Nonlinear Modes Interaction in an Acoustic Waveguide Kaëlig CASTOR (1) Philippe ROUX (1) Peter GERSTOFT (1) W. A. KUPERMAN (1) B. E. MCDONALD (2) (1)Scripps
Institution of Oceanography, La Jolla, CA 92093 USA (2)US Naval Research Laboratory, Washington DC 20375 USA Sponsored by Defense Threat Reduction Agency Contract No. DTRA01-00-C-0084
Outline OBJECTIVE : characterize high amplitude signals propagating in an ocean waveguide over very long ranges (several 1000km). 2 propagation codes used : • Nonlinear code (NPE, [McDonald & Kuperman, (1987)]) shock propagation in an ocean waveguide • Linear Normal Mode code (KRAKEN, [Porter, (1991)]) modal structure of long-range nonlinear propagation paths.
Nonlinear Progressive wave Equation (NPE) [B. E. McDonald, W. A. Kuperman, J. Acoust. Soc. Am. 81, 1406-1417, (1987)]
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- harmonic generation (2f, 3f, 4f,...)
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- parametric interaction (f1 ± f2) - shock dissipation
Nonlinear steepening Multivalued waveform no physical sense Shock dissipation Shock wave formation - more uniform modal distribution - self-refraction
Shallow water to deep water waveguide
- Nonlinear Propagation with the NPE code until 100km - NPE outputs propagated linearly with the Kraken normal mode code Environment : Source characteristics : 30Hz narrowband source depth : 100 m level : Mach number = 5 10-3.
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1500 m/s
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5km
Shallow water ocean waveguide Source characteristics : 30Hz narrowband source depth : 100 m level : Mach number = 5 10-3.
Range=100km
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Depth-averaged spectrum
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30 40 50 Frequency (Hz)
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1 Depth-averaged spectrum
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group speed (m/s)
Depth (m)
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1500 m/s
0.01 dB/λ, 1800
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1550 m/s
Nonlinearities change : • spectrum • modal distribution • time arrival structure
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Deep water ocean waveguide
- Nonlinear Propagation with the NPE code until 100km - NPE outputs propagated linearly with the Kraken normal mode code Environment : Source characteristics : 30Hz narrowband source depth : 800m level : Mach number = 5 10-3
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Deep water ocean waveguide : influence of parametric mode conversion on sea-bottom coupling /LQHDU
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