On the Boltzmann Equation and the Structure of Shock Waves

Abstract

The methods of Mott-Smith and Rosen for the shock structure problem are correlated. It is found that the application of Rosen's restricted variational technique to the Boltzmann equation yields the transport equation used by Mott-Smith, and in addition determines a transport function. The expression for the average translational temperature profile, as derived by Mott-Smith, is examined for the existence of relative minima or maxima. For a monatomic gas the temperature profiles have no relative extrema inside the shock wave for any Mach number. For a diatomic gas the temperature profiles are smooth for Mach numbers below 1.89, but above that a hump appears.