Long-Range Nonlinear Propagation
in 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
Outline
OBJECTIVE : characterisation of underwater nuclear explosions
(Comprehensive Nuclear-Test-Ban Treaty).
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)
NPE moving frame
NPE algorithm
[B. E. McDonald, W. A. Kuperman,
J. Acoust. Soc. Am. 81,
1406-1417, (1987)]
c0

 c

 t p   x c1 p 
p2   0
2 0c0  2


x

 2 p dx
Refraction + Nonlinear steepening Step :
Second order upwind flux corrected transport scheme
Diffraction Step :
Crank-Nicholson scheme
[B. E. McDonald, J. Comp. Phys. 56, 448-460, (1984)]
time incremental step  t =  x / c0 of the moving frame
to get a time waveform at a fixed location
Refraction included. Important for ocean waveguide.
Nonlinear Steepening and Shock Dissipation
Nonlinear steepening
Multivalued waveform no physical sense
Shock dissipation
Shock wave formation
Shock
formation
time
Nonlinear effects
- harmonic generation
- parametric interaction
- shock dissipation
- more uniform modal distribution
- self-refraction
Narrowband source in Shallow Water
Source characteristics :
50Hz narrowband (five-cycle sine wave)
depth : 100 m
level : Mach number = 3.5 10-3.
Linear
Shallow water Pekeris waveguide
200 m
1500 m/s
0.5 dB/, 1800 kg/m3, 1550 m/s
Nonlinear
PLEASE, LOAD FIRST BOTH MOVIES : 1 - LINEAR & 2 - NONLINEAR
THEN CLIC ON BOTH FRAMES TO WATCH THEM SIMULTANEOUSLY IN THE PRESENTATION
Nonlinear propagation peculiarities :- Nonlinear steepening
- Shock dissipation
energy distribution on each mode more homogeneous
Modal Amplitude vs Frequency in Shallow Water
Linear
Nonlinear
0 km
range
5 km
range
20 km
range
Ratio
Nonlinear/Linear
Narrowband source in Deep Water
Source characteristics :
10Hz narrowband (five-cycle sine wave),
depth : 1 km
level : Mach number = 3.5 10-3
deep-water waveguide
Munk
sound
speed
5km
profile
sediments
Linear
Nonlinear
PLEASE, LOAD FIRST BOTH MOVIES : 1 - LINEAR & 2 - NONLINEAR
THEN CLIC ON BOTH FRAMES TO WATCH THEM SIMULTANEOUSLY IN THE PRESENTATION
Deep water NL propagation peculiarities : smaller shock dissipation due to the spherical spreading
Modal Amplitude vs Frequency in Deep Water for different Source Depths
Source Depth=1 km
at 100 km range
Linear
Nonlinear
Nonlinear
Linear
Source Depth=2.5 km
Source Depth=4.5 km
Conclusion
How can we identify at long ranges a nonlinear
acoustic propagation path ?
Redistribution of the energy during the propagation
- frequency distribution
parametric and harmonic
- modal distribution
more relative energy for high order modes
What is the main difference between shallow and
deep water ?
In shallow water, lower geometrical spreading
higher amplitudes, stronger nonlinear effects