Integral equation coupled mode approach applied to internal wave problems

Journal of Computational Acoustics

Volumn 9, Issue 1, 2001, Pages 149-167

  Knobles, D P ^a   Stotts, S A ^a   Koch, R A ^a   Udagawa, T ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035611865     PISSN: 0218396X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218396X01000449     Document Type: Article

References (31)

1. J. R. Apel, Principles of Ocean Physics, International Geophysics Series 38 (Academic Press, London, 1987).
2. J. Zhou, X. Zhang, and P. H. Rogers, "Resonant interaction of sound wave with internal solitons in the coastal zone," J. Acoust. Soc. Am. 90, 2042 (1991).
3. J. Colosi, S. F. Flatte, and C. Bracher, "Internal wave effects on a 1000 km ocean acoustic pulse propagation: Simulation and comparison with experiment," J. Acoust. Soc. Am. 84, 452 (1994).
4. J. R. Apel et al., "An overview of the 1995 SWARM shallow water internal wave acoustic scattering experiment," IEEE J. Oceanic Eng. 22, 465 (1997).
5. J. C. Preisig and T. F. Duda, "Coupled acoustic mode propagation through continental-shelf internal solitary waves," IEEE J. Oceanic Eng. 22, 256 (1997).
6. R. Evans, "A coupled mode solution for acoustic propagation in a waveguide with stepwise variations of a penetrable bottom," J. Acoust. Soc. Am. 74, 188 (1983).
7. F. Jensen and C. M. Ferla, "Numerical solutions of range-dependent benchmark problems in ocean acoustics," J. Acoust. Soc. Am. 87, 1499 (1990).
8. V. Maupin, "Surface waves across 2-D structures: A method based on coupled local modes," J. Geophys. 93, 173 (1988).
9. R. I. Odom, M. Park, J. A. Mercer, R. S. Crosson, and P. Paik, "Effects of transverse isotrophy on modes and mode coupling in shallow water," J. Acoust. Am. 100, 2079 (1996).
10. O. A. Godin, "A note on the differential equations of coupled-mode propagation in a fluid," J. Acoust. Soc. Am. 103, 159 (1998).
11. J. Fawcett, "A derivation of the differential equations of coupled-mode propagation," J. Acoust. Soc. Am. 92, 290 (1992).
12. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
13. M. L. Goldberger and K. M. Watson, Collision Theory (John Wiley and Sons, New York, 1964).
14. R. G. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1966).
15. W. Kohn, "On the convergence of Born expansions," Rev. Mod. Phy. 26, 292 (1954).
16. R. P. Feynman, "Theory of positrons," Phys. Rev. 76, 749 (1949) and "Space-time approach to quantum electrodynamics," Phys. Rev. 76, 769 (1949).
17. R. P. Feynman, "Theory of positrons," Phys. Rev. 76, 749 (1949) and "Space-time approach to quantum electrodynamics," Phys. Rev. 76, 769 (1949).
18. T. Udagawa and B. T. Kim, "Random phase approximation calculations of nuclear response in the continuum," Phys. Rev. C40, 2271 (1989).
19. 208Pb," Phys. Lett. B230, 6 (1989).
20. D. Knobles and T. Udagawa, "Random phase approximation calculations of nuclear response in the continuum using a finite range interaction, Nucl. Phys. A533, 189 (1991).
21. 208Bi," Phys. Rev. C52, 2257 (1995).
22. 3He,t) reactions to the continuum," Phys. Rev. C61, 1 (2000).
23. D. P. Knobles, "Solutions of coupled-mode equations with a large dimension in underwater acoustics," J. Acoust. Soc. Am. 96, 1741 (1994).
24. E. K. Westwood and R. A. Koch, "Elimination of branch cuts from the normal mode solution using gradient half spaces," J. Acoust. Soc. Am. 106, 2513 (1999).
25. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th edition (Cambridge University Press Cambridge, 1927).
26. Equation (17) in Ref. 22 should have a plus sign. Otherwise the calculations in Ref. 22 are correct.
27. M. D. Collins, "A split step Padé solution for the parabolic equation method," J. Acoust. Soc. Am. 93, 1736 (1993).
28. The authors of this manuscript do not advocate a specific parabolic equation algorithm. The RAM algorithm was chosen due to its availability and its widespread dissemination in the ocean acoustics community.
29. E. K. Westwood, C. T. Tindle, and N. R. Chapman, "A normal mode model for acoustic-elastic ocean environments," J. Acoust. Soc. Am. 100, 3631 (1996).
30. C. T. Tindle and N. R. Chapman, "A phase function for finding mode eigenvalues over a layered elastic bottom," J. Acoust. Soc. Am. 96, 1777 (1994).
31. S. J. Levinson et al., "An efficient and robust method for underwater acoustic normal mode computations," J. Acoust. Soc. Am. 97, 1567 (1995).