Propagation of normal acoustic modes in an atmospheric boundary layer

Abstract

The Obukhov quasipotential function for the acoustic field in a boundary layer of exponential profile is used to obtain a modal description of low‐frequency sound propagation. As the wind speed approaches zero, the governing equations approach the Helmholtz equation with an impedance boundary condition. The solutions for the acoustic field with a boundary layer can be given as a continuous plane‐wave spectrum with variable amplitudes given by generalized hypergeometric functions. An analysis with the hypergeometric functions gives one or more acoustic modes, depending on frequency. The acoustic modes propagate as cylindrical waves, with amplitude varying inversely with the square root of distance. An estimate of the wavenumber of the fundamental mode shows that its attenuation is proportional to the product of wind speed and boundary layer displacement thickness. The propagation theory is compared to data from a wind turbine at Medicine Bow, Wyoming. A microphone array was used to measure low‐frequency sound at ground level at distances from 200 to 20 00(3 m from the turbine. Atmospheric temperature and wind speed profiles were measured, as was ground impedance, so that the theory may be compared without ambiguity to the data.