# Transport of power in random waveguides with turning points

## TL;DR

This paper develops a mathematical framework for understanding how random boundary fluctuations in a 2D acoustic waveguide affect wave propagation, mode coupling, and power transport, especially near turning points where modes change behavior.

## Contribution

It introduces a first-principles mode coupling theory for waveguides with random boundaries and quantifies the impact on power transport and reflection at turning points.

## Key findings

- Random boundary scattering significantly influences wave power transmission.
- Mode coupling can either increase or decrease net power depending on the source.
- The theory captures the effects of boundary randomness on wave reflection and transmission.

## Abstract

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.