Skip to main content Accessibility help
×
Home

Experiments on free-surface turbulence

  • RALPH SAVELSBERG (a1) and WILLEM VAN DE WATER (a1)

Abstract

We study the free surface of a turbulent flow, in particular the relation between the statistical properties of the wrinkled surface and those of the velocity field beneath it. Channel flow turbulence is generated using an active grid. Through a judicial choice of the stirring protocol the anisotropy of the subsurface turbulence can be controlled. The largest Taylor Reynolds number obtained is Reλ = 258. We characterize the homogeneity and isotropy of the flow and discuss Taylor's frozen turbulence hypothesis, which applies to the subsurface turbulence but not to the surface. The surface gradient field is measured using a novel laser-scanning device. Simultaneously, the velocity field in planes just below the surface is measured using particle image velocimetry (PIV). Several intuitively appealing relations between the surface gradient field and functionals of the subsurface velocity field are tested. For an irregular flow shed off a vertical cylinder, we find that surface indentations are strongly correlated with both vortical and strain events in the velocity field. For fully developed turbulence this correlation is dramatically reduced. This is because the large eddies of the subsurface turbulent flow excite random capillary–gravity waves that travel in all directions across the surface. Therefore, the turbulent surface has dynamics of its own. Nonetheless, it does inherit both the integral scale, which determines the predominant wavelength of the capillary–gravity surface waves, and the (an)isotropy from the subsurface turbulence. The kinematical aspects of the surface–turbulence connection are illustrated by a simple model in which the surface is described in terms of waves originating from Gaussian wave sources that are randomly sprinkled on the moving surface.

