Two-way coupled-mode solutions in the complex horizontal wavenumber plane

Journal of Computational Acoustics

Volumn 16, Issue 2, 2008, Pages 225-256

  Stotts, Steven A ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Coupled modes; Normal modes; Propagators

Indexed keywords

EID: 58149509611     PISSN: 0218396X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218396X08003580     Document Type: Article

References (41)

1. A. D. Pierce. Extension of the method of normal modes to sound propagation in an almost-stratified medium, J. Acoust. Soc. Am. 37 (1965) 19-27.
2. D. M. Milder, Ray and wave invariants for SOFAR channel propagation. J. Acoust. Soc. Am. 46 (1969) 1259-1263.
3. S. R. Rutherford, An examination of coupled mode theory as applied to underwater sound propagation, ARL:UT Technical Report No. ARL-TR-79-44, Applied Research Laboratories, The University of Texas at Austin, 1979.
4. S. R. Rutherford and K. E. Hawker, Consistent coupled mode theory of sound for a class of non separable problems, J. Acoust. Soc. Am. 70 (1981) 554-564.
5. J. A. Fawcett, A derivation of the differential equations in coupled-mode propagation, J. Acoust. Soc. Am. 92 (1992) 290-295.
6. G. Gillette, Coupled modes in a waveguide with a range-dependent rigid basement, J. Acoust. Soc. Am. 95 (1994) 187-200.
7. R. B. Evans, A coupled mode solution for acoustic propagation in a waveguide with stepwise variations of a penetrable bottom, J. Acoust. Soc. Am. 74 (1983) 188-195.
8. M. B. Porter, C. M. Ferla and F. B. Jensen, Coupled modes for rapid range-dependent modeling, Proceedings of the Second Parabolic Equation Workshop, May 6-9, 1991, Slidell, Louisiana (Naval Research Laboratory, Stennis Space Center, Mississippi, 1993), NRL/BE/7181-93-0001, pp. 271-281.
9. O. A. Godin, A note on differential equations of coupled-mode propagation in fluids, J. Acoust. Soc. Am. 103 (1998) 159-168.
10. C. Allan Boyles, Acoustic Waveguides: Applications to Ocean Science (John Wiley & Sons, New York, New York, 1984), Chapter 4.
11. D. P. Knobles, Solutions of coupled-mode equations with a large dimension in underwater acoustics, J. Acoust. Soc. Am. 96(3) (1994) 1741-1747.
12. S. A. Stotts, Coupled-mode solutions in generalized ocean environments, J. Acoust. Soc. Am. 111 (2002) 1623-1643.
13. D. P. Knobles, S. A. Stotts, R. A. Koch and T. Udagawa, Integral equation coupled mode approach applied to internal wave problems, J. Comp. Acoust. 9 (2001) 149-167.
14. D. P. Knobles, S. A. Stotts and R. A. Koch, Low frequency coupled mode sound propagation over a continental shelf, J. Acoust. Soc. Am. 113 (2003) 1-7.
15. A. Bohr and B. R. Mottelson, Collective and individual-particle aspects of nuclear structure, Kgl. Danske Videnskab. Selskab, Mat. Fys. Medd. 27(16) (1953) 1-169.
16. T. Tamura, Analyses of the scattering of nuclear particles by collective nuclei in terms of the coupled channel calculation, Rev. Mod. Phys. 37 (1965) 679-708.
17. T. Udagawa and B. T. Kim, Random-phase-approximation calculations of nuclear response in the continuum, Phys. Rev. C 40 (1989) 2271-2275.
18. R. R. Whitehead, A. Watt, B. J. Cole and I. Morrison, Computational methods for shell-model calculations, Adv. Nucl. Phys. 9 (1977) 123-176.
19. C. T. Tindle, L. M. O'Driscoll and C. J. Higham, Coupled mode perturbation theory of range dependence, J. Acoust. Soc. Am. 108 (2000) 76-83.
