Causality, caustics, and the structure of transient wave fields

Brown, Michael G.; Tappert, F. D.

doi:10.1121/1.394181

Cited by 12 publications

(3 citation statements)

References 13 publications

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“…4. 10,11 For the range-dependent case shown in the lower panels of Figs. 3 and 4, the effects of ray chaos are already apparent, although the number of eigenrays at depth Zϭ1000 m remains equal to four.…”

Section: Numerical Methods and Resultsmentioning

confidence: 99%

Ray chaos and eigenrays

Tappert

Tang

1996

The Journal of the Acoustical Society of America

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In a realistic range-dependent deep ocean environment that gives rise to ray chaos, a complete set of eigenrays at long ranges is computed using a numerical technique based on the shooting method. The numerical results support and illustrate the known connection between ray chaos and eigenrays, namely, that the number of eigenrays grows exponentially, on average, with increasing range. It is further found that groups of chaotic eigenrays tend to form ''clusters'' having stable envelopes.

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Section: Numerical Methods and Resultsmentioning

confidence: 99%

Ray chaos and eigenrays

Tappert

Tang

1996

The Journal of the Acoustical Society of America

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“…Caustics and focusing effects are then spatio-temporal singularities occurring during propagation in anisotropic, inhomogeneous, moving and turbulent media. These effects can be described by catastrophe theory, by specialised singular mathematical treatments and ad-hoc theoretical tools [23][24][25][26][27][28]. Most of these features are inherently related to the transient fields and to causality principles.…”

Section: Introduction and Position Of The Problemmentioning

confidence: 99%

Cuspidal caustic and focusing of acoustical waves generated by a parametric array onto a concave reflecting surface

Castagnède

Sahraoui

Tournat

et al. 2009

Comptes Rendus. Mécanique

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The present Note is devoted to the study of the so-called cuspidal caustic at the surface of a hemi-cylindrical reflector illuminated with plane waves. In order to generate low frequency (e.g. in the range of 4 kHz) acoustical plane waves, a commercially available parametric array has been used. It produces powerful ultrasonic carrier waves at 40 kHz which can be electronically modulated between 200 Hz and 10 kHz. Further self-demodulation process during propagation in air generates an ultra-directive acoustical field (i.e. quasi-planar wavefronts) enabling to accurately study the focusing process occurring along the cuspidal caustic. The focusing coefficient can be computed locally by using two numerical tools, on one hand by computing the density of tangent rays to the caustic, and on the other hand by using some numerical results provided by a ray tracing algorithm. Some preliminary experimental data are then provided in order to validate the numerical predictions (spatial position of the caustic and focusing coefficient).

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“…The literature on time-domain canonical functions is scarce. Time-domain canonical functions for simple caustics were derived in [4,24,3,15]. The canonical expressions given in [4] and in [3] are non-uniform while the expression derived in [24] does not satisfy the radiation condition.…”

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confidence: 99%