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Gridless simulations of splashing processes and near-shore bore propagation

Published online by Cambridge University Press:  30 October 2007

M. LANDRINI ,
A. COLAGROSSI ,
M. GRECO  and
M. P. TULIN
M. LANDRINI
Affiliation:
INSEAN, The Italian Ship Model Basin, Via di Vallerano 139, 00128 Roma, Italy Ocean Engineering Laboratory, UCSB, California, USAmpt6@cox.net
A. COLAGROSSI*
Affiliation:
INSEAN, The Italian Ship Model Basin, Via di Vallerano 139, 00128 Roma, Italy
M. GRECO
Affiliation:
INSEAN, The Italian Ship Model Basin, Via di Vallerano 139, 00128 Roma, Italy
M. P. TULIN
Affiliation:
Ocean Engineering Laboratory, UCSB, California, USAmpt6@cox.net
*
‡Author to whom correspondence should be addressed.
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Abstract

The generation and evolution of two-dimensional bores in water of uniform depth and on sloping beaches are simulated through numerical solution of the Euler equations using the smoothed particle hydrodynamics (SPH) method, wherein particles are followed in Lagrangian fashion, avoiding the need for computational grids. In water of uniform depth, a piston wavemaker produces cyclically breaking bores in the Froude number range 1.37–1.82, which were shown to move at time-averaged speeds in very good agreement with the requirements of global mass and momentum conservation. A single Strouhal number for the breaking period was discovered. Complex repetitive splashing patterns are observed and described, involving forward jet formation growth, impact and ricochet, and similarly, backward jet formation and impact. Observed consequences were the creation of vortical regions of both signs, dipole creation through pairing, large-scale transport of surface water downward and high tangential scouring velocities on the bed, which are quantified. These bores are further allowed to rise on linear slopes to the shoreline, where they are seen to collapse into a tongue-like flow resembling dam-break evolution.

This essentially inviscid calculation is able to reproduce the development of a highly vortical flow in excellent agreement with experimental observations and theoretical concepts. The turbulent flow behaviour is partially described by the numerical solution.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 591 , 25 November 2007 , pp. 183 - 213
Copyright
Copyright © Cambridge University Press 2007

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Footnotes

†

Deceased 26 June 2003.

