation on Rayleigh–Taylor instability of two superposed fluids with suspended particles

The Rayleigh–Taylor instability of a heavyfluid supported by a lighter one is investigated, with thesuspended dust particles and small uniform general rotation.The fluids are assumed to be incompressible. Thesolutions of the linearized equations of motion using theboundary conditions lead to deriving the dispersion equationin complex formula. The real formula of dispersionrelation has been analyzed and the behavior of growth ratewith respect to the suspended dust particles and componentsof rotation have been examined. The results showthat relaxation frequency of the suspended particles besidethe general rotation will bring about more stability on thegrowth rate of unstable configuration.