The Solution of the Boltzmann Equation for a Shock Wave

It is pointed out that the distribution of molecular velocities in a strong shock wave in a gas is bimodal. Assuming the distribution function to consist of a sum of two maxwellian terms with temperatures and mean velocities corresponding to the subsonic and supersonic streams, it is found that the space distribution, as determined by the solution of a transport equation, is appropriate to describe a shock wave. Comparison of the solutions of two different transport equations shows that the assumed distribution changes relatively slowly with time and so is an approximate stationary solution of the Boltzmann equation for strong shocks. The shock thickness found is considerably greater than that given by previous theories. The nominal thermal conduction coefficient is negative in the after part of the shock.