An exact analytical model for the interaction between an isolated shock wave and an isotropic turbulent vorticity field is presented. The interaction with a single-mode two-dimensional (2D) divergence-free vorticity field is analyzed in detail, giving the time and space evolutions of the perturbed quantities downstream. The results are generalized to study the interaction of a planar shock wave with an isotropic three-dimensional (3D) or 2D preshock vorticity field. This field is decomposed into Fourier modes, and each mode is assumed to interact independently with the shock front. Averages of the downstream quantities are made by integrating over the angles that define the orientation of the upstream velocity field. The ratio of downstream/upstream kinetic energies is in good agreement with existing numerical and experimental results for both 3D and 2D preshock vorticity fields. The generation of sound and the sonic energy flux radiated downstream from the shock front is also discussed in detail, as well as the amplification of transverse vorticity across the shock front. The anisotropy is calculated for the far downstream fields of both velocity and vorticity. All the quantities characteristic of the shock-turbulence interaction are reduced to closed-form exact analytical expressions. They are presented as explicit functions of the two parameters that govern the dynamics of the interaction: the adiabatic exponent gamma and the shock Mach number M1 . These formulas are further reduced to simpler exact asymptotic expressions in the limits of weak and strong shock waves (M_{1}-11, M_{1}1) and high shock compressibility of the gas (gamma-->1) .

Richtmyer–Meshkov instability is investigated for negative Atwood number and two-dimensional sinusoidal perturbations by comparing experiments, numerical simulations and analytic theories. The experiments were conducted on the NOVA laser with strong radiatively driven shocks with Mach numbers greater than 10. Three different hydrodynamics codes (RAGE, PROMETHEUS and FronTier) reproduce the amplitude evolution and the gross features in the experiment while the fine-scale features differ in the different numerical techniques. Linearized theories correctly calculate the growth rates at small amplitude and early time, but fail at large amplitude and late time. A nonlinear theory using asymptotic matching between the linear theory and a potential flow model shows much better agreement with the late-time and large-amplitude growth rates found in the experiments and simulations. We vary the incident shock strength and initial perturbation amplitude to study the behaviour of the simulations and theory and to study the effects of compression and nonlinearity.

An analytic theory of the Richtmyer–Meshkov (RM) instability for the case of reflected rarefaction wave is presented. The exact solutions of the linearized equations of compressible fluid dynamics are obtained by the method used previously for the reflected shock wave case of the RM instability and for stability analysis of a ‘‘stand-alone’’ rarefaction wave. The time histories of perturbations and asymptotic growth rates given by the analytic theory are shown to be in good agreement with earlier linear and nonlinear numerical results. Applicability of the prescriptions based on the impulsive model is discussed. The theory is applied to analyze stability of solutions of the Riemann problem, for the case of two rarefaction waves emerging after interaction. The RM instability is demonstrated to develop with fully symmetrical initial conditions of the unperturbed Riemann problem, identically zero density difference across the contact interface both before and after interaction, and zero normal acceleration of the interface. This confirms that the RM instability is not caused by the instant normal acceleration of the interface, and hence, is not a type of Rayleigh–Taylor instability. The RM instability is related to the growth of initial transverse velocity perturbations at the interface, which may be either present initially as in symmetrical Riemann problem, or be induced by a shock passing a corrugated interface.

We present an analytical linear model describing the interaction of a planar shock wave with an isotropic random pattern of density nonuniformities. This kind of interaction is important in inertial confinement fusion where shocks travel into weakly inhomogeneous cryogenic deuterium-wicked foams, and also in astrophysics, where shocks interact with interstellar density clumps. The model presented here is based on the exact theory of space and time evolution of the perturbed quantities generated by a corrugated shock wave traveling into a small-amplitude single-mode density field. Corresponding averages in both two and three dimensions are obtained as closed analytical expressions for the turbulent kinetic energy, acoustic energy flux, density amplification, and vorticity generation downstream. They are given as explicit functions of the two parameters (adiabatic exponent γ and shock strength M(1)) that govern the dynamics of the problem. In addition, these explicit formulas are simplified in the important asymptotic limits of weak and strong shocks and highly compressible fluids.

The classical Richtmyer–Meshkov (RM) instability develops when a planar shock wave interacts with a corrugated interface between two different fluids. A larger family of so-called RM-like hydrodynamic interfacial instabilities is discussed. All of these feature a perturbation growth at an interface, which is driven mainly by vorticity, either initially deposited at the interface or supplied by external sources. The inertial confinement fusion relevant physical conditions that give rise to the RM-like instabilities range from the early-time phase of conventional ablative laser acceleration to collisions of plasma shells (like components of nested-wire-arrays, double-gas-puff Z-pinch loads, supernovae ejecta and interstellar gas). In the laser ablation case, numerous additional factors are involved: the mass flow through the front, thermal conduction in the corona, and an external perturbation drive (laser imprint), which leads to a full stabilization of perturbation growth. In contrast with the classical RM case, mass perturbations can exhibit decaying oscillations rather than a linear growth. It is shown how the early-time perturbation behavior could be controlled by tailoring the density profile of a laser target or a Z-pinch load, to diminish the total mass perturbation seed for the Rayleigh–Taylor instability development.