Numerical Simulation of the Solitary Waves Propagation and Run-up in Shallow Water

A. Yu. Belokon✉, S. Yu. Mikhailichenko

Marine Hydrophysical Institute of RAS, Sevastopol, Russian Federation

✉ e-mail: aleksa.44.33@gmail.com

Abstract

Purpose. The paper is aimed at investigating the propagation of solitons in a shallow basin, assessing the nonlinear effects resulting from the wave run-up on a gentle coast, and at comparing the estimates obtained using different numerical models with the available analytical dependencies.

Methods and Results. The results of numerical simulations carried out using two nonlinear models of long waves (the author's model and the Simulating WAves till SHore (SWASH) one) are represented in the paper. The solitary wave profiles were obtained during its propagation in the part of a basin with constant depth conjugated with the inclined bottom. The process of a wave run-up on the coast was simulated using the algorithm of fluid movement along a dry coast. It is shown that when a soliton propagates in the basin part with constant depth, the nonlinearity effects are manifested in deformation of a wave profile. In other words, increase of the wave initial amplitude and the distance traveled by a wave is accompanied by growth of the wave front slope steepness. This, in its turn, leads to increase of a splash when the waves run-up on the coast. The estimates of the run-up heights resulted from different numerical models are in good agreement.

Conclusions. The calculated values of the maximum wave run-up on the coast for the non-deformed waves, the length of which is equal to that of the traversed path, are close to the estimates obtained analytically. For the waves with the deformed profile, the front slope steepness of which increases with propagation over long distances, the run-up heights increase with growth of the wave initial amplitude. In such a case, it is desirable to replace the analytical estimates with the numerical ones. The run-up height of the deformed waves can exceed the wave initial amplitude by four or more times. The results obtained in this study can be useful in projecting the coastal protection constructions with the regard for preserving the coastal ecology and economy.

Keywords

numerical simulation, solitons, solitary waves, nonlinear effects, run-up, hydrodynamic model SWASH

Acknowledgements

The investigation was carried out within the framework of the state task on theme No. 0555-2021-0005 “Complex interdisciplinary investigations of the oceanologic processes conditioning functioning and evolution of the Black and Azov seas’ ecosystems of the coastal zones”.

Original russian text

Original Russian Text © A. Yu. Belokon, S. Yu. Mikhailichenko, 2021, published in MORSKOY GIDROFIZICHESKIY ZHURNAL, Vol. 37, Iss. 6, pp. 742-753 (2021)

For citation

Belokon, A.Yu. and Mikhailichenko, S.Yu., 2021. Numerical Simulation of the Solitary Waves Propagation and Run-up in Shallow Water. Physical Oceanography, 28(6), pp. 691-701. doi: 10.22449/1573-160X-2021-6-691-701

DOI

10.22449/1573-160X-2021-6-691-701

References

  1. Kononkova, G.E. and Pokazeev, K.V., 1985. [Dynamics of Sea Waves]. Moscow: Publishing house of Moscow State University, 298 p. (in Russian).
  2. Shelkovnikov, N.K., 2012. Soliton Version of Formation of Freak Waves in the Ocean. Morskoy Gidrofizicheskiy Zhurnal, (5), pp. 34-42 (in Russian).
  3. 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
  4. Didenkulova, I.I. and Pelinovsky, E.N., 2019. Run-Up of a Nonlinear Monochromatic Wave on a Plane Beach in Presence of a Tide. Oceanology, 59(4), pp. 478-481. https://doi.org/10.1134/S0001437019040027
  5. Carrier, G. and Greenspan, H., 1958. Water Waves of Finite Amplitude on a Sloping Beach. Journal of Fluid Mechanics, 4(1), pp. 97-109. https://doi.org/10.1017/S0022112058000331
  6. Pedersen, G. and Gjevik, B., 1983. Run-up of Solitary Waves. Journal of Fluid Mechanics, 135, pp. 283-299. https://doi.org/10.1017/S0022112083003080
  7. Synolakis, C.E., 1987. The Run-up of Solitary Waves. Journal of Fluid Mechanics, 185, pp. 523-545. https://doi.org/10.1017/S002211208700329X
  8. Li, Y. and Raichlen, F., 2001. Solitary Wave Runup on Plane Slopes. Journal of Waterway, Port, Coastal, and Ocean Engineering, 127(1), pp. 33-44. https://doi.org/10.1061/(ASCE)0733-950X(2001)127:1(33)
  9. Dotsenko, S.F. and Sannikova, N.K.V., 2013. Characteristics of the Solitary Surface Wave Run-up on a Sloping Beach. Reports of the National Academy of Sciences of Ukraine, (2), pp. 86-91 (in Russian).
  10. Rodin, A.A., Zemlyanikin, A.Y., Likhodeev, N.M., Kurkin, A.A. and Rodina, N.A., 2017. Laboratory and Numerical Study of the Wave Run-Up on the Flat Slope. In: PSU, 2017. Non-Equilibrium Processes in Continuous Media. Materials of the international symposium. Vol. 2, pp. 166-168 (in Russian).
  11. Nikishov, V.I., Selezov, I.T. and Khomitsky, V.V., 2011. Interaction of Surface and Internal Solitary Waves with Slopes. Applied Hydromechanics, 13(2), pp. 51-63. Available at: http://dspace.nbuv.gov.ua/handle/123456789/116297 [Accessed: 20 November 2021] (in Russian).
  12. Maximov, V.V., Nudner, I.S., Lebedev, V.V., Semenov, K.K., Kshevetskii, S.P. and Amosov, A.A., 2017. Interaction of Tsunami Waves with Sloping Structures. Fundamentalnaya i Prikladnaya Gidrofizika, 10(4), pp. 53-60. doi:10.7868/S2073667317040050 (in Russian).
  13. Didenkulova, I.I., Zahibo, N., Kurkin, A.A., Levin, B.V., Pelinovsky, E.N. and Soomere, T., 2006. Runup of Nonlinearly Deformed Waves on a Coast. Doklady Earth Sciences, 411(1), pp. 1241-1243. https://doi.org/10.1134/S1028334X06080186
  14. Bazykina, A.Yu. and Fomin, V.V., 2017. Run-Up Characteristics of the Solitary Waves on the Coast in the Bays with Different Cross-Section Configurations. Ecological Safety of Coastal and Shelf Zones of Sea, (4), pp. 30-38 (in Russian).
  15. Didenkulova, I.I., 2009. New Trends in the Analytical Theory of Long Sea Wave Runup. In: E. Quak and T. Soomere, eds., 2009. Applied Wave Mathematics. Berlin, Heidelberg: Springer, pp. 265-296. https://doi.org/10.1007/978-3-642-00585-5_14
  16. Abdalazeez, A.A., Didenkulova, I.I. and Dutykh, D., 2019. Nonlinear Deformation and Run- up of Single Tsunami Waves of Positive Polarity: Numerical Simulations and Analytical Predictions. Natural Hazards and Earth System Sciences, 19(12), pp. 2905-2913. https://doi.org/10.5194/nhess-19-2905-2019
  17. Lamb, H., 1932. Hydrodynamics. Cambridge University Press, 738 p.
  18. Kowalik, Z., 2001. Basic Relations between Tsunami Calculations and Their Physics. Science of Tsunami Hazards, 19(2), pp. 99-115.

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