# Browsing by Subject "Shocks"

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Item A fragmentation model for sprays and L² stability estimates for shockes solutions of scalar conservation laws using the relative entropy method(2010-05) Leger, Nicholas Matthew; Vasseur, Alexis F.; Arbogast, Todd J.; Gamba, Irene M.; Vishik, Mikhail M.; Raman, VenkatramananShow more We present a mathematical study of two conservative systems in fluid mechanics. First, we study a fragmentation model for sprays. The model takes into account the break-up of spray droplets due to drag forces. In particular, we establish the existence of global weak solutions to a system of incompressible Navier-Stokes equations coupled with a Boltzmann-like kinetic equation. We assume the particles initially have bounded radii and bounded velocities relative to the gas, and we show that those bounds remain as the system evolves. One interesting feature of the model is the apparent accumulation of particles with arbitrarily small radii. As a result, there can be no nontrivial hydrodynamical equilibrium for this system. Next, with an interest in understanding hydrodynamical limits in discontinuous regimes, we study a classical model for shock waves. Specifically, we consider scalar nonviscous conservation laws with strictly convex flux in one spatial dimension, and we investigate the behavior of bounded L² perturbations of shock wave solutions to the Riemann problem using the relative entropy method. We show that up to a time-dependent translation of the shock, the L² norm of a perturbed solution relative to the shock wave is bounded above by the L² norm of the initial perturbation. Finally, we include some preliminary relative entropy estimates which are suitable for a study of shock wave solutions to n x n systems of conservation laws having a convex entropy.Show more Item Hydrodynamic instabilities of radiative blast waves(2013-12) Kim, In Tai; Ditmire, Todd R.Show more We present the results from a series of experimental investigations into the hydrodynamic instabilities that occur in radiative blast waves. In particular, we examine the Vishniac instability in which the perturbation modes oscillate in time and, for certain mode numbers and polytropic index of the medium, can exhibit a growth in their amplitudes. Experiments were conducted on the GHOST laser laboratory in which a source of atomic clusters was irradiated by a 1J-2J, 115fs laser pulse to produce cylindrical blast waves. The thrust of this thesis falls into two categories. First, we analyze the effects radiative cooling has on the evolution of blast waves such as the lowering of the effective polytropic index and consequently the lowering of their deceleration parameter. Radiation from the blast wave surface results in a preheated ionization precursor in the upstream material and is indicated by a gradual decline in the electron density profile of the blast wave rather than a sharp jump. This mechanism, if strong enough, can also create a secondary shock wave to form ahead of the main blast wave. The second set of experiments investigates the temporal evolution of longitudinal perturbations induced on the blast waves by use of a transverse interferometric beam that modifies the cluster medium prior to the onset of the main pump beam. These perturbations are analyzed and compared to theory set forth in Vishniac's mechanism for oscillatory instabilities and their growth rate.Show more