The influence of nonlinear interaction on the evolution of waves in a shallow basin

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  • Authors: Rodin A.A.1, Rodina N.A.1,2, Kurkin A.A.1, Pelinovsky E.N.3,4,5,6
  • Affiliations:
    1. Nizhny Novgorod State Technical University n.a. R.E. Alekseev
    2. Lobachevsky State University of Nizhni Novgorod
    3. Institute of Applied Physics Russian Academy of Sciences
    4. Special Research Bureau for Automation of Marine Researches, Far Eastern Branch of Russian Academy of Sciences
    5. National Research University – Higher School of Economics
    6. University of Southern Queensland
  • Issue: Vol 55, No 4 (2019)
  • Pages: 82-86
  • Section: ARTICLES
  • URL: https://journals.eco-vector.com/0002-3515/article/view/16125
  • DOI: https://doi.org/10.31857/S0002-351555482-86
  • Cite item

Abstract


The influence of counter interaction of nonlinear wave in the shallow water has been studied. It is shown that such an interaction leads to a change in the phase of propagation of the main wave, which is forced to propagate along the flow induced by the counter-propagating wave. Estimates of the height of the non-breaking wave at the moment of interaction are in agreement with theoretical predictions. The phase shift in the interaction of non-breaking waves is small enough, but becomes noticeable in the case of the breaking waves motion.


About the authors

A. A. Rodin

Nizhny Novgorod State Technical University n.a. R.E. Alekseev

Author for correspondence.
Email: aakurkin@gmail.com

Russian Federation, Minin Street 24, 603950, Nizhny Novgorod

N. A. Rodina

Nizhny Novgorod State Technical University n.a. R.E. Alekseev; Lobachevsky State University of Nizhni Novgorod

Email: na4aikovskaya@mail.ru

Russian Federation, Minin Street 24, 603950, Nizhny Novgorod; Gagarin Avenue, 23, 603950, Nizhny Novgorod

A. A. Kurkin

Nizhny Novgorod State Technical University n.a. R.E. Alekseev

Email: aakurkin@gmail.com

Russian Federation, Minin Street 24, 603950, Nizhny Novgorod

E. N. Pelinovsky

Institute of Applied Physics Russian Academy of Sciences; Special Research Bureau for Automation of Marine Researches, Far Eastern Branch of Russian Academy of Sciences; National Research University – Higher School of Economics; University of Southern Queensland

Email: pelinovsky@gmail.com

Russian Federation, Ul’yanov Street, 46, 603950, Nizhny Novgorod; Gorky Street, 25, 693023, Yuzhno-Sakhalinsk; Bolshaya Pecherskaya Street, 25/12, 603155, Nizhny Novgorod; West Street, Darling Heights QLD 4350 Australia

References

  1. Стокер Дж. Волны на воде. М.: Издательство иностранной литературы, 1959. 618 с.
  2. Вольцингер Н.Е., Клеванный К.А., Пелиновский Е.Н. Длинноволновая динамика прибрежной зоны. Л.: Гидрометеоиздат, 1989. 271 с.
  3. Арсеньев А.С., Шелковников Н.К. Динамика морских длинных волн. М.: МГУ, 1991. 88 с. 4. Ozer Sozdinler C., Yalciner А.С., Zaytsev А. Investigation of tsunami hydrodynamic parameters in inundation zones with different structural layouts // Pure and Applied Geophysics. 2015. V. 172. P. 931–952.
  4. Velioglu D., Kian R., Yalciner A.C., Zaytsev A. Performance Assessment of NAMI DANCE in Tsunami Evolution and Currents Using a Benchmark Problem // Journal of Marine Science and Engineering. 2016. V. 4(3). P. 49–1–8.
  5. Lynett P.J., Gately K., Wilson R., Montoya L., Arcas D., Aytore B., Bai Y., Bricker J.D., Castro M.J., Cheung K.F., David C.G., Doğan G.G., Escalante C., González-Vida J.M., Grilli S.T., Heitmann T.W., Horrillo J.J., Kânoglu U., Kian R., Kirby J.T., Li W., Macías J., Nicolsky D.J., Ortega S., Pampell-Manis A., Park Y.S., Roeber V., Sharghivand N., Shelby M., Shi F., Tehranirad B., Tolkova E., Thio H.K., Velioğlu D., Yalçiner A.C., Yamazaki Y., Zaytsev A., Zhang Y.J. Inter-model analysis of tsunami-induced coastal currents // Ocean Modelling. 2017. V. 114. P. 14–32.
  6. LeVeque R.J. Finite Volume Methods for Hyperbolic Problems. Cambridge: Cambridge University Press, 2002. 558 p.
  7. LeVeque R.J., George D.L., Berger M.J. Tsunami modeling with adaptively refined finite volume methods // Acta Numerica. 2011. V. 20. P. 211–289.
  8. Berger M., George D., LeVeque R.J., Mandli K.T. The GeoClaw software for depth-averaged flows with adaptive refinement // Advances in Water Resources. 2011. V. 34(9). P. 1195–1206.
  9. Gonzalez F.I., LeVeque R.J., Chamberlain P., Hirai Br., Varkovitzky J., George D.L. Validation of the GeoClaw model. Washington: University of Washington, 2011. 84 р.
  10. Пелиновский Е.Н. Гидродинамика волн цунами. Нижний Новгород: ИПФ РАН, 1996. 276 с.
  11. Пелиновский Е.Н., Диденкулова И.И., Куркин А.А., Родин А.А. Аналитическая теория наката морских волн на берег. Нижний Новгород: НГТУ им. Р.Е. Алексеева, 2015. 114 с.
  12. Raz A., Nicolsky D., Rybkin A., Pelinovsky E. Long wave run-up in asymmetric bays and in fjords with two separate heads // Journal of Geophysical Research – Oceanus. 2018. V. 123. № 3. P. 2066–2080.
  13. Пелиновский Е.Н., Родин А.А. Трансформация сильно нелинейной поверхностной волны в мелководном бассейне // Известия РАН. Физика атмосферы и океана. 2012. Т. 48. № 3. С. 383–390.
  14. Pelinovsky E., Kharif C., Talipova T. Large-amplitude long wave interaction with a vertical wall // European J. Mechanics – B/Fluids. 2008. V. 27. № 4. P. 409–418.
  15. Пелиновский Е.Н., Шургалина Е.Г., Родин А.А. О Критериях перехода обрушающегося бора в волнообразный // Известия РАН. Физика атмосферы и океана. 2015. T. 51. № 5. С. 598–601.
  16. Диденкулова, И.И. Заибо Н., Куркин А.А., Пелиновский Е.Н. Крутизна и спектр нелинейно деформируемой волны на мелководье // Известия РАН. Физика атмосферы и океана. 2006. Т. 42. № 6. C. 839–842.
  17. Курант Р., Фридрихс К. Сверхзвуковое течение и ударные волны. М.: Издательство иностранной литературы, 1950. 427 с.

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