Studying Hydrodynamic Instability Using Shock-Tube Experiments

The hydrodynamic instability, which develops on the contact surface between two fluids, has great importance in astrophysical phenomena such as the inhomogeneous density distribution following a supernova event. In this event acceleration waves pass across a material interface and initiate and enhance unstable conditions in which small perturbations grow dramatically. In the present study, an experimental technique aimed at investigating the above-mentioned hydrodynamic instability is presented. The experimental investigation is based on a shock-tube apparatus by which a shock wave is generated and initiates the instability that develops on the contact surface between two gases. The flexibility of the system enables one to vary the initial shape of the contact surface, the shock-wave Mach number, and the density ratio across the contact surface. Three selected sets of shock-tube experiments are presented in order to demonstrate the system capabilities: (1) large-initial amplitudes with low-Mach-number incident shock waves; (2) small-initial amplitudes with moderate-Mach-number incident shock waves; and (3) shock bubble interaction. In the large-amplitude experiments a reduction of the initial velocity with respect to the linear growth prediction was measured. The results were compared to those predicted by a vorticity-deposition model and to previous experiments with moderate- and high-Mach number incident shock waves that were conducted by others. In this case, a reduction of the initial velocity was noted. However, at late times the growth rate had a 1/t behavior as in the small-amplitude low-Mach number case. In the small-amplitude moderate-Mach number shock experiments a reduction from the impulsive theory was noted at the late stages. The passage of a shock wave through a spherical bubble results in the formation of a vortex ring. Simple dimensional analysis shows that the circulation depends linearly on the speed of sound of the surrounding material and on the initial bubble radius.     

Validating the Flash Code: Vortex-Dominated Flows

As a component of the Flash Center’s validation program, we compare FLASH simulation results with experimental results from Los Alamos National Laboratory. The flow of interest involves the lateral interaction between a planar M _a = 1.2 shock wave with a cylinder of gaseous sulfur hexafluoride (SF₆) in air, and in particular the development of primary and secondary instabilities after the passage of the shock. While the overall evolution of the flow is comparable in the simulations and experiments, small-scale features are difficult to match. We focus on the sensitivity of numerical results to simulation parameters.     

Diagnostics of the Non-Linear Richtmyer-Meshkov Instability

We study analytically and numerically the evolution of the two-dimensional coherent structure of bubbles and spikes in the Richtmyer-Meshkov instability (RMI) for fluids with a finite density ratio. New diagnostics and scalings are suggested for accurate quantification of RMI dynamics. New similarity features of the late-time instability evolution are observed. The results obtained can serve as benchmarks for high energy density laboratory experiments.     

Flash Code Simulations of Rayleigh-Taylor and Richtmyer-Meshkov Instabilities in Laser-Driven Experiments

We present two- and three-dimensional simulations involving Richtmyer–Meshkov and Rayleigh-Taylor instabilities run with the adaptive mesh refinement code, flash. Variations in the rate of mixing layer growth due to dimensionality, perturbation modes, and simulation resolution are explored. These simulations are designed for detailed comparisons with experiments run on the Omega laser to gain understanding of the mixing processes and to prepare for validation of the Flash code.