Proving Shock Thickness Decreases for Increasing Mach Number

Contrary to common belief, shock thickness in supersonic and hypersonic flow is not an unchanging function of Mach number and not simply an infinitely thin discontinuity in the flow field. This discussion proves that shock wave thickness decreases significantly as Mach number increases and is not an absolute and unchanging discontinuity in external and internal flows. To prove that shock thickness decreases significantly with Mach number the specific case of a normal shock wave in the diverging section of a converging-diverging nozzle is considered. This analysis reveals that shock wave thickness becomes significantly smaller as Mach number is increased. Therefore, a shock wave has a finite but very small thickness, dx caused by the packing of molecules during the compression process as the shock wave moves through an undisturbed fluid. In addition, fluid density in the region of the shock wave tries to distribute itself evenly during the passage of the shock wave into undisturbed fluid. In this discussion shock thickness is determined as a function of Mach number and fluid viscosity.