On the wavenumber-frequency spectrum of the wall pressure fluctuations in turbulent channel flow

Direct numerical simulations (DNS) of turbulent channel flows up to Re-tau approximate to 1000 are conducted to investigate the three-dimensional (consisting of streamwise wavenumber, spanwise wavenumber and frequency) spectrum of wall pressure fluctuations. To develop a predictive model of the wavenumber-frequency spectrum from the wavenumber spectrum, the time decorrelation mechanisms of wall pressure fluctuations are investigated. It is discovered that the energy-containing part of the wavenumber-frequency spectrum of wall pressure fluctuations can be well predicted using a similar random sweeping model for streamwise velocity fluctuations. To refine the investigation, we further decompose the spectrum of the total wall pressure fluctuations into the autospectra of rapid and slow pressure fluctuations, and the cross-spectrum between them. We focus on evaluating the assumption applied in many predictive models, that is, the magnitude of the cross-spectrum is negligibly small. The present DNS shows that neglecting the cross-spectrum causes a maximum error up to 4.7 dB in the subconvective region for all Reynolds numbers under test. Our analyses indicate that the approximation of neglecting the cross-spectrum needs to be applied carefully in the investigations of acoustics at low Mach numbers, in which the subconvective components of wall pressure fluctuations make important contributions to the radiated acoustic power.

Automated summary

Direct numerical simulations of turbulent channel flows up to Re-tau approximately 1000 were performed to investigate the three-dimensional spectrum of wall pressure fluctuations. It was found that the energy-containing part of the spectrum can be well predicted using a random sweeping model for streamwise velocity fluctuations. Neglecting the cross-spectrum between rapid and slow pressure fluctuations causes a maximum error of up to 4.7 dB in the subconvective region for all Reynolds numbers tested. This suggests that the approximation of neglecting the cross-spectrum needs to be carefully applied in low Mach number acoustics.