# Wave Scattering in Spatially Inhomogeneous Currents

## TL;DR

This paper analytically investigates how long surface waves scatter in a duct with spatially varying currents, providing solutions relevant to analog gravity experiments and hydrodynamic modeling of Hawking radiation.

## Contribution

It offers an analytical solution for wave scattering in inhomogeneous currents, covering all current types and propagation directions, advancing understanding in analog gravity contexts.

## Key findings

- Derived scattering coefficients as functions of wave frequency.
- Analyzed wave behavior in sub-, super-, and trans-critical currents.
- Linked results to analog gravity experiments and Hawking radiation modeling.

## Abstract

We analytically study a scattering of long linear surface waves on stationary currents in a duct (canal) of constant depth and variable width. It is assumed that the background velocity linearly increases or decreases with the longitudinal coordinate due to the gradual variation of duct width. Such a model admits analytical solution of the problem in hand, and we calculate the scattering coefficients as functions of incident wave frequency for all possible cases of sub-, super-, and trans-critical currents. For completeness we study both co-current and counter-current wave propagation in accelerating and decelerating currents. The results obtained are analysed in application to recent analog gravity experiments and shed light on the problem of hydrodynamic modelling of Hawking radiation.