20. C. J. Higham and C. T. Tindle, Coupled perturbed modes and internal solitary waves, J, Acoust. Soc. Am. 113 (2003) 2515-2522.
21. C. J. Higham and C. T. Tindle, Coupled perturbed modes over a sloping penetrable bottom, J. Acoust. Soc. Am. 114 (2003) 3119-3124.
22. Ahmad T. Abawi, An energy-conserving one-way coupled mode propagation model, J. Acoust. Soc. Am. 111 (2002) 160-167.
23. Robert I. Odom, A coupled mode examination of irregular waveguides including the continuum spectrum, Geophys. J. R. Astron. Soc. 86 (1986) 425-453.
24. V. Maupin, Surface waves across 2-d structures: A method based on coupled local modes, Geophys. J. 93 (1988) 173-185.
25. Jeroen Tromp, A coupled local-mode analysis of surface-wave propagation in a laterally heterogeneous waveguide, Geophys. J. Int. 117 (1994) 153-161.
26. T. W. Yudichak, G. S. Royal, D. P. Knobles, M. Gray, R. A. Koch and S. A. Stotts, Broadband modeling of downslope propagation in a wedge-shaped waveguide with penetrable bottom, J. Acoust. Soc. Am. 119 (2005) 143-152.
27. D. C Stickler and E. Ammicht, Uniform asymptotic evaluation of the continuous spectrum contribution for the Pekeris model, J. Acoust. Soc. Am. 67 (1980) 2018-2024.
28. E. Ammicht and D. C. Stickler, Uniform asymptotic evaluation of the continuous spectrum contribution for a stratified ocean, J. Acoust. Soc. Am. 76 (1984) 186-191.
29. G. V. Frisk, Ocean and Seabed Acoustics (Prentice Hall, Englewood Cliffs, New Jersey, 1994), Chapter 5.
30. C. T. Tindle and Z. Y. Zhang, Continuous modes and shallow water sound propagation, OCEANS '93: Engineering in Harmony with the Ocean, Proceedings I, Oct. 18-21, Victoria, British Columbia, Canada (IEEE, New York, New York, 1993), pp. 81-86.
31. M. J. Buckingham and E. M. Giddens, On the acoustic field in a Pekeris waveguide with attenuation in the bottom half-space, J. Acoust. Soc. Am. 119 (2005) 123-142.
32. D. P. Knobles, S. A. Stotts, R. A. Koch and E. K. Westwood, Inclusion of continuum effects in coupled mode theory using leaky modes, J. Acoust. Soc. Am. 103 (1998) 2857.
33. E. K. Westwood, C. T. Tindle and N. R. Chapman, A normal mode model for multilayered acoustoelastic ocean environments based on an analytic reflection coefficient method, J. Acoust. Soc. Am. 95(5, Pt. 2) (1994) 2908.
34. E. K. Westwood and R. A. Koch, Elimination of branch cuts from the normal mode solution using gradient halfspaces, J. Acoust. Soc. Am. 106(5) (1999) 2513-2523.
35. R. A. Koch, E. K. Westwood, J. E. LeMond and D. P. Knobles, Improving a practical broadband adiabatic normal mode model by including untrapped modes, J. Acoust. Soc. Am. 103 (1998) 2857.
36. S. J. Levinson, E. K. Westwood, R. A. Koch, S. K. Mitchell and C. V Sheppard, An efficient and robust method for underwater acoustic normal mode computations, J. Acoust. Soc. Am. 97(3) (1994) 1576-1585.
37. F. D. Tappert, The parabolic equation method, eds. J. B. Keller and J. S. Papadakis, in Wave Propagation and Underwater Acoustics (Springer, New York, 1977).
38. M. D. Collins, A split-step Padé solution for the parabolic equation method, J. Acoust. Soc. Am. 93 (1993) 1736-1742.
39. Handbook of Mathematical Functions (Dover Publications, Inc., New York, 1972), Chap. 10, pp. 443-447.
40. Roy G. Gordon, New method for constructing wavefunctions for bound states and scattering, J. Chem. Phys. 51(1) (1969) 14-25.
41. H. P. Bucker, Sound propagation in a channel with lossy boundaries, J. Acoust. Soc. Am. 48 (1970) 1187-1194.