Instabilities of rotating inclined buoyancy layers.

The boundary layer near a cooled inclined plate, which is immersed in a stably stratified fluid rotating about an axis parallel to the direction of gravity, is a model for katabatic flows at high latitudes. In this paper the base flow of such an inclined buoyancy layer is solved analytically for arbitrary Prandtl numbers. By applying linear stability analyses, five unstable modes are identified for both the fixed temperature and the isoflux boundary conditions, i.e., the stationary longitudinal roll (LR) mode, the oblique roll with low streamwise wave-number (OR-1) and high streamwise wave-number (OR-2) modes, and the Tolmien-Schlichting (TS) wave with low streamwise wave-number (TS-1) and high streamwise wave-number (TS-2) modes. It is indicated that the Coriolis effect induced by the rotation leads the critical modes to be three dimensional, and a larger tilt angle of the plate and stronger Coriolis effect cause both TS wave modes to be more unstable for both thermal boundary conditions. When the Coriolis effect is considered, the OR-1 and OR-2 modes are the most unstable mode at low and high tilt angles, respectively, but the TS-1 wave mode may be the most unstable one when the plate is nearly vertical. In addition, the spanwise phase velocities of the TS wave modes change directions as the tilt angle passes some threshold values for both thermal boundary conditions except for the TS-1 wave mode with a fixed temperature boundary condition, which propagates in the same spanwise direction for all explored tilt angles.

Three-dimensional viscous Rayleigh-Taylor instability at the cylindrical interface.

In this paper, the rotational part of the disturbance flow field caused by viscous Rayleigh-Taylor instability (RTI) at the cylindrical interface is considered, and the most unstable mode is revealed to be three-dimensional for interfaces of small radii R. With an increase in R, the azimuthal wave number of the most unstable mode increases step by step, and the corresponding axial wave number increases as well at each step of the azimuthal wave number. When the amplitude of the wave-number vector is much larger or much smaller than 1/R, the cylindrical RTI is close to the semi-infinite planar viscous RTI limit or the finite-thickness creeping-flow RTI limit, respectively. The effect of the viscosity ratio is double-edged; it may enhance or suppress the cylindrical RTI, depending on R and the amplitude range of the wave-number vector.

Origin of lobe and cleft at the gravity current front.

In this Rapid Communication, the Rayleigh-Taylor instability (RTI) along the density interfaces of gravity current fronts is analyzed. Both the location and the spanwise wave number of the most unstable mode determined by the local dispersion relation agree with those of the strongest perturbation obtained from numerical simulations, suggesting that the original formation mechanism of lobes and clefts at the current front is RTI. Furthermore, the predictions of the semi-infinite RTI model, i.e., the original dominating spanwise wave number of the Boussinesq current substantially depends on the Prandtl number and has a 1/3 scaling law with the Grashof number, are confirmed by the three-dimensional numerical simulations.

Unified decomposition method to study Rayleigh-Taylor instability in liquids and solids.

In the previous studies of Rayleigh-Taylor instability, different methods were used to consider the effects of elasticity, viscosity, and magnetic fields. In this paper, a unified method, which was first used for fluids, is validated for different physical models, where the unstable mode is decomposed into an irrotational part and a rotational part, and the latter one includes the effects of nonconservative forces and constitutive relations. Previous results of solid and liquid with or without the effects of magnetic fields and finite thickness can be easily recovered after applying the corresponding interface boundary conditions. In addition, new approximate but analytical solutions of the growth rates for a semi-infinite solid-solid interface and solid-fluid interface are obtained with substantially improved accuracy in comparison with the previous ones.

Retarding viscous Rayleigh-Taylor mixing by an optimized additional mode.

The Rayleigh-Taylor (RT) mixing induced by random interface disturbances between two incompressible viscous fluids is simulated numerically. The ensemble averaged spike velocity is found to be remarkably retarded when the random interface disturbances are superimposed with an optimized additional mode. The mode's wavenumber is selected to be large enough to avoid enhancing the dominance of long-wavelength modes, but not so large that its saturated spike and bubble velocities are too small to stimulate a growing effective density-gradient layer suppressing the long-wavelength modes. Such an optimized suppressing mode is expected to be found in the RT mixing including other diffusion processes, e.g., concentration diffusion and thermal diffusion.

Nonlinear Rayleigh-Taylor instability of rotating inviscid fluids.

It is demonstrated theoretically that the nonlinear stage of the Rayleigh-Taylor instability can be retarded at arbitrary Atwood numbers in a rotating system with the axis of rotation normal to the acceleration of the interface between two uniform inviscid fluids. The Coriolis force provides an effective restoring force on the perturbed interface, and the uniform rotation will always decrease the nonlinear saturation amplitude of the interface at any disturbance wavelength.