HYDRODYNAMICS AND ACOUSTICS

This document is licensed under CC BY-NC-ND 4.0

2024 ◊ Volume 3 (93) ◊ Issue 3 ◊ p. 283-310

I. M. Gorban^*, A. S. Korolova^*, V. A. Voskoboinick^*, V. M. Vovk^*

^* Institute of Hydromechanics of NAS of Ukraine, Kyiv, Ukraine

Solitary wave dynamics and vortex fields near submerged slotted barriers

Gidrodin. akust. 2024, 3(3):283-310     [Date of publication: 23.12.2024]

TEXT LANGUAGE: English

ABSTRACT

Protecting coastal areas employing artificial structures is an important issue for the coastal engineering community. This study proposes a submerged, vertical, bottom-mounted screen with horizontal slots for reducing wave energy. When an incident wave encounters such an obstacle, it splits into transmitted and reflected waves. In addition, part of the wave energy is converted into kinetic energy of the vortex field due to flow separation from the structure walls. The study is focused on evaluating the hydraulic performance of this breakwater in terms of wave reflection and transmission coefficients. Circulation processes around the structure are also considered for deriving information about the directions and intensity of water exchange flows and bottom erosion. The problem is analyzed in the vertical plane, where the structure is considered a slotted barrier. It is assumed that the barrier comprises three impermeable elements and takes one of two possible configurations when its lower element either lies on the bottom or there is a gap between this element and the seabed. To identify the most suitable design, a numerical investigation of solitary wave interaction with slotted barriers of various shapes and porosity is carried out. The developed numerical procedure combines the boundary integral equation method used to determine free surface deformations and the hybrid vortex scheme for simulating the vortex field generated by the wave. The validity of the methodology is checked by the experimental research in the hydrodynamic tank of the Institute of Hydromechanics and by comparison with the data from other studies available in the literature. The solitary wave of non-dimensional amplitude A_i/h=0.2 is examined for the entire numerical experiment. Analysis of the free-surface evolution, as well as energy transmission and reflection coefficients, revealed that the protective properties of the structure deteriorate with increasing barrier porosity. In addition, permeability has a greater effect on high and narrow barriers than on lower and wider ones. Analysis of the vortex field created by the solitary wave around the slotted barrier revealed an intricate flow pattern on the leeward side. This pattern consists of two pairs of large-scale counter vortices, whose interaction forms downward and upward water flows along the structure. These vortices push the liquid through the gaps to the windward side, establishing reverse flows between the close zone and the open sea. This is a reason for the increase in water exchange intensity several times between different sides of the structure compared to an impermeable barrier. The data obtained infer that a slotted barrier of porosity 0.2-0.3 will be the most successful among structures of this type, both for shore protection and sustaining the health of the coastal ecology.

KEY WORDS

solitary wave, submerged breakwater, horizontally-slotted barrier, method of boundary integral equations, vortex method

REFERENCES

[1] D. L. Kriebel, "Vertical wave barriers: wave transmission and wave forces," in Coastal Engineering Proceedings, vol. 1(23). Orlando, FL: ICCE, 1992, pp. 1313-1326.
https://doi.org/10.1061/9780872629332.099

[2] C. Lin, T.-C. Ho, S.-C. Chang, S.-C. Hsieh, and K.-A. Chang, "Vortex shedding induced by a solitary wave propagating over a submerged vertical plate," International Journal of Heat and Fluid Flow, vol. 26, no. 6, pp. 894-904, 2005.
https://doi.org/10.1016/j.ijheatfluidflow.2005.10.009

[3] I. M. Gorban, A. C. Korolova, and O. G. Lebid, "Interaction of surface solitary wave with submerged and semi-submerged breakwaters," Precarpathian Bulletin of the Shevchenko Scientific Society "Number", no. 17(64), pp. 118-132, 2022.

