On the decay of a sawtooth profile in non-ideal magneto-gasdynamics

Abstract

In the present paper, an asymptotic approach is used to analyse the main features of weakly nonlinear waves propagating in a compressible, inviscid, nonideal gas in the presence of magnetic field. An evolution equation, which characterizes the wave process in the high frequency domain and points out the possibility of wave breaking at a finite time, is derived. The growth equation governing the behaviour of an acceleration wave is recovered as a special case. Further, we consider a sufficiently weak shock at the outset and study the propagation of the disturbance given in the form of a sawtooth profile. It is observed that the non-idealness of the gas causes an early decay of the sawtooth wave as compared to ideal case however the presence of magnetic field causes to slow down the decay process as compared to non-ideal non-magnetic case. A remarkable difference in wave profiles for planar and cylindrically symmetric flows has been observed. The effect of non-idealness, in the presence of magnetic field, on the formation of shock is more dominant in case of cylindrical symmetry as compared to planar case.