On the Correlation of Acoustic Pressures Induced by a Turbulent Wake on a Nearby Wall

Turbulent jets and wakes radiate sound, and the corresponding pressure loads on nearby panels can cause acoustic fatigue. Assuming that the structural characteristics of the panel are known, the acoustic fatigue effects depend on the magnitude of the acoustic pressures and the way in which they are correlated in space and/or time. The present paper concentrates on the calculation of the correlation of acoustic pressures at the wall, using what is arguably the simplest model: (i) the incident sound field is assumed to be a plane wave, because an arbitrary source can be so decomposed; (ii) fluid-wall coupling is neglected, although the panel may be compliant, e.g. represented by a finite impedance; (iii) we consider only one reflection of sound from the turbulent wake, deferring to future work the consideration of the effects of multiple scattering. The present model accounts for the amplitude and phase changes of sound trapped between the wall panel and the turbulent jet or wake; the phases are particularly important, because they specify the interference between neighbouring wave components. Since the phases of sound become random on reflection by the turbulent jet or wake, statistical arguments are used to arrive at formulae for the correlation of acoustic pressures, which depends on the variance and correlation of the phases.