[4] M. Isaacson, S. Premasiri, and G. Yang, "Wave interactions with vertical slotted barrier," Journal of Waterway, Port, Coastal, and Ocean Engineering, vol. 124, no. 3, pp. 118-126, 1998.
https://doi.org/10.1061/(ASCE)0733-950X(1998)124:3(118)

[5] M. Isaacson, J. Baldwin, S. Premasiri, and G. Yang, "Wave interactions with double slotted barriers," Applied Ocean Research, vol. 21, no. 2, pp. 81-91, 1999.
https://doi.org/10.1016/S0141-1187(98)00039-X

[6] O. S. Rageh and A. S. Koraim, "Hydraulic performance of vertical walls with horizontal slots used as breakwater," Coastal Engineering, vol. 57, no. 8, pp. 745-756, 2010.
https://doi.org/10.1016/j.coastaleng.2010.03.005

[7] Z. Huang, Y. Li, and Y. Liu, "Hydraulic performance and wave loadings of perforated/slotted coastal structures: A review," Ocean Engineering, vol. 38, no. 10, pp. 1031-1053, 2011.
https://doi.org/10.1016/j.oceaneng.2011.03.002

[8] C. E. Synolakis, "The runup of solitary waves," Journal of Fluid Mechanics, vol. 185, pp. 523-545, 1987.
https://doi.org/10.1017/S002211208700329X

[9] O. S. Madsen and C. C. Mei, "The transformation of a solitary wave over an uneven bottom," Journal of Fluid Mechanics, vol. 39, no. 4, pp. 781-791, 1969.
https://doi.org/10.1017/S0022112069002461

[10] F. J. Seabra-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, no. 1, p. 117, 1987.
https://doi.org/10.1017/S0022112087000594

[11] M. A. Losada, C. Vidal, and R. Medina, "Experimental study of the evolution of a solitary wave at an abrupt junction," Journal of Geophysical Research: Oceans, vol. 94, no. C10, pp. 14 557-14 566, 1989.
https://doi.org/10.1029/JC094iC10p14557

[12] P. A. Madsen, R. Murray, and O. R. Sørensen, "A new form of the Boussinesq equations with improved linear dispersion characteristics," Coastal Engineering, vol. 15, no. 4, pp. 371-388, 1991.
https://doi.org/10.1016/0378-3839(91)90017-B

[13] S. Beji and J. A. Battjes, "Numerical simulation of nonlinear wave propagation over a bar," Coastal Engineering, vol. 23, no. 1-2, pp. 1-16, 1994.
https://doi.org/10.1016/0378-3839(94)90012-4

[14] Q. Chen, J. T. Kirby, R. A. Dalrymple, A. B. Kennedy, and A. Chawla, "Boussinesq modeling of wave transformation, breaking, and runup. II: 2D," Journal of Waterway, Port, Coastal, and Ocean Engineering, vol. 126, no. 1, pp. 48-56, 2000.
https://doi.org/10.1061/(ASCE)0733-950X(2000)126:1(48)

[15] J. Kim, G. K. Pedersen, F. Løvholt, and R. J. LeVeque, "A Boussinesq type extension of the GeoClaw model - a study of wave breaking phenomena applying dispersive long wave models," Coastal Engineering, vol. 122, pp. 75-86, 2017.
https://doi.org/10.1016/j.coastaleng.2017.01.005

[16] M. J. Cooker, D. H. Peregrine, C. Vidal, and J. W. Dold, "The interaction between a solitary wave and a submerged semicircular cylinder," Journal of Fluid Mechanics, vol. 215, no. 1, pp. 1-22, 1990.
https://doi.org/10.1017/S002211209000252X

[17] S. T. Grilli, M. A. Losada, and F. Martin, "Characteristics of solitary wave breaking induced by breakwaters," Journal of Waterway, Port, Coastal, and Ocean Engineering, vol. 120, no. 1, pp. 74-92, 1994.
https://doi.org/10.1061/(ASCE)0733-950X(1994)120:1(74)

[18] Y. Cheng, G. Li, C. Ji, and G. Zhai, "Solitary wave slamming on an oscillating wave surge converter over varying topography in the presence of collinear currents," Physics of Fluids, vol. 32, no. 4, p. 047102, 2020.
https://doi.org/10.1063/5.0001402

[19] C.-J. Tang and J.-H. Chang, "Flow separation during solitary wave passing over sub- merged obstacle," Journal of Hydraulic Engineering, vol. 124, no. 7, pp. 742-749, 1998.
https://doi.org/10.1061/(ASCE)0733-9429(1998)124:7(742)

