Shock formation in the presence of entropy gradients in fluids exhibiting mixed nonlinearity

Abstract

The nonlinear steepening of a finite amplitude disturbance in a quiescent gas with very high specific heat in its near-critical regime is analyzed. The atypical phenomenon of rarefaction shocks are found to occur in the region where the nonlinearity parameter is negative. The undisturbed medium is assumed to be at rest with entropy gradients (temperature gradients). The steepening of the wave front in such a nonhomentropic medium, where a variation in the nonlinearity parameter is present, is investigated using the technique of wave front expansion. A calorically imperfect gas governed by an arbitrary equation of state is considered. An exact closed form solution is obtained for the evolution of the slope of the disturbance. In particular, results have been discussed for a van der Waal’s fluid in its gaseous phase in the near-critical region. The distortion of both compression and rarefaction wave forms are examined and the corresponding shock formation distances are calculated.