Abstract
The statistical equations for a compressible gas are developed in a general form. All the properties (density, velocity, pressure, internal energy and temperature; also viscosity, heat conductivity, and specific heats) are considered to be turbulent and are separated into macroscopic quantities and fluctuations. Freedom is retained to make the most convenient definitions of these separations at a later stage. First a complete set of equations is derived from the general form, taking as the fundamental macroscopic quantities the mean values of the velocity, the temperature, the density and the pressure. Second the choice of the most convenient fundamental macroscopic quantities is discussed, which leads to the proposed use of the mean values of the massweighted velocity, the internal energy per unit volume, the density, and the pressure. The corresponding equations have simpler forms than the preceding equations, then physical interpretation is clearer, and they appear to be more convenient for theoretical work, and probably for turbulence measurements.