The Turbulent Boundary Layer
Every surface immersed in a flow develops a boundary layer — a thin region where viscosity decelerates the fluid from freestream velocity to zero at the wall. When this layer becomes turbulent (typically at Reynolds numbers above 500,000), it fills with chaotic eddies ranging from the boundary layer thickness down to the Kolmogorov microscale. These eddies create rapid, random pressure fluctuations on the wall surface.
Wall-Pressure Spectrum
The wall-pressure power spectral density has a characteristic shape: it rises at low frequencies, reaches a broad plateau, and rolls off at high frequencies. The outer-scale peak frequency is approximately U∞/(5δ), determined by the largest energy-containing eddies. The Goody model (2004) provides an accurate semi-empirical representation that captures the inner-variable high-frequency behavior controlled by viscous sublayer dynamics.
Sound Radiation
A turbulent boundary layer over a rigid infinite wall does not radiate sound directly — the wavenumber content is subsonic. However, real surfaces are finite, flexible, and have discontinuities (edges, ribs, panel joints). These features scatter the hydrodynamic pressure field into radiating acoustic waves. Trailing-edge noise, panel vibration, and edge scattering are the dominant pathways from boundary layer turbulence to far-field sound.
Engineering Significance
Boundary layer noise is the primary source of interior noise in aircraft cabins, automobiles, and submarines at cruise conditions. It also limits the performance of sonar arrays, towed hydrophone systems, and microphone arrays in wind. Modern computational aeroacoustics uses wall-resolved Large Eddy Simulation coupled with Ffowcs Williams-Hawkings surfaces to predict this noise with increasing fidelity.