Cross-wavelet analysis of wall pressure fluctuations beneath incompressible turbulent boundary layers

Abstract

Pressure fluctuations measured at the wall of a turbulent boundary layer are analysed using a bi-variate continuous wavelet transform. Cross-wavelet analyses of pressure signals obtained from microphone pairs are performed and a novel post-processing technique aimed at selecting events with strong local-in-time coherence is applied. Probability density functions and conditionally averaged equivalents of Fourier spectral quantities, usually introduced for modelling purposes, are computed. The analysis is conducted for signals obtained at low Mach numbers from two different non-equilibrium turbulent boundary layer experiments. It is found that that the selected events, though statistically independent, exhibit bi-modal statistics while the conditional coherence function coincides with its non-conditional Fourier equivalent. The physical nature of the selected events has been further explored by the computation of ensemble-averaged pressure time signatures and the results have been physically interpreted with the aid of numerical and experimental results from the literature. In both experiments, it has been found that the major physical mechanisms responsible for the observed conditional statistics are represented by sweep-type events which can be ascribed to the effect of streamwise vortices in the near-wall region. More precisely, the wavelet analysis highlights the convection of the selected structures in both cases. Conversely, compressibilty effects could be related to these events only in one case.