Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-18T22:16:36.969Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulence and mixing in unsteady breaking surface waves

Published online by Cambridge University Press:  01 June 2009

DAVID A. DRAZEN  and
W. KENDALL MELVILLE
DAVID A. DRAZEN*
Affiliation:
Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093-0213, USA
W. KENDALL MELVILLE
Affiliation:
Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093-0213, USA
*
†Present address: Naval Surface Warfare Center, Carderock Division, 9500 MacArthur Blvd, West Bethesda, MD 20817, USA. Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Laboratory measurements of the post-breaking velocity field due to unsteady deep-water breaking are presented. Digital particle image velocimetry (DPIV) is used to measure the entire post-breaking turbulent cloud with high-resolution imagery permitting the measurement of scales from O(1m) down to O(1mm). Ensemble-averaged quantities including mean velocity, turbulent kinetic energy (TKE) density and Reynolds stress are presented and compare favourably with the results of Melville, Veron & White (J. Fluid Mech., vol. 454, 2002, pp. 203–233; MVW). However, due to limited resolution, MVW's measurements were not spatially coherent across the turbulent cloud, and this restricted their ability to compute turbulent wavenumber spectra. Statistical spatial quantities including the integral length scale L11, Taylor microscale λf and the Taylor microscale Reynolds number Reλ are presented. Estimation of an eddy viscosity for the breaking event is also given based on analysis of the image data. Turbulent wavenumber spectra are computed and within 12 wave periods after breaking exhibit what have been termed ‘spectral bumps’ in the turbulence literature. These local maxima in the spectra are thought to be caused by an imbalance between the transport of energy from large scales and the dissipation at small scales. Estimates of the dissipation rate per unit mass are computed using both direct and indirect methods. Horizontally averaged terms in the TKE budget are also presented up to 27 wave periods after breaking and are discussed with regard to the dynamics of the post-breaking flow. Comparisons of the TKE density in the streamwise and cross-stream planes with the three-dimensional full TKE density are given in an appendix.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 628 , 10 June 2009 , pp. 85 - 119
Copyright
Copyright © Cambridge University Press 2009

