Abstract
We develop an approximate analytical approach for a description of the stochastic behavior of sound rays in deep-sea acoustic waveguides with paths up to 3 to 5 thousands of kilometers. The ray dynamics is studied using the Hamiltonian formalism in terms of the action–angle canonical variables. A realistic model of underwater waveguide with internal-wave-induced perturbations of the sound speed field is applied. We point out a small parameter of the problem, which allows one to linearize the Hamilton (ray) equations and approximate the action variable by a Wiener process representing the simplest model of diffusion. The stochastic ray theory based on this approximation is applied to an analysis of ray travel times, i.e., the travel times of sound pulses coming to a receiver via different ray paths. The formation of compact clusters of the chaotic-ray travel times is explained quantitatively.
Similar content being viewed by others
REFERENCES
L. M. Brekhovskikh and Yu. P. Lysanov, Fundamentals of Ocean Acoustics, Springer Verlag, Berlin (1991).
R. Dashen, W. H. Munk, K. M. Watson, F. Zachariasen, and S. M. Flatté´e, Sound Transmission Through a Fluctuating Ocean, Cambridge Univ. Press (1979).
J. B. Keller and J. S. Papadakis, eds., Lecture Notes on Wave Propagation and Underwater Acoustics, Springer, New York (1977).
J. A. Colosi and M. G. Brown, J. Acoust. Soc. Am., 103, 2232 (1998).
J. Simmen, S. M. Flatte, and G.-Y. Wan, J. Acoust. Soc. Am., 102, 239 (1997).
M. G. Brown and J. Viechnicki, J. Acoust. Soc. Am., 104, 2090 (1998).
P. F. Worcester, B. D. Cornuelle, M. A. Dzieciuch, et al., J. Acoust. Soc. Am., 105, 3185 (1999).
B. D. Dushaw, B. M. Howe, J. A. Mercer, R. C. Spindel, and the ATOC Group, IEEE J. Oceanic Engin., 24, 202 (1999).
W. H. Munk and C. Wunsch, Deep-Sea Res., 26, 123 (1979).
J. Spiesberger and K. Metzger, J. Geophys. Res., 96, 4869 (1991).
B. D. Dushaw, IEEE J. Oceanic Engin., 24, 215 (1999).
G. M. Zaslavsky, Stochastic Behaviour of Dynamical Systems, Harwood, New York (1985).
G. M. Zaslavsky and S. S. Abdullaev, Usp. Fiz. Nauk, 161, No. 8, 1 (1991).
D. R. Palmer, M. G. Brown, F. D. Tappert, and H. F. Bezdek, Geophys. Res. Lett., 15, 569 (1988).
F. D. Tappert and X. Tang, J. Acoust. Soc. Am., 99, 185 (1996).
D. R. Palmer, T. M. Georges, and R. M. Jones, Comput. Phys. Commun., 65, 219 (1991).
J. L. Spiesberger and F. D. Tappert, J. Acoust. Soc. Am., 99, 173 (1996).
L. D. Landau and E. M. Lifshits, Mechanics, Butterworth-Heinemann (1995).
A. L. Virovlyansky, J. Acoust. Soc. Am., 113, 2523 (2003).
A. L. Virovlyansky, “Ray travel times in range-dependent acoustic waveguides,” http://xxx.lanl.gov/PS-cache/nlin/pdf/0012/0012015.pdf.
M. Born and E. Wolf, Principles of Optics, Pergamon Press, Oxford (1964).
A. L. Virovlyansky, Akust. Zh., 31, No. 5, 664 (1985).
W. H. Munk and C. Wunsch, Rev. Geophys. Space. Phys., 21, 1 (1983).
A. L. Virovlyansky, J. Acoust. Soc. Am., 97, 3180 (1995).
C. W. Gardiner, Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences (Springer Series in Synergetics, Vol. 13), Springer Verlag (1996).
V. I. Tikhonov and M. A. Mironov, Markovian Processes, Sovetskoe Radio, Moscow (1977).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Virovlyansky, A.L. Ray Chaos in the Long-Range Propagation of Sound in the Ocean. Radiophysics and Quantum Electronics 46, 502–516 (2003). https://doi.org/10.1023/B:RAQE.0000019866.57376.52
Issue Date:
DOI: https://doi.org/10.1023/B:RAQE.0000019866.57376.52