Angle-of-arrival fluctuations in a turbulent atmosphere

Atmospheric turbulence causes fluctuations in the angle-of-arrival (AOA) of sound waves. These fluctuations adversely affect the performance of sensor arrays used for source detection, ranging, and recognition. This article examines, from a theoretical perspective, the variance of the AOA fluctuations measured with two microphones. The AOA variance is expressed in terms of the propagation range, transverse distance between two microphones, acoustic frequency, and effective spectrum of quasi-homogeneous and isotropic turbulence, with parameters dependent upon the height above the ground. The effective spectrum is modeled with the von Kármán and Kolmogorov spectral models. In the latter case, the results simplify significantly, and the variance depends on the path-averaged effective structure-function parameter, which characterizes the intensity of temperature and wind velocity fluctuations in the inertial subrange of turbulence. The standard deviation of the AOA fluctuations is studied numerically for typical meteorological regimes of the daytime atmospheric boundary layer. For the cases considered, the standard deviation varies from a fraction of degree to around 1°-2°, and increases with increasing friction velocity and surface heat flux.