Wave chaos and mode–medium resonances at long-range sound propagation in the ocean

Abstract

We study how the chaotic ray motion manifests itself at a finite wavelength at long-range sound propagation in the ocean. The problem is investigated using a model of an underwater acoustic waveguide with a periodic range dependence. It is assumed that the sound propagation is governed by the parabolic equation, similar to the Schrodinger equation. When investigating the sound energy distribution in the time-depth plane, it has been found that the coexistence of chaotic and regular rays can cause a "focusing" of acoustic energy within a small temporal interval. It has been shown that this effect is a manifestation of the so-called stickiness, that is, the presence of such parts of the chaotic trajectory where the latter exhibit an almost regular behavior. Another issue considered in this paper is the range variation of the modal structure of the wave field. In a numerical simulation, it has been shown that the energy distribution over normal modes exhibits surprising periodicity. This occurs even for a mode formed by contributions from predominantly chaotic rays. The phenomenon is interpreted from the viewpoint of mode-medium resonance. For some modes, the following effect has been observed. Although an initially excited mode due to scattering at the inhomogeneity breaks up into a group of modes its amplitude at some range points almost restores the starting value. At these ranges, almost all acoustic energy gathers again in the initial mode and the coarse-grained Wigner function concentrates within a comparatively small area of the phase plane.

Statistics of the ray travel times in oceanic acoustic waveguides under chaos conditions

“…The confluence regions correspond to the "shelves" on the BW travel time versus initial momentum diagrams (by a "shelf" we call the part of the plot near the point with zero slope, for which the derivative dT/dp s is equal to zero. The existence of shelves in the T versus p s diagrams is a characteristic property of refraction waveguides [5]). Most of the CW times are located near the shelves due to "sticking" of the chaotic paths to the islands [4][5][6].…”

“…The existence of shelves in the T versus p s diagrams is a characteristic property of refraction waveguides [5]). Most of the CW times are located near the shelves due to "sticking" of the chaotic paths to the islands [4][5][6].…”

“…However, in spaceinhomogeneous waveguides the ray paths are unstable, and this assumption is not always justified. Modeling of pulsed-signal propagation in such waveguides shows that the spatio-temporal structure of the received signals is of increased complexity (compared with the homogeneous waveguides) and has features which, obviously, cannot be explained without invoking the dynamic-chaos theory [2][3][4][5][6][7]. All this generates interest in a study of the properties of chaotic rays determining the above-mentioned structure of the signals.…”

“…Calculations [3][4][5][6][7] show that each cluster comprises rays having the same identifiers (numbers of turning points taken with the sign of the angle of the ray escape from the source). An analysis shows that the travel time is mainly determined by two parameters, namely the identifier and the ray depth in the receiver cross section (final depth).…”

Wave chaos in a randomly inhomogeneous waveguide: Spectral analysis of the finite-range evolution operator

“…During the last two decades ray chaos in ocean * makarov@poi.dvo.ru acoustics was an object of intense research, both theoretical and experimental [4][5][6][7][8]. Considerable attention was paid to wave chaos [3,[9][10][11][12][13][14]. The term wave chaos relates to wavefield manifestations of ray chaos.…”