Numerical Simulation of Spatial Distribution of Wave Overtopping on Non-reshaping Berm Breakwaters

Abstract

This study presents the results of a 2D numerical modeling investigation on the performance of non-reshaping berm breakwaters with a special look at the spatial distribution of irregular wave overtopping using FLOW-3D CFD code. The numerical model is based on Reynolds-Averaged Navier-Stokes solver (RANS) and volume of fluid (VOF) surface capturing scheme (RANS-VOF). The numerical model has been validated using experimental data. The armor and core porosities have been used as calibration factors to reproduce the wave overtopping distribution. The computed distributions of wave overtopping behind the structure agree well with the measurements for a non-reshaping berm breakwater. A formula is derived to relate the spatial distribution of wave overtopping water behind non-reshaping berm breakwaters to non-dimensional forms of wave height, wave period, berm width, berm height, and armor freeboard based on numerical results. This formula model agreed reasonably well with numerical model results.

Keywords

Wave overtopping / Spatial distribution / Berm breakwater / Numerical simulation / Non-reshaping

References

[1] Besley P (1999) Overtopping of seawalls: design and assessment manual. Environment Agency. Bristol, R&D Technical Report No.W178, 37

[2] Burcharth HF, Andersen OH. On the one-dimensional steady and unsteady porous flow equations. Coast Eng, 1995, 24: 233-257

[3] De Rouck J. CLASH - D46: Final report, 2005, Belgium: Ghent University

[4] Dentale F, Donnarumma G, Carratelli EP, Giovanni V, Ii P, Sa F (2014) A new numerical approach to the study of the interaction between wave motion and rubble mound breakwaters. In Proceedings of the 7th International Conference on Engineering Mechanics, Structures, Engineering Geology (EMESEG ’14), Salerno, Italy: WSEAS Press, 45–52

[5] EurOtop (2018) Wave overtopping of sea defenses and related structures: assessment manual

[6] FLOW-3D® Version 12.0 User’s Manual (2018). FLOW-3D [computer software]. Santa Fe: Flow Science, Inc. https://www.flow3d.com. Accessed 3 Feb 2019

[7] Goda Y. Statistical variability of sea state parameters as a function of wave spectrum. Coast Eng Jpn, 1988, 31: 39-52

[8] Gotoh H, Shao SD, Memita T. SPH-LES model for numerical investigation of wave interaction with partially immersed breakwater. Coast Eng Jpn, 2004, 46(1): 39-63

[9] Hirt CW, Nichols BD. Volume of fluid (VOF) method for the dynamics of free boundaries. Comput Phys, 1981, 39: 201-225

[10] Hu K, Mingham CG, Causon DM. Numerical simulation of wave overtopping of coastal structures using the non-linear shallow water equations. Coast Eng, 2000, 41: 433-465

[11] Ingram DM, Gao F, Causon DM, Mingham CG, Troch P. Numerical investigations of wave overtopping at coastal structures. Coast Eng, 2009, 56(2): 90-202

[12] Jensen OJ. A monograph on rubble mound breakwaters, 1984, Hørsholm: Danish Hydraulic Institute

[13] Kobayashi N, Wurjanto A. Wave overtopping on coastal structures. J Waterw Port Coast Ocean Eng, 1989, 115: 235-251

[14] Krom JC (2012) Wave overtopping at rubble mound breakwaters with a non-reshaping berm. Delft University of Technology, Master Thesis, Department of Hydraulic Engineering

[15] Lara JL, Losada IJ, Liu PLF (2006) Breaking waves over a mild gravel slope: experimental and numerical analysis. J Geophys Res AGU 111

[16] LeMehaute B (1969) An introduction to hydrodynamics and water waves. Technical report ERL 118-POL-3-2, U.S. Department of Commerce, Washington, DC

[17] Li TQ, Troch P, De Rouck J. Wave overtopping over a sea dike. J Comput Phys, 2004, 198: 686-726

[18] Lioutas AC (2010) Experimental research on spatial distribution of overtopping. Delft University of Technology, Master Thesis, Department of Hydraulic Engineering

[19] Liu PLF, Lin PZ, Chang KA, Sakakiyama T. Numerical modelling of wave interaction with porous structures. J Waterw Port Coast Ocean Eng ASCE, 1999, 125(6): 322-330

[20] Losada IJ (2003) Advances in modeling the effects of permeable and reflective structures on waves and nearshore flows. In: Chris Lakhan, V. (Ed.), Advances in Coastal Modeling. Elsevier Oceanography Series, 67

