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DETERMINATION OF BACKGROUND PARAMETERS OF WEAKLY DISPERSIVE STRATIFIED SHALLOW WATER

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Abstract

A method for determining the background parameters of weakly dispersive media based on the theory of low-intensity undular bores in such media is proposed. An analytical model of an undular (cnoidal) bore on a pycnocline of a stratified shallow sea is used to obtain expressions for calculating the coefficients of the extended Korteweg–de Vries equation: the velocities of linear internal waves, high-frequency dispersion, quadratic and cubic nonlinearities, i.e., the parameters characterizing the hydrophysical background over which the bore propagates. These parameters are calculated from data of direct measurements of bore characteristics: their wave records, nonlinear velocity, “mass" and amplitude of leading solitons, and the frequencies of the rear waves in the region of bore propagation. The efficiency of the proposed method is confirmed by the results of numerical simulation.

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REFERENCES

  1. Ch. R. Jackson, “An Atlas of Internal Solitary-Like Waves and Their Properties. in Alexandria: Global Ocean Associates(2004); https://www.internal_wave_atlas.com.

  2. K. R. Helfrich and W. K. Melville, “Long Nonlinear Internal Waves," Annual Rev. Fluid Mech. 38, 395–425 (2006).

  3. R. Grimshaw, K. Helfrich, and A. Scotti, “Large Amplitude Internal Waves in the Coastal Ocean," Nonlinear Process. Geophys.18, 653–665 (2011).

  4. J. R.  Apel, L. A. Ostrovsky, Y. A. Stepanyants, and J. F. Lynch, “Internal Solitons in the Ocean and Their Effect on Underwater Sound," J. Acoust. Soc. Amer. 121 (2), 695–722 (2007).

  5. B. Wang, D. Bogucki, and L. Redekopp, “Internal Solitary Waves in a Structured Thermocline with Implications for Resuspension and the Formation of Thin Particle Laden Layers," J. Geophys. Res.106 (N C5), 9565–9585 (2001).

  6. G. B. Whitham, Linear and Nonlinear Waves (Wiley Inter-Science, New York, 1974).

  7. Yu. Z. Miropol’skii, Dynamics of Internal Gravity Waves in the Ocean (Gidrometeoizdat, Leningrad, 1981) [in Russian].

  8. N. F. Smyth and P. E. Holloway, “Hydraulic Jump and Undular Bore Formation on a Shelf Break," J. Phys. Ocean. 18 (7), 947–962 (1988).

  9. R. Grimshaw, Environmental Stratified Flows(Kluwer, Boston, 2001).

  10. 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 (1), 19–25 (2016).

  11. V. Yu. Liapidevskii, V. V. Novotryasov, F. F. Khrapchenko, 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); https://doi.org/10.1134/S0021894417050066].

  12. A. V. Gurevich and L. V. Pitaevskii, “Nonstationary Structure of a Collisionless Shock Wave," Zh. Eksp. Teor. Fiz. 65, 590–604 (1973).

  13. A. V. Gurevich, A. L. Krylov, and G. A. El’, “Nonlinear Modulated Waves in Dispersive Hydrodynamics," Zh. Exp. Teor. Fiz.98, 1605–1626 (1990).

  14. A. V. Gurevich, A. L. Krylov, N. G. Mazur., and G. A. El’, “Evolution of Localized Perturbations in Korteweg–de Vries Hydrodynamics," Dokl. Sov. Fiz. 37, 198–201 (1992).

  15. A. M. Kamchatnov, Y.-H. Kuo, T.-C. Liu, et al., “Undular Bore Theory for the Gardner Equation," Phys. Rev., E 86(3), 036605 (2012).

  16. J. R. Apel, “A New Analytical Model for Internal Solitons in the Ocean," J. Phys. Ocean 33, 2247–2269 (2003).

  17. V. M. Vassilev, P. A. Djondjorov, M. Ts. Hadzhilazova, and I. M. Mladenov, “Explicit Parametrization on Willmore Surfaces," AIP Conf. Proc. 1404 (86), 201–206 (2011).

  18. V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii,Soliton Theory (Nauka, Moscow, 1980) [in Russian].

  19. 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); https://doi.org/10.1134/S0021894419030076].

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

    V. V. Novotryasov

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  1. V. V. Novotryasov
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Correspondence to V. V. Novotryasov.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Vol. 62, No. 1, pp. 88–96. https://doi.org/10.15372/PMTF20210110.

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Novotryasov, V.V. DETERMINATION OF BACKGROUND PARAMETERS OF WEAKLY DISPERSIVE STRATIFIED SHALLOW WATER. J Appl Mech Tech Phy 62, 79–85 (2021). https://doi.org/10.1134/S0021894421010107

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  • DOI: https://doi.org/10.1134/S0021894421010107

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