Modeling the Wavevector-Frequency Spectrum of Boundary-Layer Wall Pressure During Transition on a Flat Plate

Abstract

A spectral model for the wall-pressure fluctuations induced on a zero pressure gradient, flat, rigid surface by a transitioning boundary layer at low Mach number is developed in this paper. The central assumption used in this modeling is that the space-time statistics associated with the formation, convection, and interaction of turbulent spots in a naturally occurring boundary-layer transition are independent of the space-time statistics of the wall-pressure fluctuations that are induced by the turbulence in the individual spots. Space-time correlations for the spots were determined experimentally and semi-empirical formulae are developed to predict these correlations. Previously published statistical descriptions of turbulence-induced wall-pressure fluctuations are coupled with the spot statistics to arrive at the model for the wavevector-frequency spectrum of the transition region. The basic result suggests that the wall-pressure wavevector-frequency spectrum of a transitioning boundary layer is approximately that produced by a fully-turbulent layer weighted by the intermittency factor.