Random matrix theory for description of sound scattering on background internal waves in a shallow sea

   The problem of propagation of low-frequency sound in a shallow waveguide with random hydrological inhomogeneity caused by background internal waves is considered. A new approach to statistical modeling of acoustic fields, based on the application of the random matrix theory and previously successfully used for deep-water acoustic waveguides, is used to the case of shallow-water waveguides. In this approach, sound scattering on random inhomogeneity is described using an ensemble of random propagator matrices which describe the transformation of the acoustic field in the space of normal waveguide modes. A study of the effect of sound “escaping” from a waveguide was carried out. The term “escaping” here means energy transfer to modes with stronger attenuation due to scattering on internal waves. A model of an underwater sound channel with an axis at a depth of about 45 meters is considered. It is shown that the first few modes propagating inside the water column are very little subject to losses due to the “escaping”. The strongest impact of the leakage scattering is experienced by the middle group of modes capable of reaching the sea surface. It is revealed as significant increasing of losses as compared to a horizontally homogeneous waveguide. On the other hand, the existence of linear mode combinations for which loss enhancement is practically absent has been revealed. These linear combinations correspond to the eigenfunctions of an inhomogeneous waveguide. Statistical analysis of propagator eigenfunctions indicates on qualitative differences of mechanisms of scattering for frequencies of 100 and 500 Hz.

1. Tappert F.D., Xin Tang. Ray chaos and eigenrays. The Journal of the Acoustical Society of America. 1996, 99, 1, 185–195. doi: 10.1121/1.414502

2. Virovlyansky A.L., Kazarova A. Yu., Lyubavin L. Ya. The possibility of using a vertical array for estimating the delays of sound pulses at multimegameter ranges. Acoustical Physics. 2008, 54, 4, 486–494. doi: 10.1134/S1063771008040088

3. Song H.-C. An overview of underwater time-reversal communication. IEEE Journal of Oceanic Engineering. 2016, 41, 3, 644–655. doi: 10.1109/joe.2015.2461712

4. Virovlyansky A.L., Kazarova A.Y., Lyubavin L.Y. Focusing of sound pulses using the time reversal technique on 100-km paths in a deep sea. Acoustical Physics. 2012, 58, 6, 678–686. doi: 10.1134/S1063771012060152

5. Rytov S.M., Kravtsov Yu.A., Tatarsky V.I. Introduction to statistical radiophysics. Part 2. Random fields. Moscow, Nauka, 1978. 463 p. (in Russian).

6. Brown M.G., Colosi J.A., Tomsovic S., Virovlyansky A.L., Wolfson M.A. Ray dynamics in long-range deep ocean sound propagation. The Journal of the Acoustical Society of America. 2003, 113, 5, 2533–2547. doi: 10.1121/1.1563670

7. Smirnov I.P., Virovlyansky A.L., Edelman M., Zaslavsky G.M. Chaos-induced intensification of wave scattering. Physical Review E. 2005, 72, 2, 026206. doi: 10.1103/PhysRevE.72.026206

8. Virovlyansky A.L., Zaslavsky G.M. Ray and wave chaos in problems of sound propagation in the ocean. Acoustical Physics. 2007, 53, 3, 282–297. doi: 10.1134/S1063771007030050

9. Makarov D., Prants S., Virovlyansky A., Zaslavsky G. Ray and wave chaos in ocean acoustics: chaos in waveguides. Singapore: World Scientific. 2010, 388 p. doi: 10.1142/7288

10. Tomsovic S., Brown M. Ocean acoustics: a novel laboratory for wave chaos. New Directions in Linear Acoustics and Vibration. Cambridge University Press, 2010, 169–187. doi: 10.1017/CBO9780511781520.013

11. Virovlyansky A.L., Makarov D.V., Prants S.V. Ray and wave chaos in underwater acoustic waveguides. Physics-Uspekhi. 2012, 55, 1, 18–46. doi: 10.3367/UFNe.0182.201201b.0019

12. Hegewisch K.C., Tomsovic S. Random matrix theory for underwater sound propagation. Europhysics Letters. 2012, 97, 34002. doi: 10.1209/0295–5075/97/34002

13. Makarov D.V., Kon’kov L.E., Uleysky M. Yu., Petrov P.S. Wave chaos in a randomly inhomogeneous waveguide: Spectral analysis of the finite-range evolution operator. Physical Review E. 2013, 1, 012911. doi: 10.1103/PhysRevE.87.012911

