Downwind sound propagation in an atmospheric boundary layer

Abstract

A theoretical analysis is given for an acoustic monopole in an atmospheric boundary layer. The analysis is based on the Obukhov quasipotential function (which defines both acoustic pressure and velocity) and assumes an isothermal atmosphere, an exponential boundary-layer flow profile, and a ground impedance function. It is shown that acoustic waves in the boundary layer can be represented by plane waves with variable amplitude. The wave amplitudes are given by the generalized hypergeometric function oFj. The present work is an extension of previous work by Wenzel, who studied surface waves associated with a ground plane without flow, and by Chunchuzov, who identified a discrete mode spectrum in an exponential boundary layer over a hard surface. It is shown that downwind propagation of low-frequency sound can be represented by these discrete modes, which spread as cylindrical waves. The downwind attenuation of the fundamental mode is proportional to frequency squared, wind speed, boundary-layer displacement thickness, and the real part of the ground admittance. The analysis is supported by acoustic data from a wind turbine at Medicine Bow, Wyoming.