The Wavenumber-Phase Velocity Representation for the Turbulent Wall-Pressure Spectrum

Abstract

Wall-pressure fluctuations can be represented by a spectrum level that is a function of flow-direction wavenumber and frequnecy, Φ (k1 , ω). In the theory developed herein the frequency is replaced by a phase speed; ω = ck1 . At low wavenumbers the spectrum is a universal function if nondimensionalized by the friction velocity u* and the boundary layer thickness δ, while at high wavenumbers another universal function holds if nondimensionalized by u* and viscosity ν. The theory predicts that at moderate wavenumbers the spectrum must be of the form Φ+ (k+ 1 , ω+ = c+ k+ 1 ) = k+ 1 − 2 P+ (Δc+ ) where P+ (Δc+ ) is a universal function. Here Δc+ is the difference between the phase speed and the speed for which the maximum of Φ+ occurs. Similar laws exist in outer variables. New measurements of the wall-pressure are given for a large Reynolds number range; 45,000 < Re = Uo δ/ν < 113,000. The scaling laws described above were tested with the experimental results and found to be valid. An experimentally determined curve for P+ (Δc+ ) is given.