Analysis of wall-pressure fluctuation sources from DNS of turbulent channel flow

Abstract

The sources of wall-pressure fluctuations in turbulent channel flow are studied using a novel framework. The wall-pressure power spectral density (PSD) $(ϕ_{pp}(ω))$ is expressed as an integrated contribution from all wall-parallel plane pairs, $ϕ_{pp}(ω)=\int_{-δ}^{+δ}\int_{-δ}^{+δ}Γ(r,s,ω)\,\mathrm{dr}\,\mathrm{ds}$, using the Green's function. Here, $Γ(r,s,ω)$ is termed the net source cross spectral density (CSD) between two wall-parallel planes, $y=r$ and $y=s$ and $δ$ is the half channel height. Direct Numerical Simulation (DNS) data at friction Reynolds number of $180$ and $400$ are used to compute $Γ(r,s,ω)$. Analysis of the net source CSD, $Γ(r,s,ω)$ reveals that the location of dominant sources responsible for the premultiplied peak in the power spectra at $ω^+\approx 0.35$ and the wavenumber spectra at $λ^+\approx 200$ is in the buffer layer at $y^+\approx 16.5$ and $18.4$ for $Re_τ=180$ and $400$, respectively. The contribution from a wall-parallel plane (located at distance $y^+$ from the wall) to wall-pressure PSD is log-normal in $y^+$ for $ω^+>0.35$. A dominant inner-overlap region interaction of the sources is observed at low frequencies. Further, the decorrelated features of the wall-pressure fluctuation sources are analyzed using spectral Proper Orthogonal Decomposition (POD). We require the modes to be orthogonal in an inner product with a symmetric positive definite kernel. Spectral POD supports the case that the net source is composed of two decorrelated components - active (dominant mode) and inactive (remaining modes). The structure represented by the dominant POD mode at the premultiplied wall-pressure PSD peak inclines in the downstream direction. At the low-frequency linear PSD peak, the dominant mode resembles a large scale vertical pattern.