FLUCTUATING WALL-SHEAR STRESS AND PRESSURE AT LOW STREAMWISE WAVE-NUMBERS IN TURBULENT BOUNDARY-LAYER FLOW AT LOW MACH NUMBERS

For turbulent boundary-layer flow at low Mach numbers along a smooth, rigid, planar wall, in the highly subconvective range of streamwise wavenumbers, the amplitudes or spectral densities (s.d.) of wall pressure and shear stress are derived in terms of their fluctuating velocity-product "sources" with application of appropriate viscous wall conditions. Contributions of compressive source terms omitted in the similar analysis of wall pressure by Hariri & Akylas (1985), though not a priori of higher order at wave-numbers, K, in the acoustic range than the usual inviscid contribution, are found, in fact, to prove so when analysed in detail. The rotational (or viscous) contribution to the amplitudes of wall pressure and wavevector-aligned shear stress at low wavenumbers, which differ approximately by a factor i in the incompressive case treated previously by Chase (1991a), is found to be altered by compressibility in the instance of pressure by the approximate factor (1 - ω2 c2K2) -1 2 (c = speed of sound) but in the instance of shear stress to remain unchanged. Subsequently, a representative model form is introduced for the s.d. of the sources, and estimation carried out of the rough magnitude and dependence of the resulting s.d. of the rotational contribution to wall pressure and shear stress at low K. Under certain assumptions regarding the model source s.d., the result reduces to the scale-independent, wavevector-white form commonly thought best to describe the measured s.d. of turbulent wall pressure, and may have a suitable level coefficient. © 1992.