Effects of fluctuating shear stresses on the low wave number wall pressure spectrum

Abstract

The well-known Kraichnan–Phillips theorem states that the low wave number spectrum of the wall pressure on a smooth wall beneath an incompressible and inviscid turbulent boundary layer flow is proportional to the square of wave number, and the limiting value of the spectrum is zero as the wave number approaches zero. In practice, however, measurements do not support this theoretical conclusion from ideal fluids. A theory on the possible contributions by the fluctuating viscous shear stresses to the nonvanishing pressure spectrum at zero wave number has been discussed in the literature [D. M. Chase, ‘‘Fluctuations in wall-shear stress and pressure at low streamwise wave numbers in turbulent-boundary-layer flow,’’ J. Fluid Mech. 225, 545–555 (1991)]. Preliminary evidence to support the theory, based on the result of comparing measured near-zero wave number wall pressure and shear stress spectra, is discussed in this paper. [Work supported by ONR, Code 333.]