The use of a microphone array for acoustic measurements in wind tunnels is known to degrade the sound pressure levels and dynamic range of the acoustic image, due to the decorrelation between each pair of microphones, after the acoustic wave has crossed the turbulent boundary layer of the wind tunnel.
Based on a large number of studies in the areas of radiophysics, underwater acoustics and atmospheric science, this paper describes research on a physical model of wave propagation in a turbulent medium and its stochastic solution, obtaining as a solution the statistical momentum of the wave signal after it has propagated through the turbulent medium. The parabolic equation for acoustic wave propagation is considered and the Markov approximation is assumed for the stochastic solution of the wave. The signal coherence between each pair of microphones is the amount considered responsible for the decorrelation of the signals. Thus, the statistic to be considered for the stochastic solution of the equation is the coherence of the wave after it has crossed the turbulent boundary layer. In the model developed, this amount is represented by the second order coherence function.
Hot-wire measurements were carried out and the turbulence parameters were inserted into the model. Acoustic phased array measurements were performed and the results show agreement with the predictions, validating the use of the model for wind tunnel conditions and assumptions. Theoretical turbulence models for correlation were studied and the results used to validate the type of turbulent correlations for the wind tunnel.