[20] P. Lin and P. L.-F. Liu, "A numerical study of breaking waves in the surf zone," Journal of Fluid Mechanics, vol. 359, pp. 239-264, 1998.
https://doi.org/10.1017/S002211209700846X

[21] P. Lin, "A numerical study of solitary wave interaction with rectangular obstacles," Coastal Engineering, vol. 51, no. 1, pp. 35-51, 2004.
https://doi.org/10.1016/j.coastaleng.2003.11.005

[22] K.-A. Chang, T.-J. Hsu, and P. L.-F. Liu, "Vortex generation and evolution in water waves propagating over a submerged rectangular obstacle," Coastal Engineering, vol. 44, no. 1, pp. 13-36, 2001.
https://doi.org/10.1016/S0378-3839(01)00019-9

[23] C.-J. Huang and C.-M. Dong, "On the interaction of a solitary wave and a submerged dike," Coastal Engineering, vol. 43, no. 3-4, pp. 265-286, 2001.
https://doi.org/10.1016/S0378-3839(01)00017-5

[24] Y.-T. Wu, S.-C. Hsiao, Z.-C. Huang, and K.-S. Hwang, "Propagation of solitary waves over a bottom-mounted barrier," Coastal Engineering, vol. 62, pp. 31-47, 2012.
https://doi.org/10.1016/j.coastaleng.2012.01.002

[25] J. J. Monaghan, "Simulating free surface flows with SPH," Journal of Computational Physics, vol. 110, no. 2, pp. 399-406, 1994.
https://doi.org/10.1006/jcph.1994.1034

[26] S. Koshizuka, A. Nobe, and Y. Oka, "Numerical analysis of breaking waves using the moving particle semi-implicit method," International Journal for Numerical Methods in Fluids, vol. 26, no. 7, pp. 751-769, 1998.
https://doi.org/10.1002/(SICI)1097-0363(19980415)26:7<751::AID-FLD671>3.0.CO;2-C

[27] Y. Ren, M. Luo, and P. Lin, "Consistent particle method simulation of solitary wave interaction with a submerged breakwater," Water, vol. 11, no. 2, p. 261, 2019.
https://doi.org/10.3390/w11020261

[28] X. Han and S. Dong, "Interaction of solitary wave with submerged breakwater by smoothed particle hydrodynamics," Ocean Engineering, vol. 216, p. 108108, 2020.
https://doi.org/10.1016/j.oceaneng.2020.108108

[29] Y. Huang and C. Zhu, "Numerical analysis of tsunami-structure interaction using a modified MPS method," Natural Hazards, vol. 75, no. 3, pp. 2847-2862, 2014.
https://doi.org/10.1007/s11069-014-1464-1

[30] P. Koumoutsakos, A. Leonard, and F. Pepin, "Boundary conditions for viscous vortex methods," Journal of Computational Physics, vol. 113, no. 1, pp. 52-61, 1994.
https://doi.org/10.1006/jcph.1994.1117

[31] M.-Y. Lin and L.-H. Huang, "Vortex shedding from a submerged rectangular obstacle attacked by a solitary wave," Journal of Fluid Mechanics, vol. 651, pp. 503-518, 2010.
https://doi.org/10.1017/S0022112010000145

[32] I. M. Gorban and A. S. Korolyova, "Numerical simulation of the interaction of a soliton wave with immersed obstacles," Visnyk of Zaporizhzhya National University Physical and Mathematical Sciences, no. 1, pp. 22-32, 2021.

[33] P. L.-F. Liu and K. Al-Banaa, "Solitary wave runup and force on a vertical barrier," Journal of Fluid Mechanics, vol. 505, pp. 225-233, 2004.
https://doi.org/10.1017/S0022112004008547

[34] S. Shao, "SPH simulation of solitary wave interaction with a curtain-type breakwater," Journal of Hydraulic Research, vol. 43, no. 4, pp. 366-375, 2005.
https://doi.org/10.1080/00221680509500132

[35] M. J. Ketabdari, N. Kamani, and M. H. Moghaddam, "WCSPH simulation of solitary wave interaction with a curtain-type breakwater," in AIP Conference Proceedings, vol. 1648. AIP Publishing LLC, 2015, p. 770006.
https://doi.org/10.1063/1.4912976

[36] Y.-T. Wu, S.-C. Hsiao, K.-S. Hwang, T.-C. Lin, and A. Torres-Freyermuth, "Numerical study of solitary wave interaction with a slotted barrier," in International Ocean and Polar Engineering Conference. Maui, HI: International Society of Offshore and Polar Engineers, 2011, pp. ISOPE-I-11-072.

