Synchronization of Long-Wave Fluctuations of Sea Level in Adjacent Bays: The Example of the Kholmsk Bays (Sakhalin Island)

D. P. Kovalev1, P. D. Kovalev1, Yu. V. Manilyuk2, ✉

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

2 Marine Hydrophysical Institute of RAS, Sevastopol, Russian Federation

✉ e-mail: uvmsev@yandex.ru

Abstract

Purpose. The purpose of the study is to define the possibility of synchronizing long-wave fluctuations in the neighboring bays of the Kholmsk city based on the Van der Pol oscillator model, as well as the possibility for long waves to penetrate to the coastal waters adjacent to Kholmsk from the Moneron Island region and from the water areas near the cities of Gornozavodsk, Nevelsk, and Chekhov using in-situ observation data.

Methods and Results. The autonomous wave recorders ARW-14K installed in the Kholmsk bays, and the ARW-10 recorder located in the water areas nearby the cities of Gornozavodsk, Nevelsk, and Chekhov were used to obtain in situ data on sea level fluctuations. The measurement resolution of all the instruments is 1 s. The time series were researched through the spectral analysis of sea level fluctuations using the Kyma software. Calculation of the dispersion relation for the Stokes edge waves in the flat-sloping-bottom approximation has demonstrated the possibility of generating edge waves with the 8–9 min period in the water areas nearby the populated regions at the southwestern coast of Sakhalin Island. The reasons for unlimited growth of the phase difference of sea level fluctuations shown in the phase diagram for the Kholmsk-Severny and Trade Port bays were analyzed using a numerical solution of the Van der Pol equation.

Conclusions. It is established that a well pronounced wave process with the 8.27 min oscillation period is observed only in the water area nearby Gornozavodsk, and these waves do not reach the Kholmsk outer water area. The sea level fluctuations (period is approximately 8 min.) recorded by the tide gauge at Trade Port are the result of fluctuation interactions in the bays Trade Port and Kholmsk-Severny. A numerical solution of the problem on forced synchronization of a dynamic system subjected to a weak periodic stimulus using the Van der Pol equation has shown the possibility of unlimited growth of the phase differences between the phase of external force, i. e. the waves incoming from the neighboring Kholmsk-Severny Bay (period is 8.65 min), and the phase of natural oscillations in the Trade Port Bay (period is 4.7 min), which are obtained from in situ data. At a small value of the nonlinearity parameter, the oscillations of the Van der Pol oscillator are close to the harmonic ones, and in this case the phase difference of fluctuations changes abruptly and increases continuously.

Keywords

sea level fluctuations, edge waves, oscillation synchronization, Van der Pol oscillator

Acknowledgements

Numerical calculations, collection of in situ data, their processing, and subsequent analysis were carried within the framework of state assignment of the FSBSI IMGandG, FEB of RAS FWWM-2024-0002; analysis and interpretation of the results of in situ data processing, and numerical calculations were done within the framework of state assignment of the FSBSI FRC MHI FNNN-2024-0016.

About the authors

Dmitry P. Kovalev, Chief Researcher, Head of the Laboratory of Wave Dynamics and Coastal Currents, Institute of Marine Geology and Geophysics, Far Eastern Branch of the Russian Academy of Sciences (1b Nauki Str., Yuzhno-Sakhalinsk, 693022, Russian Federation), DSc. (Phys.-Math.), ОCRID ID: 0000-0002-5184-2350, ResearcherID: A-9300-2016, Scopus Author ID: 26032627700, SPIN-code: 8343-8577, d.kovalev@imgg.ru

Petr D. Kovalev, Leading Researcher, Laboratory of Wave Dynamics and Coastal Currents, Institute of Marine Geology and Geophysics, Far Eastern Branch of the Russian Academy of Sciences (1b Nauki Str., Yuzhno-Sakhalinsk, 693022, Russian Federation), DSc. (Tech.), ОCRID ID: 0000-0002-7509-4107, ResearcherID: V-8662-2018, Scopus Author ID: 16429135400, SPIN-code: 7465-3828, p.kovalev@imgg.ru

