Soliton-Like Waves in the Vicinity of the Southern Kuril Islands

V. A. Squire1, P. D. Kovalev2, ✉, D. P. Kovalev2

1 Department of Mathematics and Statistics, University of Otago, Dunedin, New Zealand

2 Institute of Marine Geology and Geophysics, Far East Branch of Russian Academy of Sciences, Yuzhno-Sakhalinsk, Russian Federation

✉ e-mail: kovalev_pd@outlook.com

Abstract

Purpose. This paper focuses on modulated solitons detected in time series of observational data on sea level oscillations in the Sea of Okhotsk, verifying the presence of nonstationary processes within a quantitative framework of methods.

Methods and Results. The paper reports an analysis of wave observation data collected using ARW-type, bottom-mounted pressure sensors in the area of the Capes Castricum, Van-der-Lind and Lovtsova in the southern Kuril Islands. The time series obtained were bandpass filtered using hardware with a passband of 20 minutes to 2.5 hours. Residual time series show the presence of wave packets generated at the beginning of the K1 (diurnal) tide, which consistently appear as a group consisting of 5–7 packets. It is shown that the synchronicity between each wave packet and the K1 wave initiation is associated with the cyclic separation of the tidal flow of the K1 oscillation at the elevation in the Urup Strait located between the islands, along with a concomitant spawning of vortices. It is speculated that the vortices generate the detected wave packets, which are each found to encase a cluster of waves with an average period of about 1.6 hours that are attributed to either edge waves or shelf seiches or a combination of both. A numerical model simulation of the detected wave packets was performed using the Korteweg – de Vries equation, confirming that the envelope of the observed wave packets is close to the modeled one and behaves like a soliton.

Conclusions. It is shown that synchronous initiation of a wave packet and a K1 wave is associated with the cyclic separation of the tidal flow of the K1 oscillations at a subsurface elevation in the Urup Strait located between the islands, with a concomitant spawning of vortices. The vortices are assumed to generate the detected wave packets. Each packet contains a cluster of waves with an average period of about 1.6 hours, which is conditioned by the period of the edge wave or shelf seiche. Spectral analysis performed for the 4.5-day-long time series with and without the groups of solitons, showed that the wave energy increases in the 0.5–5.5 hour period range when solitons occur. Application of a simple amplitude-based criterion permitted the authors to identify the waves detected in the wave packets as anomalous. Transformation of the time series into normalized time and normalized amplitude coordinates show that all the examples of anomalous wave packets could be modeled using the Korteweg – de Vries time equation.

Keywords

Sea of Okhotsk, soliton-like waves, Korteweg – de Vries equation, solitons, harmonic breathers

Acknowledgements

P. D. Kovalev and D. P. Kovalev performed this investigation in accordance with the state program of IMGG-FEB-RAS. They thank the staff of the Laboratory of Wave Dynamics and Coastal Currents for collecting the field data. V. A. Squire highly appreciates the continued support from the University of Otago throughout his long scientific career and especially acknowledges fruitful collaboration with the graduate students and the postdoctoral fellows.

Original russian text

Original Russian Text © V. A. Squire, P. D. Kovalev, D. P. Kovalev, 2021, published in MORSKOY GIDROFIZICHESKIY ZHURNAL, Vol. 37, Iss. 1, pp. 5-22 (2021)

For citation

Squire, V.A., Kovalev, P.D. and Kovalev, D.P., 2021. Soliton-like Waves in the Vicinity of the Southern Kuril Islands. Physical Oceanography, 28(1), pp. 3-19. doi:10.22449/0233-7584-2021-1-3-19