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. & Peregrine, D. H. 1993 Wave breaking in deep water. Annu. Rev. Fluid Mech. 25, 373–397.CrossRefGoogle Scholar
Battjes, J. A. & Sakai, T. 1981 Velocity field in a steady breaker. J. Fluid Mech. 111, 421–437.CrossRefGoogle Scholar
Bonmarin, P. J. 1989 Geometric properties of deep-water breaking waves. J. Fluid Mech. 209, 405–433.CrossRefGoogle Scholar
Chang, K.-A. & Liu, P. L.-F. 1998 Velocity, acceleration, and vorticity under a breaking wave. Phys. Fluids 10, 327–329.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, 3390–3400.CrossRefGoogle Scholar
Chang, K.-A. & Liu, P. L.-F. 2000 Psuedo turbulence in PIV breaking-wave measurements. Exp. Fluids 29, 331–338.CrossRefGoogle Scholar
Chen, G., Kharif, C., Zaleski, S. & Li, J. 1999 Two-dimensional Navier–Stokes simulation of breaking waves. Phys. Fluids 11, 121–133.CrossRefGoogle Scholar
Doron, P., Bertuccioli, L., Katz, J. & Osborn, T. R. 2001 Turbulence characteristics and dissipation estimates in the coastal ocean bottom boundary layer from PIV data. J. Phys. Oceanogr. 31, 2108–2131.Google Scholar
Drazen, D. A. 2006 Laboratory studies of nonlinear and breaking surface waves. PhD thesis, University of California, San Diego.Google Scholar
Drazen, D. A., Melville, W. K. & Lenain, L. 2008 Inertial estimates of dissipation in unsteady breaking waves. J. Fluid Mech. 611, 307–332.CrossRefGoogle Scholar
Duncan, J. H. 1981 An experimental investigation of breaking waves produced by a towed hydrofoil. Proc. R. Soc. Lond. A 377, 331–348.Google Scholar
Duncan, J. H. 1983 The breaking and non-breaking wave resistance of a two-dimensional hydrofoil. J. Fluid Mech. 126, 507–520.CrossRefGoogle Scholar
Duncan, J. H. 2001 Spilling breakers. Annu. Rev. Fluid Mech. 33, 519–547.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
Gonzalez, R. C. & Woods, R. E. 2002 Digital Image Processing, 2nd ed. Prentice Hall.Google Scholar
Lamarre, E. 1993 An experimental study of air entrainment by breaking waves. PhD thesis, MIT–Woods Hole Oceanographic Institution.CrossRefGoogle Scholar
Lamarre, E. & Melville, W. K. 1991 Air entrainment and dissipation in breaking waves. Nature 351, 469–472.CrossRefGoogle Scholar
Lin, J. C. & Rockwell, D. 1995 Evolution of a quasi-steady breaking wave. J. Fluid Mech. 302, 29–44.CrossRefGoogle Scholar
Loewen, M. R. 1991 Laboratory measurements of the sound generated by breaking waves. PhD thesis, MIT–Woods Hole Oceanographic Institution.CrossRefGoogle Scholar
Loewen, M. R. & Melville, W. K. 1991 Microwave backscatter and acoustic radiation from breaking waves. J. Fluid Mech. 224, 601–623.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1974 Breaking waves – in deep or shallow water. In Proceedings of the 10th Symposium on Naval Hydrodynamics (ed. Cooper, R. D. & Doroff, S. D.), pp. 597–605. Office of Naval Research.Google Scholar
Melville, W. K. 1996 The role of surface-wave breaking in air–sea interaction. Annu. Rev. Fluid Mech. 28, 279–321.CrossRefGoogle Scholar
Melville, W. K., Veron, F. & White, C. 2002 The velocity field under breaking waves: coherent structures and turbulence. J. Fluid Mech. 454, 203–233.CrossRefGoogle Scholar
Nimmo Smith, W. A. M., Katz, J. & Osborn, T. 2005 On the structure of turbulence in the bottom boundary layer of the coastal ocean. J. Phys. Oceanogr. 35, 72–93.CrossRefGoogle Scholar
Perlin, M., He, J. & Bernal, L. P. 1996 An experimental study of deep water plunging breakers. Phys. Fluids 8 (9), 2365–2374.CrossRefGoogle Scholar
Phillips, O. M. 1985 Spectral and statistical properties of the equilibrium range in wind-generated gravity waves. J. Fluid Mech. 156, 505–531.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Raffel, M., Willert, C. & Kompenhans, J. 1998 Particle Image Velocimetry. Springer.CrossRefGoogle Scholar
Rapp, R. J. & Melville, W. K. 1990 Laboratory measurements of deep-water breaking waves. Phil. Trans. R. Soc. Lond. A 331, 735–800.Google Scholar
Saddoughi, S. G. & Veeravalli, S. V. 1994 Local isotropy in turbulent boundary layers at high Reynolds number. J. Fluid Mech. 268, 333–372.CrossRefGoogle Scholar
Sreenivasan, K. R. 1995 On the universality of the Kolmogorov constant. Phys. Fluids 7 (11), 2778–2784.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. & Melville, W. K. 2007 Surface gravity wave effects in the oceanic boundary layer: large-eddy simulation with vortex force and stochastic breakers. J. Fluid Mech. 593, 405–452.CrossRefGoogle Scholar
Svendsen, I. A. 1987 Analysis of surf zone turbulence. J. Geophys. Res. 92 (C5), 5115–5130.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.CrossRefGoogle Scholar
Veron, F. & Melville, W. K. 1999 Pulse-to-pulse coherent doppler measurements of waves and turbulence. J. Atmos. Ocean. Technol. 16, 1580–1597.2.0.CO;2>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
Willert, C. E. 1997 Stereoscopic digital particle image velocimetry for application in wind tunnel flows. Meas. Sci. Technol. 8, 1465–1479.CrossRefGoogle Scholar