Yuri V. Manilyuk, Researcher, Wave Theory Department, Marine Hydrophysical Institute of RAS (2 Каpitanskaya Str., Sevastopol, 299011, Russian Federation), CSc. (Phys.-Math.), ОCRID ID: 0000-0002-5752-7562, ResearcherID: P-6662-2017, Scopus Author ID: 6602563261, SPIN-code: 4548-0051, uvmsev@yandex.ru

Original russian text

Original Russian Text © D. P. Kovalev, P. D. Kovalev, Yu. V. Manilyuk, 2026, published in MORSKOY GIDROFIZICHESKIY ZHURNAL, Vol. 42, Iss. 3, pp. 365–381 (2026)

For citation

Kovalev, D.P., Kovalev, P.D. and Manilyuk, Yu.V., 2026. Synchronization of Long-Wave Fluctuations of Sea Level in Adjacent Bays: The Example of the Kholmsk Bays (Sakhalin Island). Physical Oceanography, 33(3), pp. 404-419.

References

  1. Rabinovich, A.B., 2009. Seiches and Harbor Oscillations. In: Y. C. Kim, ed., 2009. Handbook of Coastal and Ocean Engineering. Singapore: World Scientific Publishing Company, pp. 193-236. https://doi.org/10.1142/9789812819307_0009
  2. Rabinovich, A.B., Kovalev, P.D. and Kovalev, D.P., 2025. The Noto Peninsula Tsunami of 1 January 2024 as Observed in the Northern Sea of Japan. Ocean Engineering, 327, 120892. https://doi.org/10.1016/j.oceaneng.2025.120892
  3. Manilyuk, Yu.V. and Cherkesov, L.V., 2017. Investigation of Seiche Oscillations in a Free Entrance Bay. Physical Oceanography, (4), pp. 16-25. https://doi.org/10.22449/1573-160X-2017-4-16-25
  4. Manilyuk, Yu.V., Lazorenko, D.I. and Fomin, V.V., 2020. Investigation of Seiche Oscillations in the Adjacent Bays by the Example of the Sevastopol and the Quarantine Bays. Physical Oceanography, 27(3), pp. 242-256. https://doi.org/10.22449/1573-160X-2020-3-242-256
  5. Dolgikh, G.I., Budrin, S.S., Dolgikh, S.G., Plotnikov, A.A., Chupin, V.A., Shvets, V.A. and Yakovenko, S.V., 2016. Free Oscillations of Water Level in the Posyet Gulf Bays (the Sea of Japan). Russian Meteorology and Hydrology, 41(8), pp. 559-563. https://doi.org/10.3103/S1068373916080057
  6. Medvedev, I.P. and Arkhipkin, V.S., 2015. Sea Level Oscillations in the Golubaya Bay (The Town of Gelendzhik). Vestnik Moskovskogo Universiteta. Seriya 5, Geografiya, (3), pp. 70-78 (in Russian).
  7. Cuomo, G. and Guza, R.T., 2017. Infragravity Seiches in a Small Harbor. Journal of Waterway, Port, Coastal, and Ocean Engineering, 143(5), 04017032. https://doi.org/10.1061/(asce)ww.1943-5460.0000392
  8. Vidal, C., Medina, R., Monserrat, S. and Martín, F.L., 2000. Harbor Resonance Induced by Pressure-Forced Surface Waves. In: B. L. Edge, ed., 2000. Coastal Engineering 2000. Proceedings of 27th International Conference on Coastal Engineering. Sydney, Australia: ASCE, pp. 3615-3628. https://doi.org/10.1061/40549(276)282
  9. De Jong, M.P.C. and Battjes, J.A., 2004. Seiche Characteristics of Rotterdam Harbour. Coastal Engineering, 51(5–6), pp. 373-386. https://doi.org/10.1016/j.coastaleng.2004.04.002
  10. Lepelletier, T.G. and Raichlen, F., 1987. Harbor Oscillations Induced by Nonlinear Transient Long Waves. Journal of Waterway, Port, Coastal and Ocean Engineering, 113(4), pp. 381-400. https://doi.org/10.1061/(ASCE)0733-950X(1987)113:4(381)
