Exact, approximate, and hybrid treatments of viscous Rayleigh-Taylor and Richtmyer-Meshkov instabilities.

We consider Rayleigh-Taylor and Richtmyer-Meshkov instabilities at the interface between two fluids, one or both of which may be viscous. We derive exact analytic expressions for the amplitude η(t) in the linear regime when only one of the fluids is viscous. The more general case is solved numerically using Laplace transforms.

Viscous Rayleigh-Taylor instability in spherical geometry.

We consider viscous fluids in spherical geometry, a lighter fluid supporting a heavier one. Chandrasekhar [Q. J.

Solution to Rayleigh-Taylor instabilities: Bubbles, spikes, and their scalings.

When a fluid pushes on and accelerates a heavier fluid, small perturbations at their interface grow with time and lead to turbulent mixing. The same instability, known as the Rayleigh-Taylor instability, operates when a heavy fluid is supported by a lighter fluid in a gravitational field. It has a particularly deleterious effect on inertial-confinement-fusion implosions and is known to operate over 18 orders of magnitude in dimension.

Analytic approach to nonlinear hydrodynamic instabilities driven by time-dependent accelerations.

We extend our earlier model for Rayleigh-Taylor and Richtmyer-Meshkov instabilities to the more general class of hydrodynamic instabilities driven by a time-dependent acceleration g(t). Explicit analytic solutions for linear as well as nonlinear amplitudes are obtained for several g(t)s by solving a Schrödinger-like equation d(2)eta/dt(2)-g(t)kAeta=0, where A is the Atwood number and k is the wave number of the perturbation amplitude eta(t). In our model a simple transformation k-->k(L) and A-->A(L) connects the linear to the nonlinear amplitudes: eta(nonlinear)(k,A) approximately (1/k(L))ln eta(linear)(k(L),A(L)).

Nonlinear hydrodynamic interface instabilities driven by time-dependent accelerations.

We present a model for nonlinear hydrodynamic instabilities of interfaces and the formation of bubbles driven by time-dependent accelerations g(t) . To obtain analytic solutions, we map the equation for the bubble amplitude eta(t) onto the Schrödinger equation and solve it as an initial value (eta_{0},eta[over ]_{0}) problem in time instead of an eigenvalue problem in space. Very good agreement is obtained with full hydrodynamic simulations.

Limitations and failures of the Layzer model for hydrodynamic instabilities.

We report several limitations and failure modes of the recently expanded Layzer model for hydrodynamic instabilities. The failures occur for large initial amplitudes, for stable accelerations, and for spikes in two-fluid systems.

Explicit expressions for the evolution of single-mode Rayleigh-Taylor and Richtmyer-Meshkov instabilities at arbitrary Atwood numbers.

We present explicit analytic expressions for the evolution of the bubble amplitude in Rayleigh-Taylor (RT) and Richtmyer-Meshkov RM instabilities. These expressions are valid from the linear to the nonlinear regime and for arbitrary Atwood number A. Our method is to convert from the linear to the nonlinear solution at a specific value eta* of the amplitude for which explicit analytic expressions have been given previously for A=1 [K.