Numerical Computation of Shock Waves in a Spherical Cloud of Cavitation Bubbles

The nonlinear dynamics of a spherical cloud of cavitation bubbles have been simulated numerically in order to learn more about the physical phenomena occurring in cloud cavitation. A finite cloud of nuclei is subject to a decrease in the ambient pressure which causes the cloud to cavitate. A subsequent pressure recovery then causes the cloud to collapse. This is typical of the transient behavior exhibited by a bubble cloud as it passes a body or the blade of a ship propeller. The simulations employ the fully nonlinear continuum mixture equations coupled with the Rayleigh-Plesset equation for the dynamics of bubbles. A Lagrangian integral method is developed to solve this set of equations. It was found that, with strong bubble interaction effects, the collapse of the cloud is accompanied by the formation of an inward propagating bubbly shock wave, a large pressure pulse is produced when this shock passes the bubbles and causes them to collapse. The focusing of the shock at the center of the cloud produces a very large pressure pulse which radiates a substantial impulse to the far field and provides an explanation for the severe noise and damage potential in cloud cavitation

A New Model for Black Hole Soft X-ray Transients in Quiescence

We present models of the soft X-ray transients, A0620-00, V404 Cyg, and X-ray Nova Mus 1991, in quiescence. In each source, we postulate that there is an outer region, extending outward from about 3000 Schwarzschild radii, where the accretion flow is in the form of a standard thin disk. The outer disk produces most of the radiation we observe in the infrared, optical and UV bands. We propose that the disk undergoes an instability at its inner edge, perhaps by the mechanism described recently by Meyer \& Meyer-Hofmeister for cataclysmic variables. The accreting gas is thereby converted into a hot corona which flows into the black hole as a nearly virial two-temperature flow. We describe the hot inner flow by means of a recently discovered stable solution of optically thin advection-dominated accretion. In this flow, most of the thermal energy released by viscous dissipation is advected into the black hole and only a small fraction, $\sim10^{-4}-10^{-3}$, of the energy is radiated. The radiation is in the form of Comptonized synchrotron and bremsstrahlung emission, and has a broad spectrum extending from optical to soft gamma-rays. The models we present are consistent with all the available data in the three sources. In particular, the X-ray emission from the hot inner flow fits the observed flux and spectral index of A0620-00. We derive a mass accretion rate of \sim10^{-11}\msyr in A0620-00 and Nova Mus, and \sim{\rm few}\times10^{-10}\msyr in V404 Cyg. The best fit to the data is obtained for a viscosity parameter $\alpha\sim0.1-0.3$ in the hot flow. The models predict that all three sources must have substantial flux in hard X-rays and soft $\gamma$-rays. This prediction is testable in the case of V404 Cyg with current instruments. A necessary feature of our proposal is that most of the viscousComment: 32 Pages, 6 Figures included, Compressed Postscript, To Appear in Astrophysical Journa