Scaling of pressure fluctuations in compressible turbulent plane channel flow

Abstract

The purpose of the paper is to identify Mach-number effects on pressure fluctuations in compressible turbulent plane channel flow. We use data from a specifically constructed -matrix direct numerical simulation (DNS) database, with systematic variation of the centreline streamwise Mach number and of the HCB (Huang et al., J. Fluid Mech., vol. 305, 1995, pp. 185-218) friction Reynolds number. Strong effects (enhanced by the increasingly cold-wall condition) appear for, for all, very close to the wall . Compared with incompressible flow at the same, the wall root-mean-square (in wall-units, i.e. scaled by the average wall shear stress) strongly increases with. In contrast, the peak level across the channel, slightly decreases with increasing. In order to study the near-wall coherent structures we introduce a new wall-distance-independent non-local system of units, based for all on wall friction and the extreme values of density and dynamic viscosity, namely, for cold walls. The average spanwise distance between streaks, scaled by this length-unit, is nearly independent of at constant. Using the in-plane (parallel to the wall) Laplacian we find that the wave-packet-like structures appearing inside the low-speed streaks with increasing are part of a more complex wave system with spanwise extent over several streaks, whose spatial density decreases rapidly with decreasing or increasing. These wave packets appear to be collocated with strong - events and could be responsible for compensating towards 0 the negative incompressible-flow correlation coefficient, with increasing very near the wall.