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Non-liner dynamics of underwater acoustics. (English) Zbl 1235.76171
Summary: The non-linear dynamic behavior of acoustic wave propagation in an underwater sound channel, described by the Munk’s classical sound speed profile perturbed by a single-mode internal wave, is studied using a parabolic ray theory. The amplitude and wavelength of this single-mode wave are used as the branching parameters in bifurcation analysis. The phase plane trajectory of the ray-based system can be periodic, quasi-periodic, and unstable. The regions of instability, located numerically via the bifurcation diagrams, are examined through a sequence of phase diagrams and Poincaré maps. Charts showing the maximum uninterrupted propagation distance reveal instances of anomalous vertical scattering of sound energy. Floquet multipliers were used to investigate instability of periodic orbits.
MSC:
76Q05Hydro- and aero-acoustics
86A05Hydrology, hydrography, oceanography