Modeling Sound Propagation Through an Incompressible Flow

date October 3, 2014
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Friday, October 3, 2014 4:00 p.m. ETC 4.150

Sumedh M. Joshi
Center for Applied Mathematics
Cornell University
http://www.cam.cornell.edu

Sound propagating in a moving fluid will be advected, refracted, and Doppler shifted by the patterns in the moving flow. For example, a pulse of sound impinging on an inviscid shear layer is advected in the direction of the shear flow, in addition to being reflected from the shear-layer interface. To model such sound-flow interactions, it was assumed that the background flow was known and satisfied the incompressible Navier-Stokes equations. Furthermore, it was also assumed that the sum of the acoustic and hydrodynamic fields satisfied momentum and mass conservation. Finally, the sound propagation was assumed to be linear. These assumptions lead to hyperbolic conservation laws that were discretized and solved with a time-domain finite difference model. To demonstrate, a few example flows and their resulting sound fields will be presented, and I will also discuss a modeling effort that attempts to quantify the degree to which the acoustic scattering from an idealized tornado funnel can be used to infer properties of the tornado. The modeling suggests that although there is a measurable acoustic reflection, practical concerns suggest that acoustics are not a viable method of inferring tornado properties.