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Caustic formation occurs within a ray skeleton as optical or acoustic fieldspropagate in a medium with variable refractive properties and are unphysical,their presence being an artifact of the ray approximation of the field, andmethods of correcting the field near a caustic are well known. Differentialgeometry provides a novel approach to calculating acoustic intensity, assessingray stability and locating caustics in acoustic ray traces when the propertiesof medium are completely arbitrary by identifying points on the caustic withconjugate points along various rays. The method of geodesic deviation isapplied to the problem of determining ray stability and locating caustics in2-dimensional acoustic ray traces in a layered moving medium. Specifically, ageneral treatment of caustic formation in sound ducts and in piecewisecontinuous media is presented and applied to various idealized and realisticscenarios.

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