Investigation of the turbulent model for pressure fluctuations with spectral theory

The pressure fluctuations in turbulent shear flows are investigated with the theory of spectral analysis. An expression for pressure spectra is analytically derived in terms of velocity spectra. This derivation is based on a formal solution of the Navier-Stokes equation and quasi-normal assumption to express the third and fourth order velocity correlations in terms of double velocity correlation. Then, a turbulent model for the computation of pressure fluctuation intensity with Renolds stress and mean flow velocity gradients is established. The turbulent constants in the model are calculated from the assumptions about the general behaviour of velocity spectra in high Renolds number flows. Comparison with direct simulation of turbulent boundary layer is made. It is found that the turbulent-turbulent, cross correlation, and turbulent-shear source terms for mean square value of pressure fluctuation are about the same magnitude.