Hostname: page-component-8448b6f56d-m8qmq Total loading time: 0 Render date: 2024-04-25T02:09:49.325Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulence structure and interaction with steep breaking waves

Published online by Cambridge University Press:  04 April 2011

DJAMEL LAKEHAL  and
PETAR LIOVIC
DJAMEL LAKEHAL*
Affiliation:
ASCOMP GmbH Zürich, Technoparkstrasse 1, H22, Zurich 8005, Switzerland
PETAR LIOVIC
Affiliation:
CSIRO Materials Science and Engineering, Graham Road, Highett VIC 3190, Australia
*
†Email address for correspondence: lakehal@ascomp.ch
Get access Rights & Permissions [Opens in a new window]

Abstract

Large-eddy and interface simulation using an interface tracking-based multi-fluid flow solver is conducted to investigate the breaking of steep water waves on a beach of constant bed slope. The present investigation focuses mainly on the ‘weak plunger’ breaking wave type and provides a detailed analysis of the two-way interaction between the mean fluid flow and the sub-modal motions, encompassing wave dynamics and turbulence. The flow is analysed from two points of views: mean to sub-modal exchange, and wave to turbulence interaction within the sub-modal range. Wave growth and propagation are due to energy transfer from the mean flow to the waves, and transport of mean momentum by these waves. The vigorous downwelling–upwelling patterns developing at the head and tail of each breaker are shown to generate both negative- and positive-signed energy exchange contributions in the thin sublayer underneath the water surface. The details of these exchange mechanisms are thoroughly discussed in this paper, together with the interplay between three-dimensional small-scale breaking associated with turbulence and the dominant two-dimensional wave motion. A conditional zonal analysis is proposed for the first time to understand the transient mechanisms of turbulent kinetic energy production, decay, diffusion and transport and their dependence and/or impact on surface wrinkling over the entire breaking process. The simulations provide a thorough picture of air–liquid coherent structures that develop over the breaking process, and link them to the transient mechanisms responsible for their local incidence.

