Hydrodynamics of Shocked Interfaces

Abstract

Shock waves emerge following the rapid release of energy in a flow. The interaction of shocks with interfaces separating dissimilar fluids generates complex systems of waves and stimulates mixing between those fluids. Shock waves are utilized in engineering applications for their ability to rapidly compress materials. In dynamic compression experiments, such shock waves are utilized to access extreme pressure states that can be measured in the laboratory, uncovering the behavior of materials at conditions consistent with and improving models for the interiors of gas giant planets or the atmospheres of white dwarf stars. In inertial confinement fusion, shock waves compress a spherical capsule of fusion fuel to the point where nuclear fusion may take place, releasing an enormous amount of energy that may one day be harvested to generate electricity. However, the shock-induced mixing between different layers of the fuel capsule inhibits the confinement of the fuel required for a self-sustaining reaction. The same type of mixing occurs during the cataclysmic collapse and rebound of stars during type-II supernovae and stimulates the transport of stellar core elements throughout the universe. Furthermore, shocks generated from supernovae and other astrophysical phenomena can interact with interstellar gas, stimulating the hydrodynamic motion that is responsible for the structure of molecular clouds, nebulae, and debris rings. The objective of this thesis is to advance the current understanding of shocked interfacial hydrodynamics for the development of improved dynamic compression experiments, the mitigation of mixing in inertial confinement fusion, and an enhanced understanding of how shock-induced mixing affects supernovae and other astrophysical flows.

To this end, an approach for strengthening shocks in compression experiments is developed. The method replaces sharp interfaces with an intermediate region bridging the impedance mismatch between two materials. By appropriately designing this region, up to twenty-five percent greater shock pressures can be achieved for a finite duration of time, with an exponential discretization of the intermediate region impedance being the most effective distribution for strengthening strong shocks.

Next, data are obtained from dynamic compression experiments examining helium in excess of 3.5 Mbar. The data show significant reflectivity and an increase in compressibility, likely caused by the onset of continuous ionization. The novel data serve as important benchmarks for density functional theory and models for Jovian interiors and white dwarf atmospheres.

In two spatial dimensions, the interaction of two adjacent bubbles of different sizes in a shock-induced mixing region is investigated numerically. A significant departure from existing bubble-merging models is observed, resulting in the ejection of vortex dipoles that escape the confines of the mixing region, which is well predicted from a vorticity-based criterion. Theory is subsequently developed to describe the formation and scaling of vortex rings, the azimuthally symmetric analog to vortex dipoles, emerging from shocked interfacial mixing regions.

Finally, the three-dimensional stability of vortex cores, including those generated from shock-interface interactions, is investigated, and the behavior of linear perturbations undergoing the cylindrical Crow instability is uncovered. The analysis is applied to Supernova 1987A, a system with an equatorial ring surrounding the location of the progenitor star along which there are 28 mass clumps. The dominant unstable wavenumber is consistent with the number of observed clumps, suggesting that the Crow instability initiates clumping in Supernova 1987A and other star systems with equatorial rings.