Compressibility effects on pressure fluctuation in compressible turbulent channel flows

Compressibility effects on pressure fluctuations in wall-bounded turbulent flows at various Mach numbers are investigated by deriving a pressure Poisson equation that allows splitting pressure fluctuations into rapid and slow terms, as in incompressible flows, and into additional mass-flux and viscous terms. The rapid and slow terms are further split into their solenoidal and dilatational components by using Helmholtz decomposition. The solenoidal components are found to be independent of Mach number and similar to incompressible flows, whereas the dilatational components increase quadratically with Mach number.