Transport of power in random waveguides with turning points

作     者：Borcea, Liliana Garnier, Josselin Wood, Derek 

作者机构：Department of Mathematics University of Michigan Ann ArborMI48109 United States Centre de Mathématiques Appliquées Ecole Polytechnique Palaiseau Cedex91128 France 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2017年

核心收录：

主　　题：Waveguides 

摘      要：We present a mathematical theory of time-harmonic wave propagation and reection in a two-dimensional random acoustic waveguide with sound soft boundary and turning points. The boundary has small uctuations on the scale of the wavelength, modeled as random. The waveguide supports multiple propagating modes. The number of these modes changes due to slow variations of the waveguide cross-section. The changes occur at turning points, where waves transition from propagating to evanescent or the other way around. We consider a regime where scattering at the random boundary has significant effect on the wave traveling from one turning point to another. This effect is described by the coupling of its components, the modes. We derive the mode coupling theory from first principles, and quantify the randomization of the wave and the transport and reection of power in the waveguide. We show in particular that scattering at the random boundary may increase or decrease the net power transmitted through the waveguide depending on the source. Copyright © 2017, The Authors. All rights reserved.