Activity: Talk or presentation types › Invited talk
In this talk, we present an overview of the general theory of sound generation by turbulence scattered by a solid surface in which the flow upstream of the embedded surface is transversely sheared. The solution to the latter problem represents the lowest order expansion of the Navier Stokes equations for turbulence undergoing Rapid distortion where both the time scale of the interaction and the turbulence intensity are taken as small parameters but are otherwise O(1). In the talk, we show how when interpreted asymptotically, the latter scaling implies, among other things, that the upstream boundary condition for the scattering problem can be placed at an infinite distance away from the edge on the local interaction scale but that this distance may still be smaller than the O(1) eddy decay length scale.
This asymptotic separation of scales then allows the upstream turbulence to be defined apriori, i.e. cleanly, in the undisturbed hydrodynamic field, before any interaction has taken place. The sound radiation can then be self-consistently identified as a downstream response (or, output) to this upstream boundary condition (or, input) and is worked out using both matched asymptotic expansions and the Wiener-Hopf technique in that order. We discuss a range of results we have obtained using this approach for sound scattered by both planar and non-planar jet flows. In general, our results have been able to capture the low-frequency sound amplification at a range of acoustic Mach numbers and observation angles.