  11. Ichinose, G.A., Anderson, J.G., Satake, K., Schweickert, R.A. and Lahren, M.M., 2000. The Potential Hazard from Tsunami and Seiche Waves Generated by Large Earthquakes within Lake Tahoe, California-Nevada. Geophysical Research Letters, 27(8), pp. 1203-1206. https://doi.org/10.1029/1999GL011119
  12. Giese, G.S., Chapman, D.C., Black, P.G. and Fornshell, J.A., 1990. Causation of Large-Amplitude Coastal Seiches on the Caribbean Coast of Puerto Rico. Journal of Physical Oceanography, 20(9), pp. 1449-1458. https://doi.org/10.1175/1520-0485(1990)020%3C1449:colacs%3E2.0.co;2
  13. Bowers, E.C., 1992. Low Frequency Waves in Intermediate Water Depths. In: B. L. Edge, ed., 1992. Coastal Engineering 1992. Proceedings of the 23rd International Conference on Coastal Engineering. Venice, Italy: ASCE, pp. 832-845. https://doi.org/10.1061/9780872629332.062
  14. Melito, I., Cuomo, G., Bellotti, G. and Franco L., 2006. Field Measurements of Harbour Resonance at Marina di Carrara. In: J. M. Smith, ed., 2006. Coastal Engineering 2006. Proceedings of the 30th International Conference on Coastal Engineering. California, USA: World Scientific Publishing, pp. 1280-1292. https://doi.org/10.1142/9789812709554_0109
  15. Kovalev, P.D. and Kovalev, D.P., 2018. Long-Wave Processes in Southeastern Shelf Sakhalin Island. Ecological Systems and Devices, (8), pp. 36-41. https://doi.org/10.25791/esip.08.2018.121 (in Russian).
  16. Squire, V.A., Kovalev, P.D., Kovalev, D.P. and Zarochintsev, V.S., 2021. On the Trapping of Energy from Storm Surges on the Coasts of the Sea of Okhotsk. Estuarine, Coastal and Shelf Science, 250, 107136. https://doi.org/10.1016/j.ecss.2020.107136
  17. Clarke, D.J., 1974. High Frequency Edge Waves on an Exponential Shelf. Deutsche Hydrografische Zeitschrift, 26(6), pp. 265-271. https://doi.org/10.1007/BF02226668
  18. Guerrini, M., Bellotti, G., Fan, Y. and Franco, L., 2014. Numerical Modelling of Long Waves Amplification at Marina di Carrara Harbour. Applied Ocean Research, 48, pp. 322-330. https://doi.org/10.1016/j.apor.2014.10.002
  19. Kovalev, P.D., Shevchenko, G.V. and Kovalev, D.P., 2007. [Experimental Studies of Tsunamis in the Port of Kholmsk]. News Academy of Engineering Sciences A. M. Prokhorov, 20: Applied Mathematics and Mechanics, pp. 68-79 (in Russian).
  20. Kovalev, D.P., Manilyuk, Yu.V. and Kovalev, P.D., 2024. Sea Level Oscillations in the Adjacent Bays – Trade Port and Kholmsk-Severny (Sakhalin Island). Physical Oceanography, 31(3), pp. 409-426.
  21. Vturina, A.S., Shustin, V.A., Khramushin, V.N., Shevchenko, G.V. and Ivelskaya, T.N., 2004. Research of the Hydrodynamic Conditions of the Kholmsk Seaport Water Area. Vestnik of Far East Branch of the Russian Academy of Sciences, (1), pp. 40-51 (in Russian).
  22. Plekhanov, Ph.A. and Kovalev, D.P., 2016. The Complex Program of Processing and Analysis of Time-Series Data of Sea Level on the Basis of Author’s Algorithms. Geoinformatika, (1), pp. 44-53 (in Russian).
