Gas Channel Formation: Dependence of Hydrodynamic Phenomena on the Initial Radial Pressure Profile

摘要

The hydrodynamic processes resulting from 'instantaneous' heating of a cylindrical region of gas are studied by means of numerical integration of the fluid equations. Various initial overpressures and radial profiles of initial pressure are considered. For very smooth radial profiles, e.g. the Bennett profile, the evolution is very simple: the gas expands radially, a single outgoing shock forms, the density at late times undershoots the value at pressure balance by only about 10% and then increases to pressure balance slowly, monotonically, and adiabatically. For profiles that are more square in shape, or are sharply discontinuous, the evolution is much more complicated. A strong rarefaction typically occurs, of brief duration and in a narrow region about the axis. During the rarefaction, both the density and temperature fall well below the values at pressure balance. The rarefaction is abruptly terminated by an inward-propagating shock, followed by multiple density oscillations, which can form shocks for strong overpressures. The dependence of the time scales and strengths of the rarefactions and shocks on the initial overpressure and profile shape are calculated and discussed.