GENERATION OF FLUCTUATING NORMAL STRESS IN A VISCOELASTIC LAYER BY SURFACE SHEAR-STRESS AND PRESSURE AS IN TURBULENT BOUNDARY-LAYER FLOW

At low wave numbers, according to recent indications, fluctuating wall shear stress generated by a turbulent boundary layer may be comparable with fluctuating wall pressure. Consideration is given here to the fluctuating normal stress generated within an elastic layer by both shear-stress and pressure excitation on its outer face. The transfer level from surface shear to normal stress is shown to be comparable with or exceed that from surface pressure in a significant range of low to intermediate wave numbers. This transfer from surface shear stress is enhanced by the outer fluid loading and by the imposition of vanishing displacement at an inner rigid surface. Results of computations are presented and analyzed in numerical examples based on a configuration where an elastomer layer is bounded by a fluid half-space at its excited surface and by a thin, damped plate at its inner surface, with a similar fluid half-space below the plate. Results are given also for the limiting cases of a rigid inner surface and of an elastic half-space with and without fluid loading. The transfer level from shear stress is computed also where a concomitant wall pressure is present and related to shear stress as recently determined from a theoretical treatment of the viscous boundary condition at low wave numbers in turbulent boundary-layer flow. It is thus suggested that the contribution of turbulent wall-shear stress to flow noise on recessed hydrophones in the absence of a plate-like element between these and the flow is likely an important one.