Generalized hydrodynamic theory of shock waves is phenomenologically developed for rigid diatomic molecules. The generalized hydrodynamic equations developed are thermodynamically consistent, obeying the laws of thermodynamics. They reduce to the Navier-Stokes-Fourier theory of the classical hydrodynamics in the limit of low Mach number. The theory is applied to study the one-dimensional shock wave structure of nitrogen gas, which is treated as a rigid molecule. An excellent agreement with experiment is obtained for the inverse shock widths up to Mach number 10 reported in the literature. The theory is applicable to arbitrary dimension. On the basis of direction field singularities of the velocity and temperature evolution equations of the theory, it is possible to predict that the shock solutions exist for all Mach numbers in the case of one-dimensional shock waves studied.

• Received 1 February 2001

DOI:https://doi.org/10.1103/PhysRevE.64.046303