THE WAVE-VECTOR-FREQUENCY SPECTRUM OF PRESSURE ON A SMOOTH PLANE IN TURBULENT BOUNDARY-LAYER FLOW AT LOW MACH NUMBER

Properties of the wave-vector-frequency spectrum of fluctuating pressure on a smooth planar wall in turbulent boundary-layer flow at low Mach number are reviewed. In the low but incompressive wave-number range, where omega/c less-than-or-similar-to K less-than-or-similar-to max (delta-1, U infinity/omega), consistent with the Kraichnan-Phillips hypothesis for inviscid flow, the dependence would be expected to be as K2, but no experimental substantiation exists. In a higher subconvective range where delta-1 less-than-or-similar-to K less-than-or-similar-to omega/U infinity, most pertinent experiments suggest that the spectrum is instead wave-number-white. In the acoustic domain a peak is predicted at K = omega/c. A mean-shear contribution proportional to the square of streamwise wave number appears predominant in the convective domain. An explicit model spectrum is specified that conforms in an appropriate domain to the principle of wall similarity and corresponds to boundary-layer velocity spectra that are planar isotropic in a convected frame. The model potentially encompasses the entire inviscid domain, including the acoustic range. An alternative model exhibits a factorable dependence on the wave-number components. In the acoustic range, the model forms are totally unvalidated by experiment. In the convective domain, the state of determination suffices for many applications, but a preference between model forms and assured choice of parameter values awaits further analysis and perhaps certain further measurements. An addendum based on recent work suggests that the wall pressure at low but incompressive wave numbers may be dominated by a wave-vector-white contribution originating in the viscous wall condition.