References

REFERENCES

Abadie, S., Caltagirone, J. & Watremez, P. 1998 Splash-up generation in a plunging breaker. C. R. Acad. Sci. Paris IIB Mech. Phys. Astron. 326 (9), 553–559.Google Scholar
Allen, M. P. & Tildesley, D. J. 1987 Computer Simulation of Liquids. Oxford.Google Scholar
Battjes, J. A. 1988 Surf-zone dynamics. Annu. Rev. Fluid Mech. 20, 257–291.CrossRefGoogle Scholar
Belytschko, T., Lu, Y. Y. & Gu, L. 1994 Element free Galerkin. Intl J. Numer. Meth. Engng 37, 229–256.CrossRefGoogle Scholar
Belytschko, T., Krongauz, Y., Organ, D., Fleming, M. & Krysl, P. 1996 Meshless methods: an overview and recent developments. Comput. Meth. Appl. Mech. Engng 139, 3–47.CrossRefGoogle Scholar
Belytschko, T., Krongauz, Y., Dolbow, J. & Gerlach, C. 1998 On the completeness of meshfree particle methods. Intl J. Numer. Meth. Engng 43, 785–819.3.0.CO;2-9>CrossRefGoogle Scholar
Benz, W. 1990 Smooth particle hydrodynamics: a review. In The Numerical Modelling of Nonlinear Stellar Pulsation (ed. Buchler, J. R.), pp. 269–288 Kluwer.CrossRefGoogle Scholar
Bicknell, G.V. 1991 The equations of motion of particles in smoothed particle hydrodynamics. SIAM J. Sci. Statist. Comput. 12 (5), 1198–1206.CrossRefGoogle Scholar
Bonet, J. & Lok, T.-S. L. 1999 Variational and momentum preservation aspects of SPH formulations. Comput. Meth. Appl. Mech. Engng 180, 97–115.CrossRefGoogle Scholar
Bonmarin, P. 1989 Geometric properties of deep-water breaking waves. J. Fluid Mech. 209, 405–433.CrossRefGoogle Scholar
Bradford, S. F. 2000 Numerical simulation of surf zone dynamics. J. Waterway Port Coastal Ocean Engng 126 (1), 1–13.CrossRefGoogle Scholar
Chen, G., Kharif, C., Zaleski, S. & Li, J. 1999 Two-dimensional Navier–Stokes simulations of breaking waves. Phys. Fluids 11 (1), 121–133.CrossRefGoogle Scholar
Christensen, E. D. & Deigaard, R. 2001 Large eddy simulation of breaking waves. Coast. Engng 42 (1), 53–86.CrossRefGoogle Scholar
Cointe, R. & Tulin, M. P. 1994 A theory of steady breakers. J. Fluid Mech. 276, 1–20.CrossRefGoogle Scholar
Colagrossi, A. 2005 A meshless Lagrangian method for free–surface and interface flows with fragmentation. PhD thesis, Department of Mechanical Engineering, University of Rome, ‘La Sapienza’ (http://padis.uniroma1.it).Google Scholar
Colagrossi, A. & Landrini, M. 2003 Numerical simulation of interfacial flows by smoothed particle hydrodynamics. J. Comput. Phys. 191, 448–475.CrossRefGoogle Scholar
Colagrossi, A., Landrini, M. & Tulin, M. P. 2000 Near shore bore propagation and splashing processes: gridless simulations. Proc. 6th Intl Workshop on Wave Hindcasting and Forecasting. Metereological Service of Canada, Monterey, CA.Google Scholar
Colicchio, G., Colagrossi, A., Greco, M. & Landrini, M. 2002 Free-surface flow after a dam Break: a comparative study. Ship Technol. Res. 49 (3), 95–104.Google Scholar
Di Lisio, R., Grenier, E. & Pulvirenti, M. 1998 The convergence of the SPH Method. Comput. Maths Applics 35 (1), 95–102.CrossRefGoogle Scholar
Dold, J. W. & Peregrine, D. H. 1986 An efficient boundary integral method for steep unsteady water waves. Numerical Methods for Fluid Dynamics II (ed. Morton, K. W. & Baines, M. J.), pp. 671–679. Oxford University Press.Google Scholar
Fries, T. P. & Matthies, H. G. 2004 Classification and overview of meshfree methods. Informatikbericht 2003-03, Institute of Scientific Computing, Technical University Braunschweig, Brunswick, Germany, 2003.Google Scholar
Gingold, R. A. & Monaghan, J. J. 1977 Smoothed particle hydrodynamics: theory and application to non spherical stars. Mon. Not. R. Astr. Soc. 181, 375–389.CrossRefGoogle Scholar
