Communications in Mathematical Sciences
Volume 15 (2017)
Transport of power in random waveguides with turning points
Pages: 2327 – 2371
We present a mathematical theory of time-harmonic wave propagation and reflection in a two-dimensional random acoustic waveguide with sound soft boundary and turning points. The boundary has small fluctuations 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 reflection 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.
mode coupling, turning waves, scattering, random waveguide
2010 Mathematics Subject Classification
35Q99, 60F05, 78M35
Paper received on 13 February 2017.
Paper accepted on 23 August 2017.