Stationarity and homogeneity assumptions in wavenumber-frequency representation of turbulent boundary layer wall pressure.

Abstract

The utility of the wavenumber-frequency spectrum for description and interpretation of wall pressure fluctuations beneath turbulent boundary layers has been amply demonstrated over the past decades. This representation is widely used in modelling the flow-induced noise due to boundary layers developing on vehicle surfaces. A recurring issue concerns the underlying assumptions of stationary and homogeneous wall pressure fields. Even on a flat plate, the turbulent boundary layer thickening violates the homogeneous assumption. A numerical experiment of a spatially evolving turbulent boundary layer on a flat plate provides detailed wall-pressure data to assess the stationarity and homogeneity assumptions in the computation of wavenumber-frequency spectra. High-order statistics, stationarity tests developed for random time series and modern signal processing tools, such as the empirical mode decomposition, are applied. In particular, it is shown that the nonhomogeneity due to the space-varying nature of the turbulent sources does not change the characteristics of the wavenumber-frequency representation of the wall pressure field.