An analytical and statistical examination of the low-wave-number region of the turbulent boundary layer wall pressure

Abstract

The underlying physical mechanisms that generate the low-wave-number pressure components of the turbulent boundary layer wall pressure are examined based on a solution of linearized Navier-Stokes equations in the viscous sublayer with no-slip wall condition. The result indicates that the predominant low-wave-number pressure components are generated by viscous diffusion of shear stress fluctuations at the no-slip wall. These random pressure components have a wave-number spectrum spanning from zero wave number to well beyond the convective wave number. However, their contribution to the convective ridge of the wall pressure spectrum is negligible compared to those of other sources. In the low-wave-number limit, we reach the same conclusion reached by Chase [J. Fluid Mech. 225, 545–555 (1991)], i.e., the wave number spectral density does not vanish as the streamwise wave number approaches zero. The reasons for nonvanishing wave-number spectral density as k→0, for both shear stress and wall pressure, are established analytically. A statistical model is derived based on a probabilistic area-averaging on an assumed random process which is capable of producing the measured two-point correlation functions. The result is a space-time autocorrelation function that yields the experimental low-wave-number data. [Work supported by NSWC ILIR Program and ONR.]