JFM classification

Geophysical and Geological Flows: Air/sea interactions Geophysical and Geological Flows: Coastal engineering Waves/Free-surface Flows: Wave breaking
Type
Papers
Information
Journal of Fluid Mechanics , Volume 674 , 10 May 2011 , pp. 522 - 577
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Banner, M. L. & Phillips, O. M. 1974 On the incipient breaking of small scale waves. J. Fluid Mech. 65, 647–656.CrossRefGoogle Scholar
Battjes, J. A. 1975 Surf similarity. In Proc. 14th Coastal Engrg. Conf., ASCE, New York, 466–480.Google Scholar
Battjes, J. A. & Sakai, T. 1981 Velocity field in a steady breaker. J. Fluid Mech. 111, 421–437.CrossRefGoogle Scholar
Botto, L., Narayanan, C., Fulgosi, M. & Lakehal, D. 2005 Effect of near-wall turbulence enhancement on the mechanisms of particle deposition. Intl J. Multiphase Flow 31, 940–956.CrossRefGoogle Scholar
Brackbill, J. U., Kothe, D. B. & Zemach, C. 1992 A continuum method for modeling surface tension. J. Comput. Phys. 100, 335–354.CrossRefGoogle Scholar
Calhoun, R. J. & Street, R. L. 2003 Turbulent flow over a wavy surface: neutral case. J. Geophys. Res. 106, 9277–9293.CrossRefGoogle Scholar
Chang, K. A. & Liu, P. L.-F. 1999 Experimental investigation of turbulence generated by breaking waves in water of intermediate depth. Phys. Fluids 11 (11), 3390–3400.CrossRefGoogle Scholar
Christensen, E. D. 2006 Large eddy simulation of spilling and plunging breakers. Coast. Engng 53 (5–6), 463–485.CrossRefGoogle Scholar
Christensen, E. D. & Deigaard, R. 2001 Large eddy simulation of breaking waves. Coast. Engng 42, 53–86.CrossRefGoogle Scholar
Christensen, E. D., Walstra, D. -J. & Emerat, N. 2002 Vertical variation of the flow across the surf zone. Coast. Engng 45, 169–198.CrossRefGoogle Scholar
Cox, D. T. & Shin, S. 2003 Laboratory measurements of void fraction and turbulence in the bore region of surf zone waves. J. Engng Mech. 129, 1197–1205.Google Scholar
Duncan, J. H. 1996 Spilling breakers. Annu. Rev. Fluid. Mech. 33, 519–547.CrossRefGoogle Scholar
Fadlun, E. A., Verzicco, R., Orlandi, P. & Mohd-Yusof, J. 2000 Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J. Comput. Phys. 161, 35–60.CrossRefGoogle Scholar
Fenton, J. D. 1985 A fifth-order Stokes theory for steady waves. J. Waterway Port Coastal Ocean Engng 111, 216–234.CrossRefGoogle Scholar
Fulgosi, M., Lakehal, D., Banerjee, S. & De Angelis, V. 2003 Direct numerical simulation of turbulence in a sheared air–water flow with a deformable interface. J. Fluid Mech. 482, 319–345.CrossRefGoogle Scholar
Galvin, C. J. 1968 Breaker-type classifications of three laboratory beaches. J. Geophys. Res. 73, 3651–3659.CrossRefGoogle Scholar
Gemmrich, J. R. & Farmer, D. M. 2004 Near-surface turbulence in the presence of breaking waves. J. Phys. Oceanogr. 34, 1067–1086.2.0.CO;2>CrossRefGoogle Scholar
Geurts, B. J. 2002 Buoyant turbulent mixing in shear layers. In Advances in Turbulence IX – Proc. of the Ninth European Turbulence Conference (ed. Castro, I. P. & Hancock, P. E.). CIMNE.Google Scholar
Goring, D. G. 1979 Tsunamis: the propagation of long waves onto a shelf. PhD dissertation, California Institute of Technology.Google Scholar
Hattori, M. & Aono, T. 1985 Experimental study on turbulence structures under breaking waves. Coast. Engng Japan 28, 97–116.CrossRefGoogle Scholar
Jenkins, A. D. 2002 Do strong winds blow waves flat? Proc. WAVES 2001, in Ocean Wave Measurement and Analysis (Edge, B. L. & Hemsley, J. M.), vol. 1, 494–500. American Society of Civil Engineers.Google Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Komori, S., Nagaosa, R., Murakami, Y., Chiba, S., Ishii, K. & Kuwahara, K. 1993 b Direct numerical simulation of three-dimensional open-channel flow with zero-shear gas–liquid interface. Phys. Fluids A 5 (1), 115–125.CrossRefGoogle Scholar
Labourasse, E., Lacanette, D., Toutant, A., Lubin, P., Vincent, S., Lebaigue, O., Caltagirone, J.-P. & Sagaut, P. 2007 Towards large eddy simulation of isothermal two-phase flows: governing equations and a priori tests. Intl J. Multiphase Flow 33, 1–39.CrossRefGoogle Scholar
Lakehal, D., Milelli, M. & Smith, B. L. 2002 Large-eddy simulation of bubbly turbulent shear flows. J. Turbul. 3, 1–21.CrossRefGoogle Scholar
Lakehal, D., Reboux, S. & Liovic, P. 2006 SGS modelling for the LES of interfacial gas–liquid flows. La Houille Blanche 6, 125–131.Google Scholar
Lam, K. & Banerjee, S. 1992 On the condition of streaks formation in a bounded turbulent flow. Phys. Fluids A 4 (2), 306–320.CrossRefGoogle Scholar
Lamarre, E. & Melville, W. K. 1991 Air entrainment and dissipation in breaking waves. Nature 351, 469–472.CrossRefGoogle Scholar
Lemmin, U., Scott, J. T. & Czapski, U. H. 1974 The development from two-dimensional to three-dimensional turbulence generated by breaking waves. J. Geophys. Res. 19, 3442–3448.CrossRefGoogle Scholar
Lin, C. & Hwung, H. H. 1992 External and internal flow fields of plunging breakers. Exp. Phys. 12, 229–237.Google Scholar
Lin, M.-Y., Moeng, C.-H., Tsai, W.-T., Sullivan, P. P. & Belcher, S. E. 2008 Direct numerical simulation of wind-wave generation processes. J. Fluid Mech. 616, 1–30.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
