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Evaluation of the smoothed interference pattern under conditions of ray chaos. (English) Zbl 0983.76085

Summary: A ray-based approach has been considered for the evaluation of coarse-grained Wigner function. From the viewpoint of wave propagation theory, this function represents the local spectrum of wave field smoothed over some spatial and angular scales. A simple formula has been considered which expresses the smoothed Wigner function through parameters of ray trajectories. Although the formula is ray-based, it nevertheless has no singularities at caustics, and its numerical implementation does not require looking for eigenrays. These advantages are especially important under conditions of ray chaos when fast growing numbers of eigenrays and caustics are important factors spoiling applicability of standard semiclassical approaches already in short ranges. Similar factors restrict the applicability of some semiclassical predictions in quantum mechanics at times exceeding the so-called “logarithm break time.” Numerical calculations have been carried out for a particular model of range-dependent waveguide where ray trajectories exhibit chaotic motion. These calculations have confirmed our conjecture that by choosing large enough smoothing scales, i.e. by sacrificing small details of interference pattern, one can substantially enhance the validity of ray theory.

MSC:

76Q05 Hydro- and aero-acoustics
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
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