Goldstein, S. 1965 Modern Developments in Fluid Dynamics. Dover.Google Scholar
Greenhow, M. & Lin, W. M. 1985 Numerical simulation of nonlinear free-surface flows generated by wedge entry and wavemaker motions. Proc. 4th Intl Conf. on Numerical Ship Hydrodynamics, Washington-DC, USA.Google Scholar
Grilli, S., Svendsen, A. & Subramanya, R. 1997 Breaking criterion and characteristics for solitary waves on slopes. J. Waterway Port Coastal Ocean Engng 123, 102–112.CrossRefGoogle Scholar
Hernquist, L. & Katz, N. 1989 TREESPH: a unification of SPH with the hierarchical tree method. Astrophys. J. Suppl. Ser. 70, 419–446.CrossRefGoogle Scholar
Ho, D. V. & Meyer, R. E. 1962 Climb of a bore on a beach. Part 1. Uniform beach slope. J. Fluid Mech. 14, 305–318.CrossRefGoogle Scholar
Hornung, H. G., Willert, C. & Turner, S. 1995 The flow field downstream of a hydraulic jump. J. Fluid Mech. 287, 299–316.CrossRefGoogle Scholar
Jansen, P. 1986 Laboratory observations of the kinematics in the aerated region of breaking waves. Coastal Engng 9, 453–477.CrossRefGoogle Scholar
Keller, H. B., Levine, D. A. & Witham, G. B. 1960 Motion of a bore over a sloping beach. J. Fluid Mech. 7, 302–315.CrossRefGoogle Scholar
Lamarre, E & Melville, W. K. 1991 Air entrainment and dissipation in breaking waves. Lett. Nature 341, 469–472.CrossRefGoogle Scholar
Landrini, M. & Tyvand, P. A. 2001 Generation of water waves and bores by impulsive bottom flux. J. Engng Maths 39, 131–170.CrossRefGoogle Scholar
Landrini, M., Colagrossi, A. & Tulin, M. P. 2001 Breaking bow and stern waves: numerical simulations. Proc. 16th Intl Workshop on Water Waves and Floating Bodies, Hiroshima, Japan.Google Scholar
Landrini, M., Colagrossi, A. & Faltinsen, O. M. 2003 Sloshing in 2-D flows by the SPH method. Proc. 8th Intl Conf. on Numerical Ship Hydrodynamics, Busan, South Korea.Google Scholar
Lemos, C. M. 1996 Higher-order schemes for free-surface flows with arbitrary configurations. Intl J. Numer. Meth. Fluids 23, 545–566.3.0.CO;2-R>CrossRefGoogle Scholar
Le Touzé, D., & Colagrossi, A. 2005 Free-surface prototype problems suitable to investigate particle methods. Proc. 20th Intl Workshop on Water Waves and Floating Bodies, Longyearbyen, Norway.Google Scholar
Lin, C. & Hwung, H. H. 1992 External and internal flow fields of plunging breakers. Exps. Fluids 12, 229–237.CrossRefGoogle Scholar
Lin, P. & Liu, P. L.-F. 1998 A numerical study of breaking waves in the surf zone. J. Fluid Mech. 359, 239–264.CrossRefGoogle Scholar
Lin, P. & Liu, P. L.-F. 1999 Free-surface tracking methods and their applications to wave hydrodynamics. Adv Coastal Ocean Engng 5, 213–240.CrossRefGoogle Scholar
Lucy, L. B. 1977 A numerical approach to the testing of fission hypothesis. Astron. J. 82 (12), 1013–1024.CrossRefGoogle Scholar
Mas-Gallic, S. & Raviart, P. A. 1987 A particle method for first-order symmetric systems. Numerische Mathematik 51 (3), 323–352, July.CrossRefGoogle Scholar
Miller, R. L. 1968 Experimental determination of run-up of undular and fully developed bores. J. Geophys. Res. 73 (14), 4497–4510.CrossRefGoogle Scholar
Miller, R. L. 1976 Role of vortices in surf-zone prediction: sedimentation and wave forces. Soc. Economic Paleontologists and Mineralogists Special Publication (ed. Davis, R. A & Ethington, R. L.) 24, 92–114.Google Scholar
Molteni, D., Colagrossi, A. & Colicchio, G. 2007 On the use of an alternative water state equation in SPH. Proc. SPHERIC, 2nd Intl Workshop, Universidad Politécnica de Madrid, Spain, May, pp. 23–26.Google Scholar
