Similarity criteria for spectra of pressure fluctuations in turbulent boundary layer at wall

Spectra of pressure fluctuations in turbulent boundary layers at a wall are analyzed for the purpose of generalization on the basis of three dimensionless criteria: Mach number, Reynolds number and Strouhal number. Semiempirical relations are established for the dimensionless spectral density of such fluctuations as function of those three numbers, low and high ranges of each of these numbers being charactaerized by different trends of that spectral density function. The relations are based on experimental data covering a wide range of zero-gradient flow of air past aircraft wings and through wind tunnels, those data having been analyzed statistically according to the theory of random processes and the theory of similarity. Dependence of the spectral density on the Mach number is manifested by changes in the average local frictional stresses at the wall as well as in the density and the kinematic viscosity of air. Transition from a spectral density independent of St to one inversely proportional to the two-thirds power or the ten-thirds power of St occurs within the St = 200 to 300 range and depends on whether St 1.3Re(7/8) or St= 1.3 Re(7/8) respectively. Transition from a spectral density independent of Re to one proportional to the one-seventh power of Re (while remaining independent of St) occurs within the Re = 2000 to 3000 range.