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Laboratory-scale swash flows generated by a non-breaking solitary wave on a steep slope

  • P. Higuera (a1), P. L.-F. Liu (a1) (a2) (a3), C. Lin (a4), W.-Y. Wong (a4) and M.-J. Kao (a4)...


The main goal of this paper is to provide insights into swash flow dynamics, generated by a non-breaking solitary wave on a steep slope. Both laboratory experiments and numerical simulations are conducted to investigate the details of runup and rundown processes. Special attention is given to the evolution of the bottom boundary layer over the slope in terms of flow separation, vortex formation and the development of a hydraulic jump during the rundown phase. Laboratory experiments were performed to measure the flow velocity fields by means of high-speed particle image velocimetry (HSPIV). Detailed pathline patterns of the swash flows and free-surface profiles were also visualized. Highly resolved computational fluid dynamics (CFD) simulations were carried out. Numerical results are compared with laboratory measurements with a focus on the velocities inside the boundary layer. The overall agreement is excellent during the initial stage of the runup process. However, discrepancies in the model/data comparison grow as time advances because the numerical model does not simulate the shoreline dynamics accurately. Introducing small temporal and spatial shifts in the comparison yields adequate agreement during the entire rundown process. Highly resolved numerical solutions are used to study physical variables that are not measured in laboratory experiments (e.g. pressure field and bottom shear stress). It is shown that the main mechanism for vortex shedding is correlated with the large pressure gradient along the slope as the rundown flow transitions from supercritical to subcritical, under the developing hydraulic jump. Furthermore, the bottom shear stress analysis indicates that the largest values occur at the shoreline and that the relatively large bottom shear stress also takes place within the supercritical flow region, being associated with the backwash vortex system rather than the plunging wave. It is clearly demonstrated that the combination of laboratory observations and numerical simulations have indeed provided significant insights into the swash flow processes.


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Adrian, R. J. & Westerweel, J. 2011 Particle Image Velocimetry. Cambridge University Press.
Albadawi, A., Donoghue, D. B., Robinson, A. J., Murray, D. B. & Delauré, Y. M. C. 2013 Influence of surface tension implementation in volume of fluid and coupled volume of fluid with level set methods for bubble growth and detachment. Intl J. Multiphase Flow 53, 1128.
Barnes, M. P., O’Donoghue, T., Alsina, J. & Baldock, T. 2009 Direct bed shear stress measurement in bore-driven swash. Coast. Engng 56 (8), 853867.
Berberovic, E., Hinsberg, N. P., van Jakirlic, S., Roisman, I. V. & Tropea, C. 2009 Drop impact onto a liquid layer of finite thickness: dynamics of the cavity evolution. Phys. Rev. E 79, 036306.
Boussinesq, J. 1872 Theorie des ondes et des remous qui se propagent le long d’un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond. J. Math. Pures Appl. 17, 55108.
Brackbill, J. U., Kothe, D. B. & Zemach, C. 1992 A continuum method for modeling surface tension. J. Comput. Phys. 100 (2), 335354.
Brenninkmeyer, S. J. 1976 In situ measurements of rapidly fluctuating, high sediment concentrations. Mar. Geol. 20, 117128.
Briganti, R., Torres-Freyermuth, A., Baldock, T. E., Brocchini, M., Dodd, N., Hsu, T.-J., Jiang, Z., Kim, Y., Pintado-Patiño, J. C. & Postacchini, M. 2016 Advances in numerical modeling of swash zone dynamics. Coast. Engng 115, 2641.
Cabral, B. & Leedom, L. C. 1993 Imaging vector fields using line integral convolution. Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Techniques. pp. 263270. ACM.
Chang, K. A. & Liu, P. L.-F. 2000 Pseudo turbulence in PIV breaking wave measurements. Exp. Fluids 29, 331338.
Chardón-Maldonado, P., Pintado-Patiño, J. C. & Puleo, J. A. 2016 Advances in swash-zone research: small-scale hydrodynamic and sediment transport processes. Coast. Engng 115, 825.
Chow, V. T. 1973 Open-Channel Hydraulics. McGraw-Hill.
Cowen, E. A. & Monismith, S. G. 1997 A hybrid digital particle tracking velocimetry technique. Exp. Fluids 22, 199211.
Cowen, E. A., Sou, I.-M., Liu, P. L.-F. & Raubenheimer, B. 2003 Particle image velocimetry measurements within a laboratory-generated swash zone. J. Engng Mech. 129 (10), 11191129.
