Long-Range Nonlinear Propagation
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Long-Range Nonlinear Propagation in an Ocean Waveguide. Kaëlig C ASTOR (1) Peter G ERSTOFT (1) Philippe R OUX (1) W. A. K UPERMAN (1) B. E. M C D ONALD (2). (1) Scripps Institution of Oceanography, La Jolla, CA 92093 USA (2) US Naval Research Laboratory, Washington DC 20375 USA.

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Long-Range Nonlinear Propagation in an Ocean Waveguide

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Long range nonlinear propagation in an ocean waveguide

Long-Range Nonlinear Propagationin an Ocean Waveguide

Kaëlig CASTOR (1)

Peter GERSTOFT (1)

Philippe ROUX (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


Long range nonlinear propagation in an ocean waveguide

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.

Outline

OBJECTIVE : characterisation of underwater nuclear explosions (Comprehensive Nuclear-Test-Ban Treaty).


Long range nonlinear propagation in an ocean waveguide

NPE moving frame

c0

time incremental step t =  x / c0 of the moving frame

to get a time waveform at a fixed location

Nonlinear Progressive wave Equation (NPE)

NPE algorithm

[B. E. McDonald, W. A. Kuperman,

J. Acoust. Soc. Am.81,

1406-1417, (1987)]

Diffraction Step :

Crank-Nicholson scheme

Refraction + Nonlinear steepening Step :

Second order upwind flux corrected transport scheme

[B. E. McDonald, J. Comp. Phys. 56, 448-460, (1984)]

Refraction included. Important for ocean waveguide.


Long range nonlinear propagation in an ocean waveguide

Nonlinear steepening

Multivalued waveform no physical sense

Shock dissipation

Shock wave formation

Shock

formation

time

Nonlinear Steepening and Shock Dissipation


Long range nonlinear propagation in an ocean waveguide

Nonlinear effects

- harmonic generation

- parametric interaction

- shock dissipation

- more uniform modal distribution

- self-refraction


Long range nonlinear propagation in an ocean waveguide

Shallow water Pekeris waveguide

200 m

1500 m/s

0.5 dB/, 1800 kg/m3, 1550 m/s

Narrowband source in Shallow Water

Source characteristics :

50Hz narrowband (five-cycle sine wave)

depth : 100 m

level : Mach number = 3.5 10-3.

Linear

Nonlinear

PLEASE, LOAD FIRST BOTH MOVIES : 1 - LINEAR & 2 - NONLINEAR

THEN CLIC ON BOTH FRAMES TO WATCH THEM SIMULTANEOUSLY IN THE PRESENTATION

- Nonlinear steepening

- Shock dissipation

energy distribution on each mode more homogeneous

Nonlinear propagation peculiarities :


Long range nonlinear propagation in an ocean waveguide

Ratio

Nonlinear/Linear

5 km range

20 km range

Modal Amplitude vs Frequency in Shallow Water

Linear

Nonlinear

0 km range


Long range nonlinear propagation in an ocean waveguide

deep-water waveguide

Munk sound

speed profile

5km

sediments

Narrowband source in Deep Water

Source characteristics :

10Hz narrowband (five-cycle sine wave),

depth : 1 km

level : Mach number = 3.5 10-3

Linear

Nonlinear

PLEASE, LOAD FIRST BOTH MOVIES : 1 - LINEAR& 2 - NONLINEAR

THEN CLIC ON BOTH FRAMES TO WATCH THEM SIMULTANEOUSLY IN THE PRESENTATION

smaller shock dissipation due to the spherical spreading

Deep water NL propagation peculiarities :


Long range nonlinear propagation in an ocean waveguide

Source Depth=2.5 km

Source Depth=4.5 km

Modal Amplitude vs Frequency in Deep Water for different Source Depths

Source Depth=1 km

at 100 km range

Linear

Nonlinear

Nonlinear

Linear


Long range nonlinear propagation in an ocean waveguide

Redistribution of the energy during the propagation - frequency distribution parametric and harmonic

- modal distributionmore relative energy for high order modes

In shallow water, lower geometrical spreadinghigher amplitudes, stronger nonlinear effects

Conclusion

How can we identify at long ranges a nonlinear acoustic propagation path ?

What is the main difference between shallow and deep water ?


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