THEORY OF THE RAYLEIGH-TAYLOR INSTABILITY

The theory of the Rayleigh-Taylor instability of accelerated fluid layers is systematically developed from basic fluid equations. Starting with the classical potential flow theory for moving contact surfaces, the discussion extends to various fluid systems describing inhomogeneous, viscous, compressible, and isobaric flows. Thereby an overview on the major stability issues under a broad variety of physical conditions can be given. In particular, the stability analysis is addressed to layered materials in plane and spherical geometries under various dynamical conditions, to inhomogeneous media with variable gradients and different boundary conditions, to viscous boundary layers, compressible atmospheres, and to stationary ablation fronts in laser-driven plasma experiments. The stability theory is further extended to the nonlinear stage of the Rayleigh-Taylor instability and to a discussion of bubble dynamics in two and three dimensions for closed and open bubble domains. For this purpose simple flow models are studied that can describe essential features of bubble rise and bubble growth in buoyancy-driven mixing layers.