Statistical Properties of the Turbulent Wake behind Hypervelocity Spheres

Abstract

Autocorrelation functions and spectra of the gas density fluctuations have been obtained from microdensitometer tracings of schlieren photographs of the turbulent wakes behind hypervelocity spheres ⅜ in. in diameter traveling with a velocity of about 8 kft/sec (≅ Mach 8). Schlieren photographs of wakes 100 to 10 000 body diameters behind the spheres at pressures ranging from 10 to 160 mmHg were taken and densitometer tracings from these films were analyzed. The relationship between the statistical properties of the film density and that of the gas density has been derived. The results show that the normalized autocorrelation functions and spectra of the turbulent wake of spheres are independent both of pressure and of position behind the body. Further, to the accuracy of the measurements, the turbulent wake appears to be statistically isotropic and homogeneous, and the three‐dimensional spectrum of the gas density falls off as the 5.5 power of the wavenumber.