Monaghan, J. J. 1985 Particle methods for hydrodynamics. Comput. Phys. Rep. 3 (2), 71–124.CrossRefGoogle Scholar
Monaghan, J. J. 1992 Smoothed particle hydrodynamics. Annu. Rev. Astron. Astrophys. 30, 543–574.CrossRefGoogle Scholar
Monaghan, J. J. 1994 Simulating free surface flows with SPH. J. Comput. Phys. 110, 399–406.CrossRefGoogle Scholar
Monaghan, J. J. 2005 Smoothed particle hydrodynamics. Rep. Prog. Phys. 68, 1703–1759.CrossRefGoogle Scholar
Monaghan, J. J. & Gingold, R. A. 1983 Shock simulation by the particle method SPH. J. Comput. Phys. 52, 374–389.CrossRefGoogle Scholar
Monaghan, J. J. & Kos, A. 1999 Solitary waves on a Cretan beach. J. Waterway Port Coastal Ocean Engng 125 (3), 145–154.CrossRefGoogle Scholar
Monaghan, J. J. & Kos, A. 2000 Scott Russell's wave generator. Phys. Fluids 12 (3), 622–630.CrossRefGoogle Scholar
Monaghan, J. J., Kos, A. & Issa, N. 2003 Fluid motion generated by impact. J. Waterway Port Coastal Ocean Engng 129 (6), 250–259.CrossRefGoogle Scholar
Morris, J. P. 1996 A study of the stability properties of smooth particle hydrodynamics. Publ. Astron. Soc. Australia 13 (1), 97–102.CrossRefGoogle Scholar
Morris, J. P., Fox, P. & Zhu, Y. 1997 Modeling low Reynolds number incompressible flows using SPH. J. Comput. Phys. 136, 214–226.CrossRefGoogle Scholar
Moussa, B. B. & Vila, J. P. 2000 Convergence of SPH method for scalar nonlinear conservation laws. SIAM J. Numer. Anal. 37, 863–887.CrossRefGoogle Scholar
Nelson, R. P. & Papaloizou, J. 1994 Variable smoothing lengths and energy conservation in smoothed particle hydrodynamics. Mon. Not. R. Astron. Soc. 270, 1–20.CrossRefGoogle Scholar
Peregrine, D. H. 1983 Breaking waves on beaches. Annu. Rev. Fluid Mech. 15, 149–178.CrossRefGoogle Scholar
Raviart, P. A. 1985 An analysis of particle methods. Numerical Methods in Fluid Dynamics (ed. Brezzi, F.) Lecture Notes in Mathematics, vol. 1127, pp. 243–324. Springer.CrossRefGoogle Scholar
Stoker, J. J. 1957 Water Waves: the Mathematical Theory with Applications. Interscience.Google Scholar
Svendsen, I. A., Madsen, P. A. & Hansen, J. B. 1978 Wave characteristics in the surf zone. Proc. 16th Coastal Engineering Conf. ASCE, Hamburg, Germany, pp. 520–539.Google Scholar
Takeda, H., Miyama, S. M. & Sekiya, M. 1994 Numerical simulation of viscous flow by smoothed particle hydrodynamics. Prog. Theoret. Phys. 92 (5), 939–960.CrossRefGoogle Scholar
Telesda Silva, A. F. da Silva, A. F. & Peregrine, D. H. 1990 Unsteady free surface waves by domain decomposition approach. Proc. 16th Intl Workshop of Water Waves and Floating Bodies, Hiroshima, Japan.Google Scholar
Trivellato, F., Bertolazzi, E. & Colagrossi, A. 2004 Two flow solvers for liquid–liquid impacts. Vorticity and Turbulence Effects in Fluid–Solid Interactions, Advanced Fluid Mechanics. WIT Press.Google Scholar
Tulin, M. P. & Landrini, M. 2000 Breaking waves in the ocean and around ships. Proc. 23rd Symp. on Naval Hydrodyn. vol. 4, pp. 1–32. National Academy Press, Val de Reuil, France.Google Scholar
Wang, P., Yao, Y. & Tulin, M. P. 1995 An efficient numerical tank for nonlinear water waves based on the multi-subdomain approach with BEM. Intl J. Numer. Meth. Fluids 20, 1315–1336.CrossRefGoogle Scholar
Welton, W. C. & Pope, S. B. 1997 PDF model calculations of compressible turbulent flows using smoothed particle hydrodynamics. J. Comput. Phys. 134, 150–168.CrossRefGoogle Scholar
Yeh, H., Ghazali, A. & Marton, I. 1989 Experimental study of bore run-up. J. Fluid Mech. 207, 563–578.CrossRefGoogle Scholar