  23. Kovalev, D.P., 2018. Kyma. PC Software. Yuzhno-Sakhalinsk: IMGiG FEB RAS. State Registration No. RU2018618773 (in Russian).
  24. Ursell, F., 1952. Edge Waves on a Sloping Beach. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 214(1116), pp. 79-97. https://doi/org/10.1098/rspa.1952.0152
  25. Holman, R.A. and Bowen, A.J., 1984. Longshore Structure of Infragravity Wave Motions. Journal of Geophysical Research: Oceans, 89(C4), pp. 6446-6452. https://doi.org/10.1029/JC089iC04p06446
  26. Kovalev, P.D., Kovalev, D.P. and Shishkin, A.A., 2020. Study of Waves in the Bays and on the Coast of Shikotan Island in the Lesser Kuril Ridge. Geosystems of Transition Zones, 4(2), pp. 250-258. https://doi.org/10.30730/gtrz.2020.4.2.250-258
  27. Levin, B.V. and Tikhonov, I.N., eds., 2009. [The Nevelskoye Earthquake and Tsunami of August 2, 2007, Sakhalin Island]. Moscow: Janus-K, 204 p. (in Russian).
  28. Yaffee, R.A. and McGee, M., 2000. Introduction to Time Series Analysis and Forecasting: With Applications of SAS and SPSS. New York: Academic Press Inc., 513 p.
  29. Marple, S.L., 1987. Digital Spectral Analysis: With Applications. Upper Saddle River, New Jersey: Prentice-Hall, 492 p.
  30. Ott, E., 2002. Chaos in Dynamical Systems. Second Edition. Cambridge: Cambridge University Press, 490 p. https://doi.org/10.2277/0521811961
  31. Horita, T., Ouchi, K., Yamada, T. and Fujisaka, H., 2008. Stochastic Model of Chaotic Phase Synchronization. II. Progress of Theoretical Physics, 119(2), pp. 223-235. https://doi.org/10.1143/PTP.119.223
  32. Fujiwara, N. and Kurths, J., 2009. Spectral Universality of Phase Synchronization in Non-Identical Oscillator Networks. The European Physical Journal B, 69(1), pp. 45-49. https://doi.org/10.1140/epjb/e2009-00078-6
  33. Pazó, D., Mariño, I.P., Pérez-Villar, V. and Pérez-Muñuzuri, V., 2000. Transition to Chaotic Phase Synchronization through Random Phase Jumps. International Journal Bifurcation and Chaos, 10(11), pp. 2533-2539. https://doi.org/10.1142/S0218127400001699
  34. Vadivasova, T.E., Strelkova, G.I. and Anishchenko, V.S., 2001. Phase-Frequency Synchronization in a Chain of Periodic Oscillators in the Presence of Noise and Harmonic Forcings. Physical Review E, 63(3), 036225. https://doi.org/10.1103/PhysRevE.63.036225
  35. Kovacic, I. and Brennan, M.J., eds., 2011. The Duffing Equation: Nonlinear Oscillators and Their Behaviour. Brennan, Hoboken: John Wiley & Sons, 369 p. https://doi.org/10.1002/9780470977859
  36. Ruby, L., 1996. Applications of the Mathieu Equation. American Journal of Physics, 64(1), pp. 39-44. https://doi.org/10.1119/1.18290
  37. Zaks, M.A., Park, E.-H. and Kurths, J., 2000. On Phase Synchronization by Periodic Force in Chaotic Oscillators with Saddle Equilibria. International Journal Bifurcation and Chaos, 10(11), pp. 2649-2667. https://doi.org/10.1142/S0218127400001626

Files

Full text

JATS XML

We use Yandex Metrics. Read more.

Мы используем Яндекс Метрику. Подробнее.