Self-preservation scaling of turbulence in free axisymmetric compressible jets

The influence of compressibility on shear flow turbulence is investigated within a self-preservation framework. This study focuses on the axisymmetric jet to examine compressibility effects in a slowly spatially evolving flow, unlike mixing layers, where the convective Mach number remains constant. Revisiting self-preservation, an a priori description of the compressible scaling for Reynolds stresses and higher-order velocity moments is developed. Turbulence moments are found to scale with powers of the spreading rate, suggesting Reynolds stress anisotropy results from compressibility effects consistent with self-preservation of the governing equations. Particle image velocimetry measurements for Mach 0.3 and perfectly expanded Mach 1.25 jets confirm the scaling predictions. The attenuation function, (Mc) , describing the relationship between the convective Mach number, Mc , and the spreading rate, follows a similar trend in jets and mixing layers, where a higher Mc results in reduced spreading rates. In the jet where Mc decays, the relationship between the local Mc and turbulence attenuation remains captured through (Mc) , which scales proportionally with the spreading rate. A new scale is introduced, where the pressure in the mean momentum equation is substituted. The difference between the streamwise and radial-Reynolds-normal stresses was found to be a scale which is independent of Mach number and spreading rate. Further analysis of the Reynolds-stress-transport budget shows that internal redistribution of energy occurs within the Reynolds-normal stresses, and the role of pressure modification in turbulence attenuation supports previous observations. These findings confirm that the compressible axisymmetric jet exhibits self-preservation, with scaling extending into supersonic regimes.