Nonlinear Behavior of Acoustic Rays Underwater Sound Channels

Marian Wiercigroch*, Alexander H.D. Cheng, Jeffrey Simmen, Mohsen Badiey

*Corresponding author for this work

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

The nonlinear behavior ot acoustic rays in underwater sound channels is examined using a set of parabolic ray equations. Two sound speed profiles, a Munk canonical and a double-duct profile, are investigated. For range-independent but stratified ocean sound speed profiles, analytical results concerning the sound ray trajectory and wave length are obtained. The stability of the system is found to be marginal stable, which leads to the phenomenon of wave front folding. Next, a perturbed system attributed to a single-mode internal wave is examined. The stability, bifurcation and other nonlinear dynamic issues of the nearly integrable system are explored using a combination of phase plane trajectories, Poincaré maps, bifurcation diagrams, Lyapunov exponents and Floquet multipliers.

Original languageEnglish
Pages (from-to)193-207
Number of pages15
JournalChaos, Solitons and Fractals
Volume9
Issue number1-2
DOIs
Publication statusPublished - 1 Jan 1998

Fingerprint

Half line
Acoustics
Floquet multipliers
Trajectory
Internal Waves
Phase Plane
Perturbed System
Bifurcation Diagram
Single Mode
Integrable Systems
Folding
Wave Front
Lyapunov Exponent
Ocean
Nonlinear Dynamics
Bifurcation
Wavelength
Sound
Range of data
Profile

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Nonlinear Behavior of Acoustic Rays Underwater Sound Channels. / Wiercigroch, Marian; Cheng, Alexander H.D.; Simmen, Jeffrey; Badiey, Mohsen.

In: Chaos, Solitons and Fractals, Vol. 9, No. 1-2, 01.01.1998, p. 193-207.

Research output: Contribution to journalArticle

Wiercigroch, Marian ; Cheng, Alexander H.D. ; Simmen, Jeffrey ; Badiey, Mohsen. / Nonlinear Behavior of Acoustic Rays Underwater Sound Channels. In: Chaos, Solitons and Fractals. 1998 ; Vol. 9, No. 1-2. pp. 193-207.
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