Geodesic
Chaotic diffusion at sound propagation in a range-dependent underwater sound channel
Russian journal of nonlinear dynamics, Tome 3 (2007) no. 2, pp. 157-174.

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Problem of sound propagation in a range-dependent underwater sound channel is studied in the scope of the problem of the ray-wave correspondence. Small-scale vertical oscillations of a sound channel inhomogeneity act on near-axial rays in a resonant way. Scattering of rays on resonance leads to forming of a wide chaotic layer with fast mixing in the underlying phase space. The Husimi distribution function is used for examining of dynamics of wavepackets belonging to the chaotic layer. At high frequencies of a signal, a wavepacket diverges rapidly with range. Decreasing of frequency leads to suppressing of resonance induced by vertical oscillations of an inhomogeneity, wavepacket stops diverging and its width in the action space starts to oscillate irregularly. At the frequency of 50 Hz these oscillations are regular, that indicates suppression of chaotic diffusion.
Keywords: ray chaos, wave chaos, ocean acoustics, nonlinear resonance, ray-wave correspondence. 
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     author = {D. V. Makarov and L. E. Kon'kov},
     title = {Chaotic diffusion at sound propagation in a range-dependent underwater sound channel},
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D. V. Makarov; L. E. Kon'kov. Chaotic diffusion at sound propagation in a range-dependent underwater sound channel. Russian journal of nonlinear dynamics, Tome 3 (2007) no. 2, pp. 157-174. http://geodesic.mathdoc.fr/item/ND_2007_3_2_a2/