THE WALL-PRESSURE SPECTRUM IN TURBULENT-FLOW OVER A RANDOMLY INHOMOGENEOUS ELASTIC SOLID

The characteristics of the low-wave-number and acoustic domains of the turbulent boundary layer wall-pressure specturum are critically dependent on the structural properties of the wall. This dependence is examined in this paper in terms of a theoretical model of turbulent flow of water over an elastomeric material containing a random distribution of rigid (but movable) filaments. The interaction of hydrodynamic, convective boundary layer pressure fluctuations with the filaments generates a secondary pressure field by scattering. The intensities of the secondary pressures are negligible compared to the convective pressures responsible for their generation, but may nonetheless be large enough to produce significant changes in the relatively weak, low-wave-number region of the wall pressure. The magnitude of the changes depends on the relative mass density of the material of the filaments, on their diameters relative to the boundary layer thickness, and on their fractional volume density. Numerical results indicate that increases of the order of 10-20 dB (compared to theoretical estimates for the homogeneous elastomer) can be produced by filaments occupying only 1% by volume of the elastomer. Predictions of this kind suggest that experimental data relating to the low-wave-number and acoustic domains are easily contaminated by the presence of relatively small nonuniformities in wall properties.