Deshpande, S. S., Anumolu, L. & Trujillo, M. F. 2012 Evaluating the performance of the two-phase flow solver InterFoam. Comput. Sci. Disc. 5, 014016.
Devolder, B., Rauwoens, P. & Troch, P. 2017 Application of a buoyancy-modified k-𝜔 SST turbulence model to simulate wave run-up around a monopile subjected to regular waves using OpenFOAM® . Coast. Engng 125, 8194.
Elfrink, B. & Baldock, T. 2002 Hydrodynamics and sediment transport in the swash zone: a review and perspectives. Coast. Engng 45 (3), 149167.
Francois, M. M., Cummins, S. J., Dendy, E. D., Kothe, D. B., Sicilian, J. M. & Williams, M. W. 2006 A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework. J. Comput. Phys. 213, 141173.
Gopala, V. R. & van Wachem, B. G. M. 2008 Volume of fluid methods for immiscible-fluid and free-surface flows. Chem. Engng J. 141, 204221.
Goring, D. G.1978 Tsunami: the propagation of long waves onto a shelf. Tech. Rep. KH-R-38, W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena, California, USA.
Grilli, S. T., Svendsen, I. A. & Subramanya, R. 1997 Breaking criterion and characterisitics for solitary waves on slopes. J. Waterways Port Coast. Ocean Engng 123 (3), 102112.
Grimshaw, R. 1971 The solitary wave in water of variable depth. Part 2. J. Fluid Mech. 46, 611622.
Gupta, N. 1993 An analytic solution describing the motion of a bore over a sloping beach. J. Fluid Mech. 253, 167172.
Higuera, P., Lara, J. L. & Losada, I. J. 2013a Realistic wave generation and active wave absorption for Navier–Stokes models: application to OpenFOAM. Coast. Engng 71, 102118.
Higuera, P., Lara, J. L. & Losada, I. J. 2013b Simulating coastal engineering processes with OpenFOAM. Coast. Engng 71, 119134.
Higuera, P., Lara, J. L. & Losada, I. J. 2014 Three–dimensional interaction of waves and porous coastal structures using OpenFOAM. Part I: formulation and validation. Coast. Engng 83, 243258.
Hirt, C. W. & Nichols, B. D. 1981 Volume of fluif (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201225.
Ho, D. V. & Meyer, R. E. 1962 Climb of a bore on a beach. Part 1. Uniform beach slope. J. Fluid Mech. 14 (2), 305318.
Holthuijsen, L. H. 2010 Waves in Oceanic and Coastal Waters. Cambridge University Press.
Jasak, H.1996 Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College of Science, Technology and Medicine.
Keane, R. D. & Adrian, R. J. 1992 Theory of cross-correlation analysis of PIV images. Appl. Sci. Res. 49, 191215.
Keller, H. B., Levine, D. A. & Whitman, G. B. 1960 Motion of a bore over a sloping beach. J. Fluid Mech. 7 (2), 302316.
Lafaurie, B., Nardone, C., Scardovelli, R., Zaleski, S. & Zanetti, G. 1994 Modelling merging and fragmentation in multiphase flows with SURFER. J. Comput. Phys. 113, 134147.
Lin, C., Hseih, S. C., Lin, I. J., Chang, K. A. & Raikar, R. 2012 Flow property and self-similarity in steady hydraulic jumps. Exp. Fluids 53, 15911616.
Lin, C., Kao, M.-J., Tzeng, G.-W., Wong, W.-Y., Yang, J., Raikar, R. V., Wu, T.-R. & Liu, P. L.-F. 2015a Study on flow fields of boundary-layer separation and hydraulic jump during rundown motion of shoaling solitary wave. J. Earthquake Tsunami 9 (5), 1540002.
Lin, C., Yeh, P. H., Hseih, S. C., Shih, Y. N., Lo, L. F. & Tsai, C. P. 2014 Pre-breaking internal velocity field induced by a solitary wave propagating over a 1:10 slope. Ocean Engng 80, 112.
Lin, C., Yeh, P. H., Kao, M. J., Yu, M. H., Hseih, S. C., Chang, S. C., Wu, T. R. & Tsai, C. P. 2015b Velocity fields in near-bottom and boundary layer flows in pre-breaking zone of solitary wave propagating over a 1:10 slope. J. Waterways Port Coast Ocean Engng 141 (3), 04014038.
Liu, P. L.-F. & Cho, Y.-S. 1994 Integral equation model for wave propagation with bottom frictions. J. Waterway Port Coast Ocean Engng 120, 594608.
