Adiabatic self-similar blast waves, their radial instabilities, and their application to supernova remnants

An investigation shows that the adiabatic self-similar motion is unstable to radial perturbations for almost all physically allowable values of the parameters, including those thought to apply to the motion of supernova remnants. It appears, therefore, unlikely that an initially chaotic motion will decay to an adiabatic self-similar state. The self-similar solution and the perturbation equations are considered and a normal mode analysis of the linearized perturbation equations is conducted, taking into account the linearized normal-mode equation, a full normal-mode analysis of the critical case, short-wavelength perturbations near the origin, and short-wavelength perturbations near the shock. A full spherically symmetric nonlinear instability is also considered.