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The coupled-mode method based on the direct global matrix (DGMCM) approach for sound propagation in range-dependent waveguides [Luo et al., "A numerically stable coupled-mode formulation for acoustic propagation in range-dependent waveguides," Sci. China-Phys. Mech. Astron. 55, 572 (2012)] is further developed. The normal mode model KRAKEN is adopted to provide local modal solutions and their associated coupling matrices. As a result, the model DGMCM is capable of providing full two-way solutions for the two-dimensional realistic problems characterized by a penetrable bottom and a depth-varying sound speed profile. In addition, the closed-form expressions of coupling matrices for sound propagation in a range-dependent, two-layer waveguide are proposed. The numerical solutions of the coupling matrices by DGMCM agree well with the analytical solutions. Sound propagation in a penetrable wedge is solved by the updated DGMCM model. The numerical results indicate that the updated DGMCM model is numerically stable and accurate, and can provide benchmark solutions for realistic range-dependent problems.
[1] Collis J M, Siegmann W L, Jensen F B, Zampolli M, KÜsel E T, Collins M D 2008 J. Acoust. Soc. Am. 123 51
[2] Evans R B 1983 J. Acoust. Soc. Am. 74 188
[3] Pierce A D 1965 J. Acoust. Soc. Am. 37 19
[4] Luo W Y, Schmidt H 2009 J. Acoust. Soc. Am. 125 52
[5] Collins M D, Schmidt H, Siegmann W L 2000 J. Acoust. Soc. Am. 107 1964
[6] Thompson L L 2006 J. Acoust. Soc. Am. 119 1315
[7] Zampolli M, Tesei A, Jensen F B, Malm N, Blottman III J B 2007 J. Acoust. Soc. Am. 122 1472
[8] Peng Z H, Zhang R H 2005 Acta Acustica 30 97 (in Chinese) [彭朝晖, 张仁和 2005 声学学报 30 97]
[9] Milder D M 1969 J. Acoust. Soc. Am. 46 1259
[10] Rutherford S R, Hawker K E 1981 J. Acoust. Soc. Am. 70 554
[11] Fawcett J A 1992 J. Acoust. Soc. Am. 92 290
[12] Godin O A 1998 J. Acoust. Soc. Am. 103 159
[13] Athanassoulis G A, Belibassakis K A, Mitsoudis D A, Kampanis N A, Dougalis V A 2008 J. Comp. Acoust. 16 83
[14] Ferla C M, Porter M B, Jensen F B 1993 C-SNAP: Coupled SACLANTCEN normal mode propagation loss model (La Spezia, Italy: SACLANT Undersea Research Center) Technical Report SM-274
[15] Porter M B, Jensen F B, Ferla C M 1991 J. Acoust. Soc. Am. 89 1058
[16] Evans R B 1986 J. Acoust. Soc. Am. 80 1414
[17] Luo W Y, Yang C M, Zhang R H 2012 Chin. Phys. Lett 29 014302
[18] Luo W Y, Yang C M, Qin J X, Zhang R H 2012 Sci. China-Phys. Mech. Astron. 55 572
[19] Schmidt H, Jensen F B 1985 J. Acoust. Soc. Am. 77 813
[20] Schmidt H 1993 J. Acoust. Soc. Am. 94 2420
[21] Ricks D C, Schmidt H 1994 J. Acoust. Soc. Am. 95 3339
[22] Jensen F B, Kuperman W A, Porter M B, Schmidt H 2011 Computational Ocean Acoustics (2nd Ed.) (New York: Springer)
[23] Porter M B 1991 The KRAKEN normal mode program (La Spezia, Italy: SACLANT Undersea Research Centre) Technical Report SM-245
[24] Stotts S A 2002 J. Acoust. Soc. Am. 111 1623
[25] Felsen L B 1986 J. Acoust. Soc. Am. Suppl. 1 80 S36
[26] Felsen L B 1987 J. Acoust. Soc. Am. Suppl. 1 81 S39
[27] Jensen F B 1998 J. Acoust. Soc. Am. 104 1310
[28] Evans R B, Gilbert K E 1985 Comp. Maths. Appl. 11 795
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[1] Collis J M, Siegmann W L, Jensen F B, Zampolli M, KÜsel E T, Collins M D 2008 J. Acoust. Soc. Am. 123 51
[2] Evans R B 1983 J. Acoust. Soc. Am. 74 188
[3] Pierce A D 1965 J. Acoust. Soc. Am. 37 19
[4] Luo W Y, Schmidt H 2009 J. Acoust. Soc. Am. 125 52
[5] Collins M D, Schmidt H, Siegmann W L 2000 J. Acoust. Soc. Am. 107 1964
[6] Thompson L L 2006 J. Acoust. Soc. Am. 119 1315
[7] Zampolli M, Tesei A, Jensen F B, Malm N, Blottman III J B 2007 J. Acoust. Soc. Am. 122 1472
[8] Peng Z H, Zhang R H 2005 Acta Acustica 30 97 (in Chinese) [彭朝晖, 张仁和 2005 声学学报 30 97]
[9] Milder D M 1969 J. Acoust. Soc. Am. 46 1259
[10] Rutherford S R, Hawker K E 1981 J. Acoust. Soc. Am. 70 554
[11] Fawcett J A 1992 J. Acoust. Soc. Am. 92 290
[12] Godin O A 1998 J. Acoust. Soc. Am. 103 159
[13] Athanassoulis G A, Belibassakis K A, Mitsoudis D A, Kampanis N A, Dougalis V A 2008 J. Comp. Acoust. 16 83
[14] Ferla C M, Porter M B, Jensen F B 1993 C-SNAP: Coupled SACLANTCEN normal mode propagation loss model (La Spezia, Italy: SACLANT Undersea Research Center) Technical Report SM-274
[15] Porter M B, Jensen F B, Ferla C M 1991 J. Acoust. Soc. Am. 89 1058
[16] Evans R B 1986 J. Acoust. Soc. Am. 80 1414
[17] Luo W Y, Yang C M, Zhang R H 2012 Chin. Phys. Lett 29 014302
[18] Luo W Y, Yang C M, Qin J X, Zhang R H 2012 Sci. China-Phys. Mech. Astron. 55 572
[19] Schmidt H, Jensen F B 1985 J. Acoust. Soc. Am. 77 813
[20] Schmidt H 1993 J. Acoust. Soc. Am. 94 2420
[21] Ricks D C, Schmidt H 1994 J. Acoust. Soc. Am. 95 3339
[22] Jensen F B, Kuperman W A, Porter M B, Schmidt H 2011 Computational Ocean Acoustics (2nd Ed.) (New York: Springer)
[23] Porter M B 1991 The KRAKEN normal mode program (La Spezia, Italy: SACLANT Undersea Research Centre) Technical Report SM-245
[24] Stotts S A 2002 J. Acoust. Soc. Am. 111 1623
[25] Felsen L B 1986 J. Acoust. Soc. Am. Suppl. 1 80 S36
[26] Felsen L B 1987 J. Acoust. Soc. Am. Suppl. 1 81 S39
[27] Jensen F B 1998 J. Acoust. Soc. Am. 104 1310
[28] Evans R B, Gilbert K E 1985 Comp. Maths. Appl. 11 795
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