Lo, H.-Y., Park, Y. S. & Liu, P. L.-F. 2013 On the run-up and back-wash processes of single and double solitary waves—An experimental study. Coast. Engng 80, 114.
Lubin, P., Vincent, S., Abadie, S. & Caltagirone, J.-P. 2006 Three-dimensional large Eddy simulation of air entrainment under plunging breaking waves. Coast. Engng 53 (8), 631655.
Masselink, G. & Puleo, J. A. 2006 Swash-zone morphodynamics. Cont. Shelf Res. 26, 661680.
Matsunaga, N. & Honji, H. 1980 The backwash vortex. J. Fluid Mech. 99 (4), 813815.
O’Donoghue, T., Pokrajak, D. & Hondebrink, L. J. 2010 Laboratory and numerical study of dambreak-generated swash on impermeable slopes. Coast. Engng 57, 513530.
Omenyi, S. N., Smith, R. P. & Neumann, A. W. 1980 Determination of solid/melt interfacial tensions and of contact angles of small particles from the critical velocity of engulfing. J. Colloid Interface Sci. 75 (1), 117125.
Peregrine, D. H. 1974 Surface shear waves. J. Hydraul. Div. 100 (9), 12151227.
Pilliod, J. E. & Puckett, E. G. 2004 Second-order accurate volume-of-fluid algorithms for tracking material interfaces. J. Comput. Phys. 199 (2), 465502.
Pintado-Patiño, J. C., Torres-Freyermuth, A., Puleo, J. A. & Pokrajac, D. 2015 On the role of infiltration and exfiltration in swash zone boundary layer dynamics. J. Geophys. Res. 120, 63296350.
Pujara, N., Liu, P. L.-F. & Yeh, H. 2015 The swash of solitary waves on a plane beach: flow evolution, bed shear stress and run-up. J. Fluid Mech. 779, 556597.
Puleo, J. A., Holland, K. T., Slinn, D. N., Smith, E. & Webb, B. M. 2002 Numerical modelling of swash zone hydrodynamics. In 28th International Coastal Engineering Conference (ICCE), Cardiff, Wales, pp. 968979.
Roenby, J., Bredmose, H. & Jasak, H. 2016 A computational method for sharp interface advection. R. Soc. Open Sci. 3, 160405.
Schlichting, H. 1979 Boundary Layer Theory, 7th edn. McGraw-Hill.
Shen, M. C. & Meyer, R. E. 1963 Climb of a bore on a beach. Part 3. Run-up. J. Fluid Mech. 16 (1), 113125.
Smith, L., Jensen, A. & Pedersen, G. 2017 Investigation of breaking and non-breaking solitary waves and measurements of swash zone dynamics on a 5° beach. Coast. Engng 120, 3846.
Sou, I.-M., Cowen, E. A. & Liu, P. L.-F. 2010 Evolution of the turbulence structure in the surf and swash zones. J. Fluid Mech. 644, 193216.
Sumer, B. M., Guner, H. A. A., Hansen, N. M., Fuhrman, D. R. & Fredsøe, J. 2013 Laboratory observations of flow and sediment transport induced by plunging regular waves. J. Geophys. Res. 118, 61616182.
Sumer, B. M., Jensen, P. M., Sørensen, L. B., Fredsøe, J., Liu, P. L.-F. & Carstensen, S. 2010 Coherent structures in wave boundary layers. Part 2. Solitary motion. J. Fluid Mech. 646, 207231.
Sumer, B. M., Sen, M. B., Karagali, I., Ceren, B., Fredsøe, J., Sottile, M., Zilioli, L. & Fuhrman, D. R. 2011 Flow and sediment transport induced by a plunging solitary wave. J. Geophys. Res. 116, C01008.
Synolakis, C. E. 1987 The runup of solitary waves. J. Fluid Mech. 185, 523545.
Torres-Freyermuth, A., Puleo, J. A. & Pokrajac, D. 2013 Modeling swash-zone hydrodynamics and shear stresses on planar slopes using Reynolds-averaged Navier–Stokes equations. J. Geophys. Res. 118 (2), 10191033.
Vukcevic, V., Jasak, H. & Gatin, I. 2017 Implementation of the ghost fluid method for free surface flows in polyhedral finite volume framework. Comput. Fluids 153, 119.
Weller, H., Tabor, G., Jasak, H. & Fureby, C. 1998 A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput. Phys. 12 (6), 620631.
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