A Hamiltonian method for finding broadband modal eigenvalues

Wang, Haozhong; Wang, Ning; Gao, Dazhi

doi:doi:10.1121/1.3672687

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Journal of the Acoustical Society of America / Volume 131 / Issue 2 / UNDERWATER SOUND [30]

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A Hamiltonian method for finding broadband modal eigenvalues

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. 1047-1054 (2012); (8 pages)

Haozhong Wang, Ning Wang, and Dazhi Gao

College of Information Science and Technology, Ocean University of China, 238 Songling Road, Qingdao, 266100, People’s Republic of China

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Abstract

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For shallow water waveguides over a layered elastic bottom, modal eigenvalues can be determined by searching the locations in the complex plane of the horizontal wave number at which the complex phase function is a multiple of π [C. T. Tindle and N. R. Chapman, J. Acoust. Soc. Am. 96, 1777–1782 (1994)]. In this paper, a Hamiltonian method is introduced for tracing the path in the complex plane along which the phase function keeps real. The Hamiltonian method can also be extended to compute the broadband modal eigenvalues or the modal dispersion curves in the Pekeris waveguide with fluid/elastic bottoms. For each proper or leaky normal mode, a different Hamiltonian is constructed in the complex plane and used to trace automatically the complex dispersion curve with the eigenvalue in a reference frequency as the initial value. In contrast to the usual methods, the dispersion curve for each mode is determined individually. The Hamiltonian method shows good performance by comparing with kraken.

ACKNOWLEDGMENTS

This work was supported by State Key Laboratory of Acoustics, Chinese Academy of Sciences, Grant No. SKLOA201006.

Article Outline

INTRODUCTION
NORMAL MODE THEORY
HAMILTONIAN METHOD FOR FINDING MODAL EIGENVALUES
1. Hamilton mechanics
2. Hamiltonian method for tracing the curve Im Φ = 0 and finding the eigenvalues
3. Hamiltonian method for tracing the modal dispersion curves
NUMERICAL SIMULATION
1. Tracing isovalue curve Im Φ = 0 and finding eigenvalues
2. Sensibility to initial value iterative convergence and accuracy
3. Tracing modal dispersion curves
SUMMARY

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KEYWORDS and PACS

Keywords

acoustic dispersion, acoustic waveguides, eigenvalues and eigenfunctions, modal analysis, underwater sound

PACS

43.30.Bp

Normal mode propagation of sound in water
43.30.Ma

Acoustics of sediments; ice covers, viscoelastic media; seismic underwater acoustics
43.20.Mv

Waveguides, wave propagation in tubes and ducts

ARTICLE DATA

History

Received 25 Mar 2011
Accepted 21 Nov 2011
Revised 16 Nov 2011

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http://dx.doi.org/10.1121/1.3672687

PUBLICATION DATA

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0001-4966 (print)

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Acoustical Society of America

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A Hamiltonian method for finding broadband modal eigenvalues