Nonlinear Modes Interaction in an Acoustic Waveguide

OBJECTIVE : characterize high amplitude signals propagating in an ocean waveguide over very long ranges (several 1000km). • Linear Normal Mode code ...
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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)]

 c  β p2  − 0 ∂ t p = −∂ x c1 p + 2 ρ0c0  2  5HIUDFWLRQ1RQOLQHDUVWHHSHQLQJ

δ 2 c0 p dx p ∇ + ∂ + 0.02 α ( dB / λ ) x ∫ +∞ 2 2

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NPE moving frame

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time incremental step ∆ t = ∆ x / c0 of the moving frame to get a time waveform at a fixed location

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Nonlinear effects $GGLWLRQDOIUHTXHQFLHV

- 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

0.01 dB/λ, 1800 kg/m3, 1550 m/s

5km

Shallow water ocean waveguide Source characteristics : 30Hz narrowband source depth : 100 m level : Mach number = 5 10-3.

Range=100km

150

-15

200

-20

250

-25 0.5

-30

2.5

dB

Nonlinear

0

Depth (m)

1 1.5 2 Reduced time (s)

0

50

-5

100

-10

150

-15

200

-20

250

-25

300 0

0.5

1 1.5 2 Reduced time (s)

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-30

1500 1495 1490

Depth-averaged spectrum

-10

Linear, r=100km

1470

0.6

Shallow water fondamental frequency first harmonic

1 0.4 1 0.2

2 10

20

30 40 50 Frequency (Hz)

60

70

3

1480 1475

kg/m3,

0.8

0

1485

Nonlinear, r=100km

1 Depth-averaged spectrum

100

group speed (m/s)

Depth (m)

-5

1500 m/s

0.01 dB/λ, 1800

1

0

50

300 0

200 m

dB

Linear

0

Shallow water Pekeris waveguide

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2

0.8

4

0.6 0.4

1510

1520 1530 phase speed (m/s)

1540

0.2 0

10

20

30 40 50 Frequency (Hz)

60

70

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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+ Different source positions

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Parametric low frequency S hallo w w ate r, r=100km 1

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0.2

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10

20

30 40 50 Fre que nc y (Hz)

60

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0.4

0.2

0

70

10

20

1

0.8

0.8

0.6

0.4

0.2

0

10

20

30 40 50 Fre que nc y (Hz)

60

70

60

70

De e p w ate r, r=100km

1

De pth-ave rag e d s pe c trum

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30 40 50 Fre que nc y (Hz)

60

70

0.6

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0.4

0.2

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Deep water ocean waveguide : influence of parametric mode conversion on sea-bottom coupling /LQHDU

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