Understanding Roughness Noise: Progress in Analytical Modeling and Testing, Part 1—Shear Rapid Distortion Theory

This is the first of a two-part paper that lays out a theory of broadband noise from rough surfaces and uses it to interpret recent experimental data. The analysis in Part 1 is based on an application of Rapid Distortion Theory to an incident field of correlated micro-velocities defined upstream of the roughened region. Those velocity disturbances are linked to the frequency-wavenumber spectrum of wall pressures from a standard model of turbulent boundary-layer flow. The field of incident microvelocities distorts as it is convected irregularly around and over the roughness elements and thereby generates the predicted broadband sound. Computed results in the Part-2 paper will gauge the role of a boundary layer’s mean shear in the noise-production process relative to the rapid distortions carried by an artificially irrotational mean flow (for reasons to be described in Part 2, shear effects turn out to be insignificant for the application of immediate interest). Calculations in support of recent measurements will be presented for a range of operating conditions and for their associated set of dimensionless scaling parameters.