THE WAVE-NUMBER-PHASE VELOCITY REPRESENTATION FOR THE TURBULENT WALL-PRESSURE SPECTRUM

Wall-pressure fluctuations can be represented by a spectrum level that is a function of flow-direction wavenumber and frequency, PHI (k1, omega). In the theory developed herein the frequency is replaced by a phase speed; omega=ck1. At low wavenumbers the spectrum is a universal function if nondimensionalized by the friction velocity u* and the boundary layer thickness delta, while at high wavenumbers another universal function holds if nondimensionalized by u * and viscosity nu. The theory predicts that at moderate wavenumbers the spectrum must be of the form PHI+ (k1+, omega+=c+k1+) = k1+-2P+ (DELTAc+) where P+ (DELTAc+) is a universal function. Here DELTAc+ is the difference between the phase speed and the speed for which the maximum of PHI+ occurs. Similar laws exist in outer variables. New measurements of the wall-pressure are given for a large Reynolds number range; 45,000 < Re = U(o)delta/p < 113,000. The scaling laws described above were tested with the experimental results and found to be valid. An experimentally determined curve for P+ (Ac+) is given.