Liovic, P. & Lakehal, D. 2007 a Interface–turbulence interactions in large-scale bubbling processes. Intl J. Heat Fluid Flow 28, 127–144.CrossRefGoogle Scholar
Liovic, P. & Lakehal, D. 2007 b Multi-physics treatment in the vicinity of arbitrarily deformable gas–liquid interfaces. J. Comput Phys. 222, 504–535.CrossRefGoogle Scholar
Liovic, P. & Lakehal, D. 2009 Interface–turbulence interactions and bubble dynamics. In Proc. 7th Intl Conf. CFD Mineral Process Industries, CSIRO, Melbourne, 1–6.Google Scholar
Liovic, P., Liow, J.-L. & Rudman, M. 2001 A volume-of-fluid (VOF) method for the simulation of metallurgical flows. ISIJ Intl 41, 225–233.CrossRefGoogle Scholar
Liovic, P., Rudman, M., Liow, J.-L., Lakehal, D. & Kothe, D. B. 2006 A 3D unsplit-advection volume tracking algorithm with planarity-preserving interface reconstruction. Comput. Fluids 35, 1011–1032.CrossRefGoogle Scholar
Lombardi, P., DeAngelis, V. & Banerjee, S. 1996 Direct numerical simulation of near-interface turbulence in coupled gas–liquid flow. Phys. Fluids 8, 1643–1665.CrossRefGoogle Scholar
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), 631–655.CrossRefGoogle Scholar
Melville, W. K. 1996 The role of surface-wave breaking in air–sea interaction. Annu. Rev. Fluid. Mech. 28, 279–321.CrossRefGoogle Scholar
Moum, J. N. & Smyth, W. D. 2001 Upper ocean mixing. In Encyclopedia of Ocean Sciences, vol. 6, 3093–3100. Academic Press.CrossRefGoogle Scholar
Nadaoka, K., Hino, M. & Koyano, Y. 1989 Structure of the turbulent flow field under breaking waves in the surf zone. J. Fluid Mech. 204, 359–387.CrossRefGoogle Scholar
Narayanan, C. & Lakehal, D. 2006 DNS of particle-laden mixing-layers. Part I. One-way coupled flow and dispersed-phase features. Phys. Fluids 18 (9), 093302.CrossRefGoogle Scholar
Peregrine, D. H. 1983 Breaking waves on beaches. Annu. Rev. Fluid. Mech. 15, 149–178.CrossRefGoogle Scholar
Reboux, S., Sagaut, P. & Lakehal, D. 2006 Large-eddy simulation of sheared interfacial two-fluid flow using the variational multiscale approach. Phys. Fluids 18 (10), 105105.CrossRefGoogle Scholar
Roelvink, J. A. & Stive, M. J. F. 1989 Bar-generating corss-shore flows mechanisms on a beach. J. Geophys. Res. 94 (C4), 4785–4800.CrossRefGoogle Scholar
Schlicke, T. 2001 Breaking waves and the dispersion of surface films. PhD thesis, University of Edinburgh.Google Scholar
Smith, E. & Kraus, N. C. 1991 Laboratory study of wave-breaking over bars and artificial reefs. J. Waterway Port Coastal Ocean Engng 117, 307–325.CrossRefGoogle Scholar
Sullivan, P. P. & McWilliams, J. C. 2002 Turbulent flow over water waves in the presence of stratification. Phys. Fluids 14, 1182–1195.CrossRefGoogle Scholar
Sullivan, P. P., McWilliams, J. C. & Melville, W. K. 2004 The oceanic boundary layer driven by wave breaking with stochastic variability. Part 1. Direct numerical simulations. J. Fluid Mech. 507, 143–174.CrossRefGoogle Scholar
Sullivan, P. P., McWilliams, J. C. & Moeng, C. H. 2000 Simulation of turbulent flow over idealized water waves. J. Fluid Mech. 404, 47–85.CrossRefGoogle Scholar
Svendsen, I. A. 1987 Analysis of surf zone turbulence. J. Geophys. Res. 92 (C5), 5115–5124.Google Scholar
Svendsen, I. A. 2006 Introduction to Nearshore Hydrodynamics. Advanced Series on Ocean Engineering, vol. 24. World Scientific.CrossRefGoogle Scholar
Thorpe, S. A. 1993 Energy loss by breaking waves. J. Phys. Oceanogr. 23, 2498–2502.2.0.CO;2>CrossRefGoogle Scholar
Thorpe, S. A. 1995 Dynamical processes at the sea surface. Prog. Oceanogr. 35, 315–352.CrossRefGoogle Scholar
Thorpe, S. A., Osborn, T. R., Jackson, J. F. E., Hall, A. J. & Lueck, R. G. 2003 Measurements of turbulence in the upper-ocean mixing layer using Autosub. J. Phys. Oceanogr. 33, 122–145.2.0.CO;2>CrossRefGoogle Scholar
Ting, F. C. K. 2001 Laboratory study of wave and turbulence velocities in a broad-banded irregular wave surf zone. Coast. Engng 43, 183–208.CrossRefGoogle Scholar
Ting, F. C. K. & Kirby, J. T. 1994 Observations of undertow and turbulence in a laboratory surf zone. Coast. Engng 24, 51–80.CrossRefGoogle Scholar
Ting, F. C. K. & Kirby, J. T. 1995 Dynamics of surf-zone turbulence in a strong plunging breaker. Coast. Engng 24, 177–204.CrossRefGoogle Scholar
Ting, F. C. K. & Kirby, J. T. 1996 Dynamics of surf-zone turbulence in a spilling breaker. Coast. Engng 27, 131–160.CrossRefGoogle Scholar
Tsai, C.-P, Chen, H.-B., Hwung, H.-H., & Huang, M.-J. 2005 Examination of empirical formulas for wave shoaling and breaking on steep slopes. Ocean Engng 32, 469–483.CrossRefGoogle Scholar
Watanabe, Y. & Saeki, H. 1999 Three-dimensional large eddy simulation of breaking waves. Coast. Engng 41, 281–301.CrossRefGoogle Scholar
Watanabe, Y., Saeki, H. & Hosking, R. J. 2005 Three-dimensional vortex structures under breaking waves. J. Fluid Mech. 545, 291–328.CrossRefGoogle Scholar
Zhao, Q., Armfield, S. & Tanimoto, K. 2004 Numerical simulation of breaking waves by a multi-scale turbulence model. Coast. Engng 51, 53–80.CrossRefGoogle Scholar