Current-vortex-sheet model of the magnetic Rayleigh-Taylor instability.

This study investigates the Rayleigh-Taylor instability in the magnetic field applied parallel to the interface. The motion of the interface is described using a current-vortex-sheet model. The growth rate of the interface is obtained from a linear stability analysis of the model.

Motion of a current-vortex sheet in the magnetic Kelvin-Helmholtz instability.

In this paper, we consider the Kelvin-Helmholtz instability in the magnetohydrodynamic flow. The motion of the interface is described by a current-vortex sheet. We examine the linear stability of the current-vortex sheet model and determine the growth rate of the interface.

Stability of barotropic vortex strip on a rotating sphere.

We study the stability of a barotropic vortex strip on a rotating sphere, as a simple model of jet streams. The flow is approximated by a piecewise-continuous vorticity distribution by zonal bands of uniform vorticity. The linear stability analysis shows that the vortex strip becomes stable as the strip widens or the rotation speed increases.

Long-time simulations of the Kelvin-Helmholtz instability using an adaptive vortex method.

The nonlinear evolution of an interface subject to a parallel shear flow is studied by the vortex sheet model. We perform long-time computations for the vortex sheet in density-stratified fluids by using the point vortex method and investigate late-time dynamics of the Kelvin-Helmholtz instability. We apply an adaptive point insertion procedure and a high-order shock-capturing scheme to the vortex method to handle the nonuniform distribution of point vortices and enhance the resolution.

Effects of surface tension and viscosity on the growth rates of Rayleigh-Taylor and Richtmyer-Meshkov instabilities.

We present an analytical model for unstable interfaces with surface tension in fluids of arbitrary viscosity. Linear and nonlinear asymptotic solutions are obtained for growth rates of Rayleigh-Taylor and Richtmyer-Meshkov instabilities. In Rayleigh-Taylor instability, both surface tension and viscosity decrease the asymptotic bubble velocity.

Quantitative modeling of bubble competition in Richtmyer-Meshkov instability.

We present a quantitative model for the evolution of single and multiple bubbles in the Richtmyer-Meshkov (RM) instability. The higher-order solutions for a single-mode bubble are obtained, and distinctions between RM and Rayleigh-Taylor bubbles are investigated. The results for multiple-bubble competition from the model shows that the higher-order correction to the solution of the bubble curvature has a large influence on the growth rate of the RM bubble front.

Bubble interaction model for hydrodynamic unstable mixing.

The analytic model for the evolution of single and multiple bubbles in Rayleigh-Taylor mixing is presented for the system of arbitrary density ratio. The model is the extension of Zufiria's potential theory, which is based on the velocity potential with point sources. We present solutions for a single bubble, at various stages, from the model and show that the solutions for the bubble velocity and curvature are in good agreement with numerical results.

Density dependence of a Zufiria-type model for Rayleigh-Taylor bubble fronts.

We present the analytic model for the evolution of bubbles of arbitrary density ratio in Rayleigh-Taylor and Richtmyer-Meshkov instabilities. The model is the generalization of Zufiria's potential theory, which is based on the velocity potential with a point source and previously applied only for the interface of infinite density ratio. The analytic expressions for asymptotic solutions of bubbles are obtained.

Vortex model and simulations for Rayleigh-Taylor and Richtmyer-Meshkov instabilities.

The vortex method is applied to simulations of Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities. The numerical results from the vortex method agree well with analytic solutions and other numerical results. The bubble velocity in the RT instability converges to a constant limit, and in the RM instability, the bubble and spike have decaying growth rates, except for the spike of infinite density ratio.

Simple potential-flow model of Rayleigh-Taylor and Richtmyer-Meshkov instabilities for all density ratios.

We generalize the Layzer-type model for unstable interfaces to the system of arbitrary density ratio. The predictions from the generalized model for bubble growth rates of Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities are in good agreement with numerical results. We present the theoretical prediction for asymptotic growth rates for RT and RM bubbles for finite density ratios in two and three dimensions.