Concerning isothermal self-similar blast waves

Abstract

We investigate the one-dimensional self-similar flow behind a blast wave from a plane explosion in a medium whose density varies with distance asx−ω with the assumption that the flow is isothermal. If ω ω>0 one critical point exists. To be physically acceptable the flow must by-pass this critical point. It is shown that a continuous solution passing through both the origin and through the shock and by-passing the critical point does exist. If 1>ω>1/3 the first critical point does not exist but a second one appears. To be physically acceptable the flow must again by-pass this new critical point. We show that a continuous solution passing through both the origin and the shock and by-passing the new critical point exists in this case. If ω>1 no physically acceptable solution exists since the mass behind the shock is infinite.