Spectral Analysis of the Budget Equation of Pressure Fluctuation

This study examines the budget equation for pressure variance in incompressible turbulent channel flow, focusing on near-wall behavior and the mechanisms of production and destruction. The evolution equation for pressure variance is derived through the pressure Poisson equation and the governing equation of velocity fluctuations. We conduct spectral analysis of the budget terms to quantify their scale-by-scale contributions across wall-normal distances. Direct numerical simulation data obtained at friction Reynolds numbers up to 5200 are used for this analysis. Results indicate that terms containing mean velocity gradients primarily destroy pressure variance, whereas terms containing velocity fluctuations without mean gradients primarily produce it. While these terms display isotropic characteristics at the wall, they exhibit spanwise-elongated structures in the buffer layer, suggesting a transition in the dominant flow topology with distance from the wall.