Long-Range Nonlinear Propagationin an Ocean WaveguideKalig 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 USASponsored by Defense Threat Reduction Agency Contract No. DTRA01-00-C-0084

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

Nonlinear Progressive wave Equation (NPE)NPE algorithmRefraction + Nonlinear steepening Step :Second order upwind flux corrected transport scheme[B. E. McDonald, J. Comp. Phys. 56, 448-460, (1984)]Diffraction Step :Crank-Nicholson schemeRefraction included. Important for ocean waveguide.[B. E. McDonald, W. A. Kuperman,J. Acoust. Soc. Am. 81,1406-1417, (1987)]

Nonlinear Steepening and Shock Dissipation

Nonlinear effects- harmonic generation - parametric interaction

- shock dissipation

- more uniform modal distribution

- self-refraction

Narrowband source in Shallow WaterLinear- Nonlinear steepening- Shock dissipation energy distribution on each mode more homogeneousNonlinear propagation peculiarities :Source characteristics : 50Hz narrowband (five-cycle sine wave)depth : 100 m level : Mach number = 3.5 10-3.NonlinearPLEASE, LOAD FIRST BOTH MOVIES : 1 - LINEAR & 2 - NONLINEARTHEN CLIC ON BOTH FRAMES TO WATCH THEM SIMULTANEOUSLY IN THE PRESENTATION

Modal Amplitude vs Frequency in Shallow Water0 km rangeNonlinearLinear

Narrowband source in Deep WaterLinearNonlinearSource characteristics : 10Hz narrowband (five-cycle sine wave), depth : 1 km level : Mach number = 3.5 10-3 smaller shock dissipation due to the spherical spreadingDeep water NL propagation peculiarities :PLEASE, LOAD FIRST BOTH MOVIES : 1 - LINEAR & 2 - NONLINEARTHEN CLIC ON BOTH FRAMES TO WATCH THEM SIMULTANEOUSLY IN THE PRESENTATION

Modal Amplitude vs Frequency in Deep Water for different Source DepthsLinearNonlinearSource Depth=1 kmNonlinearLinearat 100 km range

ConclusionHow can we identify at long ranges a nonlinear acoustic propagation path ? What is the main difference between shallow and deep water ?