A theoretical expression for the far-field acoustic power spectral density produced by an airfoil in a subsonic turbulent stream is given in terms of quantities characteristic of the turbulence. For an observer directly above the airfoil the relevant quantities are the spanwise correlation length of the turbulence as a function of frequency and the PSD of the vertical velocity fluctuations, both quantities being measured in an airfoil fixed co-ordinate system. In the derivation it is assumed that the spanwise correlation length is much smaller than the airfoil span.
A more solid theoretical foundation is developed for a lift expression given by Liepmann for an airfoil in turbulence. Also, the analysis shows why it is not necessary, within certain limitations, to integrate over all gust wavenumbers in order to calculate the sound at a given observer location. Rather, for small turbulence length scales the observer hears only the sound produced by a particular wavenumber component of the turbulence, and thus the analysis can be simplified considerably.
A comparison of the theory with experimental acoustic and lift measurements available in the literature shows good agreement.