The Ray-Wave correspondence and the suppression of chaos in long-range sound propagation in the ocean

Макаров, Денис В.; Kon’kov, L. E.; Uleysky, M. Yu.

doi:10.1134/s1063771008030147

Cited by 13 publications

(4 citation statements)

References 26 publications

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“…In the present work we use only one of them. Ray chaos can lead to intense energy exchange between normal modes [9,13,24], therefore, a "chaotic" eigenfunction is a compound of many modes. The stronger chaos, the larger number of contributing modes.…”

Section: B Eigenfunction Statisticsmentioning

confidence: 99%

“…Numerous experiments on long-range sound propagation in the North-Eastern Pacific Ocean (see, for instance, [47][48][49][50][51]) indicate on strong irregularity of flat near-axial rays, associated with ray chaos [52,53]. The "deterministic" mechanism of near-axial chaos is ray scattering on vertical resonances caused by small-scale depth oscillations of the sound-speed perturbation [12,13,15]. These oscillations are contributed from high-number modes of an internal-wave field.…”

Section: One-step Poincar é Mapmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2013

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The proplem of sound propagation in an oceanic waveguide is considered. Scattering on random inhomogeneity of the waveguide leads to wave chaos. Chaos reveals itself in spectral properties of the finite-range evolution operator (FREO). FREO describes transformation of a wavefield in course of propagation along a finite segment of a waveguide. We study transition to chaos by tracking variations in spectral statistics with increasing length of the segment. Analysis of the FREO is accompanied with ray calculations using the one-step Poincaré map which is the classical counterpart of the FREO. Underwater sound channel in the Sea of Japan is taken for an example. Several methods of spectral analysis are utilized. In particular, we approximate level spacing statistics by means of the Berry-Robnik and Brody distributions, explore the spectrum using the procedure elaborated by A. Relano with coworkers (Relano et al, Phys. Rev. Lett., 2002; Relano, Phys. Rev. Lett., 2008), and analyze modal expansions of the eigenfunctions. We show that the analysis of FREO eigenfunctions is more informative than the analysis of eigenvalue statistics. It is found that near-axial sound propagation in the Sea of Japan preserves stability even over distances of hundreds kilometers. This phenomenon is associated with the presence of a shearless torus in the classical phase space. Increasing of acoustic wavelength degrades scattering, resulting in recovery of localization near periodic orbits of the one-step Poincaré map. Relying upon the formal analogy between wave and quantum chaos, we suggest that the concept of FREO, supported by classical calculations via the one-step Poincaré map, can be efficiently applied for studying chaos-induced decoherence in quantum systems.

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Section: B Eigenfunction Statisticsmentioning

confidence: 99%

Section: One-step Poincar é Mapmentioning

confidence: 99%

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

et al. 2013

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“…where 0 < φ < 2π, f * , p * and φ * are values of f , p and φ, respectively, when the trajectory hits the resonant region. ∆E depends extremely on φ * , therefore multiple recurrences to the resonant area cause chaotic diffusion in phase space [17,18,19]. With fixed values of k and ν, the resonant condition (4) has the simplest form…”

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confidence: 99%

Giant acceleration in slow-fast space-periodic Hamiltonian systems

Макаров

Uleysky

2007

Phys. Rev. E

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The motion of an ensemble of particles in a space-periodic potential well with a weak wavelike perturbation imposed is considered. We found that slow oscillations of the wave number of the perturbation lead to the occurrence of directed particle current. This current is amplified with time due to the giant acceleration of some particles. It is shown that giant acceleration is linked to the existence of resonant channels in phase space.

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