Copyright

Corresponding author

Email address for correspondence: w.v.d.water@tue.nl

References

Hide All
Bernal, L. P. & Kwon, J. T. 1989 Vortex ring dynamics at a free surface. Phys. Fluids A 1, 449451.
Borue, V., Orszag, S. A. & Staroslesky, I. 1995 Interaction of surface waves with turbulence: direct numerical simulations of turbulent open channel flow. J. Fluid Mech. 286, 123.
Brocchini, M. & Peregrine, D. H. 2001 a The dynamics of strong turbulence at free surfaces. Part 1. Description. J. Fluid Mech. 449, 225254.
Brocchini, M. & Peregrine, D. H. 2001 b The dynamics of strong turbulence at free surfaces. Part 2. Free-surface boundary conditions. J. Fluid Mech. 449, 255290.
Brumley, B. H. & Jirka, G. H. 1987 Near-surface turbulence in a grid-stirred tank. J. Fluid Mech. 183, 235263.
Calmet, I. & Magnaudet, J. 2003 Statistical structure of high-Reynolds-number turbulence close to the free surface of an open-channel flow. J. Fluid Mech. 474, 355378.
Comte-Bellot, G. & Corrsin, S. 1966 The use of a contraction to improve the isotropy of grid-generated turbulence. J. Fluid Mech. 25, 657682.
Cressman, J. R., Davoudi, J., Goldburg, W. I. & Schumacher, J. 2004 Eulerian and lagrangian studies in surface flow turbulence. New J. Phys. 6, 53, doi: 10.1088/1367-2630/6/1/053.
Dabiri, D. 2003 On the interaction of a vertical shear layer with a free surface. J. Fluid Mech. 480, 217232.
Dabiri, D. & Gharib, M. 2001 Simultaneous free surface deformation and near surface velocity measurements. Exp. Fluids 30, 381390.
Forbes, C., Leman, K., Olson, D. & Brown, O. 1993 Eddy and wave dynamics in the south Atlantic as diagnosed from geosat altimeter data. J. Geophys. Res. 12, 297314.
Gharib, M. & Weigand, A. 1996 Experimental studies of vortex disconnection and surface connection at a free surface. J. Fluid Mech. 321, 5986.
Gledzer, E. 1997 On the Taylor hypothesis corrections for measured energy spectra of turbulence. Physica D 104 (2), 163183.
Handler, R. A., Swean, T. F., Leighton, R. I. & Swearingen, J. D. 1993 Length scales and the energy balance for turbulence near a free surface. AIAA J. 31, 19982007.
Hong, W.-L. & Walker, D. T. 2000 Reynolds-averaged equations for free-surface flows with application to high-Froude-number jet spreading. J. Fluid Mech. 417, 183209.
Hunt, J. C. R. 1984 Turbulence structure and turbulent diffusion near gas-liquid interfaces. In Gas Transfer at Water Surfaces (ed. Brutsaert, W. & Jirka, G. H.), pp. 6782. Reidel.
Hunt, J. C. R. & Graham, J. M. R. 1978 Free-stream turbulence near plane boundaries. J. Fluid Mech. 84, 209235.
Komori, S., Nagaosa, R. & Murakami, Y. 1990 Mass transfer into a turbulent liquid across the zero-shear gas–liquid interface. AIChE J. 36, 957960.
Kumar, S., Gupta, R. & Banerjee, S. 1998 An experimental investigation of the characteristics of free-surface turbulence in channel flow. Phys. Fluids 10, 437456.
Li, F.-C., Kawaguchi, Y., Segawa, T. & Suga, K. 2005 Wave-turbulence interaction of a low-speed plane liquid wall-jet investigated by particle image velocimetry. Phys. Fluids 17, 082101.
Loewen, S., Ahlborn, B. & Filuk, A. B. 1986 Statistics of surface flow structures on decaying grid turbulence. Phys. Fluids 29, 23882397.
Magnaudet, J. 2003 High-Reynolds-number turbulence in a shear-free boundary layer: revisting the Hunt–Graham theory. J. Fluid Mech. 484, 167196.
Makita, H. 1991 Realization of a large scale turbulence field in a small wind tunnel. Fluid Dyn. Res. 8, 5364.
Mydlarski, L. & Warhaft, Z. 1990 On the onset of high-Reynolds-number grid-generated wind tunnel turbulence. J. Fluid Mech. 320, 331368.
Nagaosa, R. 1999 Direct numerical simulation of vortex structures and turbulent scalar transfer across a free surface in a fully developed turbulence. Phys. Fluids 11, 15811595.
Nagaosa, R. & Handler, R. A. 2003 Statistical analysis of coherent vortices near a free surface in a fully developed turbulence. Phys. Fluids 15, 375394.
Pan, Y. & Banerjee, S. 1995 A numerical study of free-surface turbulence in channel flow. Phys. Fluids 7, 12881290.
Pearson, B. R., Krogstad, P.-Å. & van de Water, W. 2002 Measurements of the turbulent energy dissipation rate. Phys. Fluids 14, 12881290.
Perot, B. & Moin, P. 1995 Shear-free turbulent boundary layers. Part 1. Physical insights into near-wall turbulence. J. Fluid Mech. 295, 199227.
Phillips, O. M. 1957 On the generation of waves by turbulent wind. J. Fluid Mech. 2, 417445.
Poorte, R. E. G. 1998 On the motion of bubbles in active grid generated turbulent flows. PhD thesis, University Twente, Enschede, The Netherlands.
Poorte, R. E. G. & Biesheuvel, A. 2002 Experiments on the motion of gas bubbles in turbulence generated by an active grid. J. Fluid Mech. 461, 127154.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Rashidi, M. & Banerjee, S. 1988 Turbulence structure in open channel flows. Phys. Fluids 31, 24912503.
Savelsberg, R., Holten, A. P. C. & van de Water, W. 2006 Measurement of the gradient field of a turbulent free surface. Exp. Fluids 41, 629640.
Shen, L., Zhang, X., Yue, D. K. P. & Triantafyllou, G. S. 1999 The surface layer for free-surface turbulent flows. J. Fluid Mech. 386, 167212.
Smolentsev, S. & Miraghaie, R. 2005 Study of a free surface in open-channel water flows in the regime from ‘weak’ to ‘strong’ turbulence. Intl J. Multiphase flow 31, 921939.
Song, M., Bernal, L. P. & Tryggvason, G. 1992 Head-on collision of a large vortex ring with a free surface. Phys. Fluids A 4, 14571466.
Stammer, D. 1997 Global characteristics of ocean variability from regional topex/poseidon altimeter measurements. J. Phys. Oceanogr. 27, 17431769.
Taylor, G. I. 1960 On the dissipation of eddies. In The Scientific Papers of Sir Geoffrey Ingram Taylor, Volume 2: Meteorology, Oceanography and Turbulent Flow (ed. Batchelor, G. K.). Cambridge University Press. pp. 96101.
Teixeira, M. A. C. & Belcher, S. E. 2000 Dissipation of shear-free turbulence near boundaries. J. Fluid Mech. 422, 167191.
Teixeira, M. A. C. & Belcher, S. E. 2006 On the initiation of surface waves by turbulent shear flow. Dyn. Atmos. Oceans 41, 127.
Thomas, N. H. & Hancock, P. E. 1977 Grid turbulence near a moving wall. J. Fluid Mech. 82, 481496.
Tsai, W.-T. 1998 A numerical study of the evolution and structure of a turbulent shear layer under a free surface. J. Fluid Mech. 354, 239276.
Variano, E. A., Bodenschatz, E. & Cowen, E. A. 2004 A random synthetic jet array driven turbulence tank. Exp. Fluids 37, 613615.
Walker, D. T., Leighton, R. I. & Garza-Rios, L. O. 1996 Shear-free turbulence near a flat free surface. J. Fluid Mech. 320, 1951.
Weigand, A. 1996 Simultaneous mapping of the velocity and deformation field at a free surface. Exp. Fluids 20, 358364.
Zakharov, V., L'Vov, V. & Falkovich, G. 1992 Kolmogorov Spectra of Turbulence. Springer.
Zhang, C., Shen, L. & Yue, D. K. P 1999 The mechanism of vortex connection at a free surface. J. Fluid Mech. 384, 207241.
Zhang, X. 1995 Capillary–gravity and capillary waves generated in a wind wave tank: observations and theories. J. Fluid Mech. 289, 5182.
Zhang, X. & Cox, C. S. 1994 Measuring the two-dimensional structure of a wavy water surface optically: a surface gradient detector. Exp. Fluids 17, 225237.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Experiments on free-surface turbulence

  • RALPH SAVELSBERG (a1) and WILLEM VAN DE WATER (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed