Scaling of wall pressure and the streamwise turbulence intensity peak in compressible wall flows

This paper develops scaling laws for wall-pressure root mean square and the streamwise turbulence intensity peak, accounting for both variable-property and intrinsic compressibility effects – those associated with changes in fluid volume due to pressure variations. To develop such scaling laws, we express the target quantities as an expansion series in powers of an appropriately defined Mach number. The leading-order term is represented using the scaling relations developed for incompressible flows, but with an effective Reynolds number. Higher-order terms capture intrinsic compressibility effects and are modelled as constant coefficients, calibrated using flow cases specifically designed to isolate these effects. The resulting scaling relations are shown to be accurate for a wide range of turbulent channel flows and boundary layers.