[37] Y.-T. Wu and S.-C. Hsiao, "Propagation of solitary waves over a submerged slotted barrier," Journal of Marine Science and Engineering, vol. 8, no. 6, p. 419, 2020.
https://doi.org/10.3390/jmse8060419

[38] V. O. Gorban and I. M. Gorban, "Vortical flow structure near a square prism: numerical model and algorithms of control," Applied Hydromechanics, vol. 7(79), no. 2, pp. 8-26, 2005.

[39] I. M. Gorban, A numerical study of solitary wave interactions with a bottom step. Cham, Germany: Springer International Publishing, 2015, pp. 369-387.
https://doi.org/10.1007/978-3-319-19075-4_22

[40] J. G. Telste, "Potential flow about two counter-rotating vortices approaching a free surface," Journal of Fluid Mechanics, vol. 201, no. 1, p. 259, 1989.
https://doi.org/10.1017/S0022112089000935

[41] G. R. Baker, D. I. Meiron, and S. A. Orszag, "Generalized vortex methods for free-surface flow problems," Journal of Fluid Mechanics, vol. 123, pp. 477-501, 1982.
https://doi.org/10.1017/S0022112082003164

[42] H. Lamb, Hydrodynamics. Cambridge, UK: Cambridge University Press, 1932.

[43] G.-H. Cottet and P. D. Koumoutsakos, Vortex methods: theory and practice. Cambridge, UK: Cambridge University Press, 2000.
https://doi.org/10.1017/CBO9780511526442

[44] I. M. Gorban and O. V. Khomenko, Flow control near a square prism with the help of frontal flat plates. Cham, Germany: Springer International Publishing, 2016, pp. 327-350.
https://doi.org/10.1007/978-3-319-40673-2_17

[45] I. M. Gorban and O. G. Lebid, Numerical modeling of the wing aerodynamics at angle-of-attack at low Reynolds numbers. Cham, Germany: Springer International Publish- ing, 2018, pp. 159-179.
https://doi.org/10.1007/978-3-319-96755-4_10

[46] D. Clamond and D. Dutykh, "Fast accurate computation of the fully nonlinear solitary surface gravity waves," Computers & Fluids, vol. 84, pp. 35-38, 2013.
https://doi.org/10.1016/j.compfluid.2013.05.010

[47] A. S. Kotelnikova, V. I. Nikishov, and S. M. Srebnyuk, "On the interaction of surface solitary waves and underwater obstacles," Reports of the National Academy of Sciences of Ukraine, no. 7, pp. 54-59, 2012.

[48] J. G. B. Byatt-Smith, "An integral equation for unsteady surface waves and a comment on the Boussinesq equation," Journal of Fluid Mechanics, vol. 49, no. 4, pp. 625-633, 1971.
https://doi.org/10.1017/S0022112071002295

[49] R. K.-C. Chan and R. L. Street, "A computer study of finite-amplitude water waves," Journal of Computational Physics, vol. 6, no. 1, pp. 68-94, 1970.
https://doi.org/10.1016/0021-9991(70)90005-7

[50] T. Maxworthy, "Experiments on collisions between solitary waves," Journal of Fluid Mechanics, vol. 76, no. 1, pp. 177-186, 1976.
https://doi.org/10.1017/S0022112076003194

[51] D. Lo and D. Young, "Arbitrary Lagrangian-Eulerian finite element analysis of free surface flow using a velocity-vorticity formulation," Journal of Computational Physics, vol. 195, no. 1, pp. 175-201, 2004.
https://doi.org/10.1016/j.jcp.2003.09.019

[52] Y. Li and F. Raichlen, "Energy balance model for breaking solitary wave runup," Journal of Waterway, Port, Coastal, and Ocean Engineering, vol. 129, no. 2, pp. 47-59, 2003.
https://doi.org/10.1061/(ASCE)0733-950X(2003)129:2(47)