1. 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 Sponsored by Defense Threat Reduction Agency Contract No. DTRA01-00-C-0084

2. Outline OBJECTIVE : characterisation of underwater nuclear explosions (Comprehensive Nuclear-Test-Ban Treaty). Linear Normal Mode code (KRAKEN, [Porter, (1991)]) modal structure of long-range nonlinear propagation paths. 2 propagation codes used : Nonlinear code (NPE, [McDonald & Kuperman, (1987)]) shock propagation in an ocean waveguide

3. Nonlinear Progressive wave Equation (NPE) NPE algorithm Refraction + Nonlinear steepening Step : Second order upwind flux corrected transport scheme [B. E. McDonald, J. Comp. Phys. 56, 448-460, (1984)] Diffraction Step : Crank-Nicholson scheme c0c0 NPE moving frame time incremental step  t =  x / c 0 of the moving frame to get a time waveform at a fixed location Refraction included. Important for ocean waveguide. [B. E. McDonald, W. A. Kuperman, J. Acoust. Soc. Am. 81, 1406-1417, (1987)]

4. Shock formation time Nonlinear steepening Nonlinear Steepening and Shock Dissipation Multivalued waveform no physical sense Shock dissipation Shock wave formation

5. Nonlinear effects - harmonic generation - parametric interaction - shock dissipation - more uniform modal distribution - self-refraction

6. Narrowband source in Shallow Water Linear - Nonlinear steepening - Shock dissipation energy distribution on each mode more homogeneous Nonlinear propagation peculiarities : 200 m 0.5 dB/, 1800 kg/m 3, 1550 m/s Shallow water Pekeris waveguide 1500 m/s Source characteristics : 50Hz narrowband (five-cycle sine wave) depth : 100 m level : Mach number = 3.5 10 -3. Nonlinear PLEASE, LOAD FIRST BOTH MOVIES : 1 - LINEAR & 2 - NONLINEAR1 - LINEAR2 - NONLINEAR THEN CLIC ON BOTH FRAMES TO WATCH THEM SIMULTANEOUSLY IN THE PRESENTATION

7. Modal Amplitude vs Frequency in Shallow Water 0 km range Ratio Nonlinear/Linear 5 km range NonlinearLinear 20 km range

8. Narrowband source in Deep Water LinearNonlinear deep-water waveguide Munk sound speed profile sediments 5km Source characteristics : 10Hz narrowband (five-cycle sine wave), depth : 1 km level : Mach number = 3.5 10 -3 smaller shock dissipation due to the spherical spreading Deep water NL propagation peculiarities : PLEASE, LOAD FIRST BOTH MOVIES : 1 - LINEAR & 2 - NONLINEAR1 - LINEAR 2 - NONLINEAR THEN CLIC ON BOTH FRAMES TO WATCH THEM SIMULTANEOUSLY IN THE PRESENTATION

9. Source Depth=4.5 km Modal Amplitude vs Frequency in Deep Water for different Source Depths Linear Nonlinear Source Depth=1 kmSource Depth=2.5 km Nonlinear Linear at 100 km range

10. Conclusion How can we identify at long ranges a nonlinear acoustic propagation path ? What is the main difference between shallow and deep water ? In shallow water, lower geometrical spreading higher amplitudes, stronger nonlinear effects - modal distribution more relative energy for high order modes Redistribution of the energy during the propagation - frequency distribution parametric and harmonic