same order of magnitude as the speed of sound , the Reynolds number turns out to be of the same order of magnitude as the ratio of the dimensions of system to the length of the molecule path .
The condition stated above according to which , and according to which it is possible to ignore dissipation forces (viscosity and thermal conduction), leads to the requirement that the dimensions of the system be considerably greater than the length of the free path of molecules. We see further, however, that the fulfillment of that condition, i.e., a system of large size, does in reality not always ensure small dissipation forces and the possibility of studying adiabatic processes only. We shall see in the following that in the presence of shock waves in a flow there occur exceedingly large gradients of all the quantities studied; the magnitude of these gradients does no longer depend upon the dimension of the system, and also does not drop as the dimensions of the system increase. In these cases, we will have to consider the possibility of changing entropy no matter how large the Reynolds number is.
Generally speaking, the possibility of an increase in entropy does, in principle, depend upon the dissipation forces; all the observed large-size properties of the flow, however, and, specifically, the numerical value of entropy increase in a shock wave, do not depend upon the magnitude of viscosity and thermal conductivity (they are self-modeling with respect to thermal conductivity and viscosity); the laws of the change of state in a shock wave can thus be derived without investigating the structure of its front from the equations of conservation of matter, the amount of motion and energy, applied to the states prior and after the passage of the wave.
In the case of high Reynolds numbers, we could expect a considerable effect of turbulence. In matter of fact, however, studies of the simultaneous effect of turbulence and extremely high (of the order of the speed of sound) velocities are very few. To some extent, this lack appears to be due to the complexity of such a comparatively
