Theoretical pressure correlation functions in turbulent boundary layers

A Poisson equation is constructed for the pressure in terms of velocity fluctuations and is solved. The pressure correlation has a second-order velocity fluctuation contribution (usually assumed dominant in past work) and a fourth-order velocity correlation contribution. The velocity correlations are assumed to be those, suitably weighted, found from homogeneous turbulence measurements. Results are computed for two boundary layers: an idealized (canonical) turbulent boundary layer and a deliberately thickened boundary layer. The pressure variances are found to be essentially the same as the measured values. The correlations are positive except the streamwise, x correlations. The canonical layer shows a pressure variance which peaks very close to the wall, near the laminar sublayer. The fourth-order velocity fluctuations may generally be neglected for the thickened boundary layer; close to the wall they are an important part of the variance and correlation for the canonical layer.