Recent results regarding turbulent wall pressure and shear stress in boundary-layer flow and the role of the viscous wall condition.

Abstract

Recently, the relation between fluctuating wall pressure and shear stress at low streamwise (subconvective) wave numbers, and between these and their fluctuating Reynolds-stress ‘‘sources,’’ has been examined analytically for nominally homogeneous, slightly compressible turbulent boundary-layer flow. At low-wave-vector magnitude (but within the incompressive domain), the contributions to the wall pressure and to the wave-vector-directed component of shear stress associated with imposition of the viscous wall condition prove to be equal, perfectly coherent, and differing in phase by π/2. Assuming apparently plausible source scaling and properties, this viscous contribution is then expected to be nearly wave-vector-white and of such magnitude as to dominate the low-wave-number spectrum of wall pressure as well as shear stress and account for currently measured levels. The lack of experimental evidence for the decrease in the spectrum of turbulent wall pressure toward low wave numbers that would be expected if the Kraichnan–Phillips theorem applies as in inviscid flow might thereby be accounted for. Likewise, the level of turbulent wall-shear stress at low wave numbers obtained by model-based extrapolation of measured sublayer velocity spectra is comparable with the level of wall pressure, as predicted. But a recent treatment seems to imply that the spectrum of wall pressure vanishes toward low wave numbers even for real, viscous flow. This result is suggested to relate only to wave numbers on the order of the reciprocal streamwise extent of the turbulent boundary layer, not to wave numbers which, though perhaps smaller than the reciprocal boundary-layer thickness, are great enough to lie in the domain of interest where the condition of streamwise homogeneity is met. Controversy and conflicting views of the role of the viscous wall condition in determining turbulent boundary-layer pressure at low wave numbers thus endure. [Work supported by ONR, Code 1132F.]