Shock waves in nonuniform gas

Shock waves propagating through a stratified gas are investigated numerical ly and analytically. A shock wave is produced by a piston that begins to mo ve from rest abruptly at some constant velocity in a two-dimensional horizo ntal duct. Initially the gas in the duct has a temperature or density distr ibution only along the vertical axis at a constant pressure. The initial de nsity distribution, which is assumed to change monotonically, has a zero sp atial gradient at the upper and lower walls and then has a single inflectio n point. It is confirmed that at least three types of shock patterns can be realized asymptotically. The first is a single curved shock, the second is a shock with a Mach stem (Mach reflection), and the last is a shock with a reflected branch (regular reflection). The first is substantially steady b ut the latter two are essentially unsteady. The time evolution of the induc ed flow field is investigated in detail. Based on this information, an anal ytical solution for the substantially steady curved shock is obtained in th e coordinate system fixed on the shock. The shock profile as well as the in duced flow field is investigated in detail with this solution. It is shown that the analytical results can predict quite well the numerical results. F inally, the flow instability of this shock-induced flow is investigated, be cause the induced flow has a nonuniform horizontal velocity distribution al ong the vertical axis at a constant pressure. (C) 1999 American Institute o f Physics. [S1070-6631(99)03606-5].