[21] Losada IJ, Lara JL, Guanche R, Gonzalez-Ondina JM. Numerical analysis of wave overtopping of rubble mound breakwaters. Coast Eng, 2008, 55(1): 47-62

[22] Lykke Andersen T (2006) Hydraulic response of rubble mound breakwaters (scale effects-berm breakwaters). Doctoral Thesis. University of Aalborg, Denmark

[23] Mingham CG, Causon DM. High-resolution finite-volume method for shallow water flows. J Hydraul Eng ASCE, 1998, 124(6): 605-614

[24] Moghim MN, Tørum A. Wave induced loading of the reshaping rubble mound breakwaters. Appl Ocean Res, 2012, 37: 90-97

[25] Moghim MN, Forouzan Boroujeni R, Mohammad Rezapour Tabari M. Wave overtopping on reshaping berm breakwaters based on wave momentum flux. Appl Ocean Res, 2015, 53: 23-30

[26] Orszag SA, Staroselsky I, Flannery WS, Zhang Y. Gatski TB, Hussaini MY, Lumley JL. Introduction to renormalization group modeling of turbulence. Simulation and modeling of turbulent flows, 1996, New york: Oxford University Press, 155-183

[27] Owen MW (1980) Design of sea walls allowing for wave overtopping, Report EX. 924. Hydraulics Research Station, Wallingford, UK

[28] PIANC (2003) State-of-the-art of designing and constructing berm breakwaters. PIANC, Brussels

[29] Shao S, Ji C, Graham DI, Reeve DE, James PW, Chadwick AJ. Simulation of wave overtopping by an incompressible SPH model. Coast Eng, 2006, 53: 723-735

[30] Shih RWK (1990) Permeability characteristics of rubble material - new formulae.22nd International Conference on Coastal Engineering. p. 1499–1512

[31] Sigurdarson S, Van der Meer JW (2012) Wave overtopping at berm breakwaters in line with EurOto. In: Proceedings of the 33rd International Conference on Coastal Engineering, ICCE 2012, Santander

[32] Soliman ASM (2003) Numerical study of irregular wave overtopping and overflow. Ph.D. Thesis, University of Nottingham, UK

[33] Stansby PK, Feng T. Surf zone wave overtopping a trapezoidal structure: 1-D modelling and PIV comparison. Coast Eng, 2004, 51: 483-500

[34] TAW (2002) Technical report wave run-up and wave overtopping at dikes. Technical Advisory Committee on Flood Defense, Delft

[35] Thanyamanta W, Herrington P, Molyneux D (2011) Wave patterns, wave induced forces and moments for a gravity based structure predicted using CFD. In: Proceedings of the ASME 2011, 30th International Conference on Ocean. Offshore and Arctic Engineering, (OMAE), The Netherlands, p. 19–24

[36] Troch P, De Rouck J (1998) Development of two-dimensional numerical wave flume for wave interaction with rubble mound breakwaters. 26th Int. Coastal Engineering Conference. p. 1638–1649

[37] Tuan TQ, Oumeraci H. A numerical model of wave overtopping on seadikes. Coast Eng, 2010, 57: 757-772

[38] Van der Meer JW (1988) Rock slopes and gravel beaches under wave attack. Doctoral Thesis. Delft University of Technology, Also: Delft Hydraulics Communication No. 396

[39] Van der Meer JW, Janssen JPFM (1995) Wave run-up and wave overtopping at dikes. In: Wave Forces on Inclined and Vertical Wall Structures. ASCE. Ed. N. Kobayashi and Z. Demirbilek, 1–27

[40] Van Gent MRA (1995) Wave interaction with permeable coastal structures. Delft University of Technology, Ph.D. Thesis

[41] Van Kester D (2009) Spatial distribution of wave overtopping. Delft University of Technology, Master Thesis, Department of Hydraulic Engineering

[42] Vanneste D, Altomare C, Suzuki T, Troch P, Verwaest T (2014) Comparison of numerical models for wave overtopping and impact on a sea wall. 34th International Conference on Coastal Engineering, Proceedings. p.1–14

[43] Yakhot V, Orszag SA. Renormalization group analysis of turbulence. J Sci Comput, 1986, 1: 39-35

[44] Zhang Y, Chen G, Hu J, Chen X, Yang W, Tao A, Zheng J. Experimental study on mechanism of sea-dike failure due to wave overtopping. Appl Ocean Res, 2017, 68: 171-181