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Nonlinear Internal Waves in Multilayer Shallow Water

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Abstract

Within the framework of the second approximation of the shallow water theory, the flow of a multilayer fluid stratified in density is under study. A mathematical model for the propagation of near-bottom and near-surface large-amplitude internal waves is constructed, taking into account the influence of the fine structure of thermocline (pycnocline). Using the resulting solutions describing the propagation of solitary waves and wave bores, field data are interpreted.

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References

  1. K. R. Helfrich and W. K. Melville, “Long Nonlinear Internal Waves,” Ann. Rev. Fluid Mech. 38, 395–425 (2006); DOI: https://doi.org/10.1146/annurev.fluid.38.050304.092129.

    Article  MathSciNet  ADS  Google Scholar 

  2. V. V. Novotryasov and M. S. Permyakov, “Experimental and Theoretical Determination of the Limiting Amplitude and Minimal Length of Solitary Waves in a Weakly Dispersed Shallow Sea,” Prikl. Mekh. Tekh. Fiz. 60 (3), 67–72 (2019) [J. Appl. Mech. Tech. Phys. 60 (3), 457–461 (2019)].

    MathSciNet  Google Scholar 

  3. A. Scotti and J. Pineda, “Observation of Very Large and Steep Internal Waves of Elevation near the Massachusetts Coast,” Geophys. Res. Lett. 31, L22307 (2004); DOI: https://doi.org/10.1029/2004GL021052.

    Article  ADS  Google Scholar 

  4. D. Bourgault, M. D. Blokhina, R. Mirshak, and D. E. Kelley, “Evolution of a Shoaling Internal Solitary Wavetrain,” Geophys. Res. Lett. 34 L03601 (2007); DOI: https://doi.org/10.1029/2006GL028462.

    Article  ADS  Google Scholar 

  5. V. F. Kukarin, V. Yu. Liapidevskii, V. V. Navrotsky, and F. F. Khrapchenkov, “Evolution of Large Amplitude Internal Waves of in a Swash Zone,” Fund. Prikl. Gidrofiz. 6 (2), 35–45 (2013).

    Google Scholar 

  6. W. Choi and R. Camassa, “Fully Nonlinear Internal Waves in a Two-Fluid System,” J. Fluid Mech. 386, 1–36 (1999); DOI: https://doi.org/10.1017/S0022112099005820.

    Article  MathSciNet  ADS  Google Scholar 

  7. V. Liapidevskii and N. Gavrilov, “Large Internal Solitary Waves in Shallow Waters,” in The Ocean in Motion: Circulation, Waves, Polar Oceanography, Ed. by M. G. Velarde, R. Yu. Tarakanov, and A. V. Marchenko (Springer Oceanography, 2018); DOI: https://doi.org/10.1007/978-3-319-71934-4J9.

  8. N. I. Makarenko, J. L. Maltseva, E. G. Morozov, et al., “Steady Internal Waves in Deep Stratified Flows,” Prikl. Mekh. Tekh. Fiz. 60 (2), 74–83 (2019) [J. Appl. Mech. Tech. Phys. 60 (2), 248–256 (2019)].

    MathSciNet  MATH  Google Scholar 

  9. W. Choi, “Modeling of Strongly Nonlinear Internal Gravity Waves,” in Proc. of the 4th Int. Conf. on Hydrodynamics, Yokohama, September 7–9, 2000, Ed. by Y. Goda, M. Ikehata, and K. Suzuki (Yokohama, 2000).

  10. N. V. Gavrilov, V. Yu. Liapidevskii, and Z. A. Liapidevskaya, “Transformation of Large Amplitude Internal Waves over a Shelf,” Fund. Prikl. Gidrofiz. 8 (3), 32–43 (2015).

    Google Scholar 

  11. V. Yu. Liapidevskii, V. V. Novotryasov, F. F. Khrapchenkov, and I. O. Yaroshchuk, “Internal Wave Bore in the Shelf Zone of the Sea,” Prikl. Mekh. Tekh. Fiz. 58 (5), 60–71 (2017) [J. Appl. Mech. Tech. Phys. 58 (5), 809–818 (2017)]; DOI: https://doi.org/10.15372/PMTF20170506.

    MathSciNet  Google Scholar 

  12. N. Gavrilov, V. Liapidevskii, and K. Gavrilova, “Large Amplitude Internal Solitary Waves over a Shelf,” Natural Hazards Earth System Sci. 11, 17–25 (2011); DOI: https://doi.org/10.5194/nhess-11-17-2011.

    Article  ADS  Google Scholar 

  13. V. V. Novotryasov, D. V. Stepanov, and I. O. Yaroshchuk, “Observations of Internal Undular Bores on the Japan/East Sea Shelf-Coastal Region,” Ocean Dyn. 66, 19–25 (2016).

    Article  ADS  Google Scholar 

  14. A. P. Leontyev, I. O. Yaroshchuk, S. V. Smirnov, et al., “A Spatially Distributed Measuring Complex for Monitoring Hydrophysical Processes on the Ocean Shelf,” Prib. Tekh. Eksp., No. 1, 128–135 (2017) [Instrum. Exp. Tech. 60 (1), 130–136 (2017)]; DOI: https://doi.org/10.7868/S0032816216060227.

  15. R.-Ch. Lien, F. Henyey, B. Ma, and Y. J. Yang, “Large-Amplitude Internal Solitary Waves Observed in the Northern South China Sea: Properties and Energetic,” J. Phys. Oceanogr. 44 (4), 1095–1115 (2014); DOI: https://doi.org/10.1175/JPO-D-13-088.1.

    Article  ADS  Google Scholar 

  16. V. F. Kukarin, V. Yu. Liapidevskii, F. F. Khrapchenkov, and I. O. Yaroshchuk, “Nonlinear Internal Waves in the Shelf Zone of the Sea,” Izv. Ross. Akad. Nauk, Mekh. Zhid. Gaza, No. 3, 38–47 (2019).

  17. V. F. Kukarin, V. Yu. Liapidevskii, F. F. Khrapchenkov, and I. O. Yaroshchuk, Fluid Dyn. 54(3), 329–338 (2019) https://doi.org/10.1134/S001546281903008X.

    Article  Google Scholar 

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Authors and Affiliations

  1. Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    V. Yu. Liapidevskii

  2. Voronezh State University, Voronezh, 394018, Russia

    V. Yu. Liapidevskii, M. V. Turbin & F. F. Khrapchenkov

  3. Il’ichev Pacific Oceanological Institute, Far Eastern Branch, Russian Academy of Science, Vladivostok, 690041, Russia

    F. F. Khrapchenkov

  4. Nikolaev Institute of Inorganic Chemistry, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    V. F. Kukarin

Authors
  1. V. Yu. Liapidevskii
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  2. M. V. Turbin
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  3. F. F. Khrapchenkov
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  4. V. F. Kukarin
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Corresponding author

Correspondence to V. Yu. Liapidevskii.

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__________

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 61, No. 1, pp. 53–62, January–February, 2020.

Original Russian Text © V.Yu. Liapidevskii, M.V. Turbin, F.F. Khrapchenkov, V.F. Kukarin.

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Liapidevskii, V.Y., Turbin, M.V., Khrapchenkov, F.F. et al. Nonlinear Internal Waves in Multilayer Shallow Water. J Appl Mech Tech Phy 61, 45–53 (2020). https://doi.org/10.1134/S0021894420010058

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  • DOI: https://doi.org/10.1134/S0021894420010058

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