Self-similarity scaling of second and third velocity moments due to compressibility*

The influence of compressibility on turbulence attenuation and self-preservation of axisymmetric turbulent free jets are investigated. Second and third velocity moments containing the streamwise, u, and radial velocity fluctuations, v, are obtained using 2-D planar Particle Image Velocimetry (PIV). Two Mach numbers are chosen, at Mach 0.3 and Mach 1.25, to compare the effect of compressibility.  Interest is capturing the influence of compressibility on Reynolds stress anisotropy, which remains an important challenge to the development of reliable turbulence models. Using the jet half-width, b, and the centerline velocity,Um, as length and velocity scales, the mean streamwise velocity profile collapses. For self-preserving turbulent axisymmetric jets the Reynolds shear stress scales according to uv ∝  U²_m db/dx [1]. Our recent study [2] have shown that in the compressible axisymmetric jet, the attenuation on the Reynolds shear stress and the shear layer thickness growth rate are proportional - allowing for a collapse of the Reynolds shear stress profiles. Although there is agreement on scaling of uv, the effect of compressibility on other turbulent moments remains unclear. By performing an order-of-magnitude analysis, self-similarity solutions of the Reynolds stress transport equation are investigated which find that the radial and azimuthal velocity moments are attenuated by compressibility, while the streamwise velocity moment remains unaffected.  Moreover, the analysis allows for the inference of the effect of pressure-strain correlations as related to compressibility. Comparisons between the supersonic and subsonic cases will be provided to highlight the influence of compressibility.