DOI

10.22449/0233-7584-2021-1-3-19

References

  1. Peregrine, D.H., 1983. Water Waves, Nonlinear Schrödinger Equations and Their Solutions. The ANZIAM Journal, 25(1), pp. 16-43. https://doi.org/10.1017/S0334270000003891
  2. Jaworski, M., 1984. Breather-Like Solution of the Korteweg-de Vries Equation. Physics Letters A, 104(5), pp. 245-247. https://doi.org/10.1016/0375-9601(84)90060-4
  3. Kovalyov, M., 1998. Modulating Properties of Harmonic Breather Solutions of KdV. Journal of Physics A: Mathematical and General, 31(22), pp. 5117-5128. https://doi.org/10.1088/0305-4470/31/22/012
  4. Kovalyov, M., 2005. On a Class of Solutions of KdV. Journal of Differential Equations, 213(1), pp. 1-80. https://doi.org/10.1016/j.jde.2003.07.016
  5. Akhmediev, N., Ankiewicz, A. and Taki M., 2009. Waves That Appear from Nowhere and Disappear without a Trace. Physics Letters A, 373(6), pp. 675-678. https://doi.org/10.1016/j.physleta.2008.12.036
  6. Chabchoub, A., Mozumi, K., Hoffmann, N., Babanin, A.V., Toffoli, A., Steer, J.N., van den Bremer, T.S., Akhmediev, N., Onorato, M. and Waseda, T., 2019. Directional Soliton and Breather Beams. Proceedings of the National Academy of Sciences, 116(20), pp. 9759-9763. https://doi.org/10.1073/pnas.1821970116
  7. Nakamura, T., Awaji, T., Hatayama, T., Akitomo, K., Takizawa, T., Kono, T., Kawasaki, Y. and Fukasawa, M., 2000. The Generation of Large-Amplitude Unsteady Lee Waves by Subinertial K1 Tidal Flow: A Possible Vertical Mixing Mechanism in the Kuril Straits. Journal of Physical Oceanography, 30(7), pp. 1601-1621. https://doi.org/10.1175/1520-0485(2000)030%3C1601:TGOLAU%3E2.0.CO;2
  8. Apel, J.R., 2004. Oceanic Internal Waves and Solitons. In: C. R. Jackson and J. R. Apel, Eds., 2004. Synthetic Aperture Radar Marine User’s Manual. Washington, DC.: U.S. Department of Commerce, Chapter 7, pp. 189-206. Available at: https://www.sarusersmanual.com/ManualPDF/NOAASARManual_CH07_pg189-206.pdf [Accessed: 10 November 2020].
  9. Apel, J.R., Ostrovsky, L.A., Stepanyants, Y.A. and Lynch, J.F., 2006. Internal Solitons in the Ocean. Woods Hole, MA: Woods Hole Oceanographic Institution, 108 p. doi:10.1575/1912/1070
  10. Chang, P.K., 1970. Separation of Flow. Oxford, UK: Pergamon, 796 p. https://doi.org/10.1016/C2013-0-05541-7
  11. Korteweg, D.J. and de Vries, G., 1895. XLI. On the Change of Form of Long Waves Advancing in a Rectangular Canal, and on a New Type of Long Stationary Waves. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 39(240), pp. 422-443. https://doi.org/10.1080/14786449508620739
  12. Giovanangeli, J.-P., Kharif, C. and Stepanyants, Y.A., 2018. Soliton Spectra of Random Water Waves in Shallow Basins. Mathematical Modelling of Natural Phenomena, 13(4), 40. https://doi.org/10.1051/mmnp/2018018
  13. De Jong, M.P.C., 2004. Origin and Prediction of Seiches in Rotterdam Harbour Basins: doctoral thesis. Delft, The Netherlands: Delft University of Technology, 119 p. Available at: http://resolver.tudelft.nl/uuid:d7ce7779-bf81-47b7-bc14-e01ce5e6856b [Accessed: 10 November 2020].
  14. Osborne, A.R., Segre, E., Boffetta, G. and Cavaleri, L., 1991. Soliton Basis States in Shallow-Water Ocean Surface Waves. Physical Reviews Letters, 67(5), pp. 592-595. https://doi.org/10.1103/PhysRevLett.67.592
  15. Costa, A., Osborne, A.R., Resio, D.T., Alessio, S., Chrivì, E., Saggese, E., Bellomo, K. and Long, C.E., 2014. Soliton Turbulence in Shallow Water Ocean Surface Waves. Physical Reviews Letters, 113(10), 108501. https://doi.org/10.1103/PhysRevLett.113.108501
  16. Efimov, V.V., Ed., 1985. Waves in the Border Regions of the Ocean. Leningrad: Gidrometeoizdat, 280 p. (in Russian).
  17. Rabinovich, A.B., 1993. Long Gravitational Waves in the Ocean: Capture, Resonance, and Radiation. Saint Petersburg: Gidrometeoizdat, 325 p. (in Russian).
  18. Kovalev, P.D. and Rabinovich, A.B., 1980. Measurements of Bottom Tidal Currents in the Vicinity of the Kuril-Kamchatka Arc. Oceanology, 20(3), pp. 451-458.
  19. Thomas, J.A., Lerczak, J.A. and Moum, J.N., 2016. Horizontal Variability of High-Frequency Nonlinear Internal Waves in Massachusetts Bay Detected by an Array of Seafloor Pressure Sensors. Journal of Geophysical Research: Oceans, 121(8), pp. 5587-5607. https://doi.org/10.1002/2016JC011866
  20. Zdunkowski, W. and Bott, A., 2003. Dynamics of the Atmosphere: A Course in Theoretical Meteorology. Cambridge, UK : Cambridge University Press, 719 p. https://doi.org/10.1017/CBO9780511805462
  21. Rabinovich, A.B., 2009. Seiches and harbor oscillations. In: Young C. Kim, Ed., 2009. Handbook of Coastal and Ocean Engineering. Singapore : World Scientific, pp. 193-236. https://doi.org/10.1142/9789812819307_0009
  22. Kovalev, P.D. and Kovalev, D.P., 2013. Seiche Vibrations Features in Bays and Inlets of Far East: Primorye, Sakhalin, Southern Kuril Islands. Tambov University Reports. Series: Natural and Technical Sciences, 18(4), pp. 1377-1382. Available at: http://journals.tsutmb.ru/go/1810-0198/2013/4/1377-1382/ [Accessed: 10 November 2020] (in Russian).
  23. Zaitsev, A., Malashenko, A., Kostenko, I., Pelinovsky, E. and Kuznetsov, K., 2012. Freak Waves Registration in the Aniva Bay, Okhotsk Sea. Transactions of Nizhni Novgorod State Technical University n. a. R.Y. Alexeev, (1), pp. 33-41. Available at: https://www.nntu.ru/frontend/web/ngtu/files/nauka/izdaniya/trudy/2012/01/2012-01.pdf [Accessed: 10 November 2020] (in Russian).
  24. Cazaubiel, A., Michel, G., Lepot, S., Semin, B., Aumaître, S., Berhanu, M., Bonnefoy, F. and Falcon, E., 2018. Coexistence of Solitons and Extreme Events in Deep Water Surface Waves. Physical Reviews Fluids, 3(11), 114802. doi:10.1103/PhysRevFluids.3.114802
  25. Miura, R.M., 1968. Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation. Journal of Mathematical Physics, 9(8, pp. 1202-1204. https://doi.org/10.1063/1.1664700
  26. Ablowitz, M.J., 1978. Lectures on the Inverse Scattering Transform. Studies in Applied Mathematics, 58(1, pp. 17-94. https://doi.org/10.1002/sapm197858117

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