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Item type:Publication, Access status: with files , Ray tracing via SnelliusA wave travelling between two media denoted by different wave propagation velocities is subject to refraction at the interface between the media. The refraction is regulated by the Snellius law, where the interface is assumed infinitesimally thin. The jump in propagation velocity at the interface results in a discontinuous propagation direction for the wave. We consider a continuously changing medium, where the wave propagation velocity is assumed to be a continuous field. We reduce the Snellius law to its linear expansion at the interface between two regions of the medium with infinitesimally different propagation velocities. The linearised Snellius law connects the curvilinear coordinates associated with the propagation process from a point source and the spatial distribution of the propagation velocity. The coordinates map the rays evolving from the source and the wavefronts, orthogonal to the rays. Curved rays determine local osculating planes, spanned by the tangent to the ray and the gradient of the propagation velocity. The wavefront curvature is determined parallel to the tracing of each ray. Intersections of the wavefront are considered, with the osculating plane and with the longitudinal plane of the ray. For curved rays, the determined wavefront curvatures are different for the different planes. A numerical implementation of the model is used to approach an exemplary test case, regarding sound radiation in a stratified medium.Publicationtype: Journal Article31 17 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Wave propagation in non‐uniform media by linear expansion of the refraction lawThe propagation of mechanical waves in an unbounded, non‐uniform medium can be described by using curvilinear coordinates centered at the source position. The Frenet coordinate system, with origin on a point riding a wave, is used as a basis for the curvilinear coordinates. In this way a principal coordinate stating the evolution of the wave field and running along a ray, orthogonally to the successive wave fronts, is determined. A linear expansion of the refraction law at the rider point connects the gradient of the speed of sound field to the curvatures of the wave path and of the wave front. We use this connection in developing a numerical solution for the wave field, after recalling recent developments about the historical determination of the refraction law.Publicationtype: Journal Article18 7