  The sources of wall-pressure fluctuations in turbulent channel flow are
studied using a novel framework. The wall-pressure power spectral density (PSD)
$(\phi_{pp}(\omega))$ is expressed as an integrated contribution from all
wall-parallel plane pairs,
$\phi_{pp}(\omega)=\int_{-\delta}^{+\delta}\int_{-\delta}^{+\delta}\Gamma(r,s,\omega)\,\mathrm{dr}\,\mathrm{ds}$,
using the Green's function. Here, $\Gamma(r,s,\omega)$ is termed the net source
cross spectral density (CSD) between two wall-parallel planes, $y=r$ and $y=s$
and $\delta$ is the half channel height. Direct Numerical Simulation (DNS) data
at friction Reynolds number of $180$ and $400$ are used to compute
$\Gamma(r,s,\omega)$. Analysis of the net source CSD, $\Gamma(r,s,\omega)$
reveals that the location of dominant sources responsible for the premultiplied
peak in the power spectra at $\omega^+\approx 0.35$ and the wavenumber spectra
at $\lambda^+\approx 200$ is in the buffer layer at $y^+\approx 16.5$ and
$18.4$ for $Re_{\tau}=180$ 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 $\omega^+>0.35$. 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.
