HYDRODYNAMICS AND ACOUSTICS

2018 ◊ Volume 1 (91) ◊ Issue 1 ◊ p. 42-52

A. S. Kotelnikova^*, V. I. Nikishov^*, S. M. Sribnyuk^**

^* Institute of Hydromechanics of NAS of Ukraine, Kyiv, Ukraine
^** Poltava National Technical Yuriy Kondratyuk University, Ukraine

Experimental study of interaction of a surface solitary wave with an underwater step

Gidrodin. akust. 2018, 1(1):42-52

https://doi.org/10.15407/jha2018.01.042

TEXT LANGUAGE: Russian

ABSTRACT

The results of experimental studies of the interaction process of solitary waves with a rectangular step are presented. It is shown that there is a wave transformation above the obstacle with further its separation into the reflected and transmitted waves in the process of transition from deep water to shallow. The estimations of reflection and transmission coefficients are obtained. The results are compared with known analytical relations and experimental data. The transmission and reflection coefficients demonstrate the dependence not only on the relative height of the obstacle, but also on the amplitude of the incident wave. This observation is beyond the bounds of estimates obtained according to the linear theory of shallow water.

KEY WORDS

solitary wave, underwater step, reflection and transmission coefficients

REFERENCES 

1. E. Pelinovsky, B. H. Choi, T. Talipova, S. D. Woo, and D. C. Kim, “Solitary wave transformation on the underwater step: Asymptotic theory and numerical experiments”, AppliedMathematics and Computation, vol. 217, pp. 1704–1718, 2010. https://doi.org/10.1016/j.amc.2009.10.029.
2. P. L. F. Liu and Y. Cheng, “A numerical study of evolution of a solitary wave over a shelf”, Physics of Fluids, vol. 13, no. 6, pp. 1660–1667, 2001. https://doi.org/10.1063/1.1366666.
3. L. Ji and Y. Xi-Ping, “Numerical study of solitary wave fission over an underwater step”, Journal of Hydrodynamics, vol. 20, no. 3, pp. 398–402, 2008. https://doi.org/10.1016/s1001-6058(08)60073-6.
4. H. Lamb, Hydrodynamics. New York: Dover, 1947.
5. P. Lin, “A numerical study of solitary wave interaction with rectangular obstacles”, Coast. Eng, vol. 51, pp. 35–51, 2004. https://doi.org/10.1016/j.coastaleng.2003.11.005.
6. F. J. Sebra-Santos, D. P. Renouard, and A. M. Temperville, “Numerical and experimental study of the transformation of a solitary wave over a shelf or isolated obstacle”, Journal of Fluid Mechanics, vol. 176, pp. 117–134, 1987. https://doi.org/10.1017/s0022112087000594.
7. O. V. Gorodetsky, A. S. Kotelnikova, V. I. Nikishov, V. V. Oleksuk, P. Y. Romanenko, L. V. Selezova, G. P. Sokolovsky, and S. M. Sribnuk, “Generation, propagation and run-up of solitary waves on slopes”, Applied Hydromechanics, vol. 12(84), no. 1, pp. 40–47, 2010.
8. J. L. Hammack and H. Segur, “The Korteweg—de Vries equation and water waves. Part 2. Comparison with experiments”, Journal of Fluid Mechanics, vol. 65, pp. 289–314, 1974. https://doi.org/10.1017/s002211207400139x.
9. A. S. Kotelnikova, V. I. Nikishov, and S. M. Srebnyuk, “On the interaction of surface solitary waves and underwater obstacles”, Dopovidi NAN Ukrainy, no. 7, pp. 54–59, 2012.
10. N. Sugimoto, N. Nakajima, and T. Kakutani, “Edge-layer theory for shallow-water waves over a step — reflection and transmission of a soliton”, Journal of PhysicalSocietyof Japan, vol. 56, no. 5, pp. 1717–1730, 1987. https://doi.org/10.1143/JPSJ.56.1717.
11. R. A. Ruziev and G. S. Khakimzyanov, “Numerical modeling of a solitary wave transformation over an underwater ledge”, Vychilitelnye Tehnologii, vol. 1, no. 1, pp. 5–21, 1992.
12. G. S. Khakimzyanov and M. G. Khazhoyan, “Numerical simulation of the interaction between surface waves and submerged obstacles”, Russian Journal of Numerical Analysis and Mathematical Modeling, vol. 19, no. 1, pp. 17–34, 2004. https://doi.org/10.1163/156939804322802576.
13. C. C. Mei, M. Stiassnie, and D. K. P. Yue, Theory and applications of ocean surface waves: in 2 vols. Singapore: World Scientific, 2005.