14. Makarov D.V. Random matrix theory for low-frequency sound propagation in the ocean: A spectral statistics test. Journal of Theoretical and Computational Acoustics. 2018, 26, 1, 205–217. doi: 10.1142/S2591728518500020

15. Makarov D.V. Random matrix theory for an adiabatically-varying oceanic acoustic waveguide. Wave Motion. 2019, 90, 205–217. doi: 10.1016/j.wavemoti.2019.05.007

16. Makarov D.V., Komissarov A.A. Chaos and wavefront reversal for long-range sound propagation. Doklady Earth Sciences. 2022, 507, 2, 1118–1123. doi: 10.1134/S1028334X22600931

17. Makarov D.V., Uleysky M. Yu., Prants S.V. Ray chaos and ray clustering in an oceanic waveguide. Chaos. 2004, 14, 1, 79–95. doi: 10.1063/1.1626392

18. Makarov D.V., Uleyskiy M. Yu. Ray escape from a range-dependent underwater sound channel. Acoustical Physics. 2007, 53, 4, 495–502. doi: 10.1134/S1063771007040100

19. Jensen F.B., Kuperman W.A., Porter M.B., Schmidt H., Tolstoy A. Computational Ocean Acoustics. New York, Springer New York, 2011.

20. Kuz’kin V.M., Petnikov V.G., Lavrova O. Yu., Pereselkov S.A., Sabinin K.D. Anisotropic field of background internal waves on a sea shelf and its effect on low-frequency sound propagation. Acoustical Physics. 2006, 52, 1, 65–76. doi: 10.1134/S106377100601009X

21. Thomson D.J., Chapman N.R. A wide-angle split-step algorithm for the parabolic equation. The Journal of the Acoustical Society of America. 1983, 74, 6, 1848–1854. doi: 10.1121/1.390272

22. Tielburger D., Finette S., Wolf S. Acoustic propagation through an internal wave field in a shallow water waveguide. The Journal of the Acoustical Society of America. 1997, 101, 2, 789–808. doi: 10.1121/1.418039

23. Makarov D.V., Kon’kov L.E., Petrov P.S. Influence of oceanic synoptic eddies on the duration of modal acoustic pulses. Radiophysics and Quantum Electronics. 2016, 59, 7, 576–591. doi: 10.1007/s11141-016-9724-4

24. Colosi J.A., Brown M.G. Efficient numerical simulation of stochastic internal-wave-induced sound-speed perturbation fields. The Journal of the Acoustical Society of America. 1998, 103, 4, 2232–2235. doi: 10.1121/1.421381

25. Makarov D.V., Prants S.V., Uleysky M. Yu. Structure of spatial nonlinear resonance of rays in an inhomogeneous underwater sound channel. Doklady Earth Sciences. 2002, 382, 1, 106–108.

26. Makarov D.V., Uleysky M. Yu., Prants S.V. On the possibility of determining internal wave characteristics from the ray arrival time distribution in an underwater sound channel under conditions of ray chaos. Technical Physics Letters. 2003, 29, 5, 430–432. doi: 10.1134/1.1579816

27. Kon’kov L.E., Makarov D.V., Sosedko E.V., Uleysky M. Yu. Recovery of ordered periodic orbits with increasing wavelength for sound propagation in a range-dependent waveguide. Physical Review E. 2007, 76, 5, 056212. doi: 10.1103/PhysRevE.76.056212

28. Yang T.C., Yoo K. Internal wave spectrum in shallow water: measurement and comparison with the Garrett-Munk model. IEEE Journal of Oceanic Engineering. 1983, 74, 6, 1848–1854. doi: 10.1109/48.775295

29. Makarov D.V., Kon’kov L.E. Chaotic diffusion at sound propagation in a range-dependent underwater sound channel. Russian Journal of Nonlinear Dynamics. 2007, 3, 2, 157–174. doi: 10.20537/nd0702003 (in Russian)

30. Makarov D.V., Kon’kov L.E., Uleysky M. Yu The ray-wave correspondence and the suppression of chaos in long-range sound propagation in the ocean. Acoustical Physics. 2008, 54, 3, 382–391. doi: 10.1134/S1063771008030147

31. Makarov D.V., Kon’kov L.E., Uleysky M. Yu. Wave chaos in underwater acoustics. Journal of Siberian Federal University. 2010, 3, 3, 336–348. URL: https://elib.sfu-kras.ru/handle/2311/1734

32. Makarov D.V., Uleysky M. Yu., Budyansky M.V., Prants S.V. Clustering in randomly driven Hamiltonian systems. Physical Review E. 2006, 73, 6, 066210. doi: 10.1103/PhysRevE.73.066210