Analysis of ray stability and caustic formation in a layered moving fluid medium

TL;DR

This paper introduces a differential geometric approach using geodesic deviation to analyze ray stability and locate caustics in layered moving media, improving understanding of acoustic field artifacts in complex environments.

Contribution

It presents a novel method based on differential geometry for calculating acoustic intensity, assessing ray stability, and locating caustics in arbitrary layered moving media.

Findings

The method effectively identifies caustics in layered moving media.

Application to idealized and realistic scenarios demonstrates its versatility.

Provides insights into caustic formation in sound ducts and piecewise media.

Abstract

Caustic formation occurs within a ray skeleton as optical or acoustic fields propagate in a medium with variable refractive properties and are unphysical, their presence being an artifact of the ray approximation of the field, and methods of correcting the field near a caustic are well known. Differential geometry provides a novel approach to calculating acoustic intensity, assessing ray stability and locating caustics in acoustic ray traces when the properties of medium are completely arbitrary by identifying points on the caustic with conjugate points along various rays. The method of geodesic deviation is applied to the problem of determining ray stability and locating caustics in 2-dimensional acoustic ray traces in a layered moving medium. Specifically, a general treatment of caustic formation in sound ducts and in piecewise continuous media is presented and applied to various idealized and realistic scenarios.