Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-14T16:49:55.578Z Has data issue: false hasContentIssue false
  • English
  • Français

On the microphysical behaviour of wind-forced water surfaces and consequent re-aeration

Published online by Cambridge University Press:  05 March 2014

William L. Peirson ,
James W. Walker  and
Michael L. Banner
William L. Peirson*
Affiliation:
Water Research Laboratory, School of Civil and Environmental Engineering, University of New South Wales, King St, Manly Vale, NSW 2093, Australia
James W. Walker
Affiliation:
Water Research Laboratory, School of Civil and Environmental Engineering, University of New South Wales, King St, Manly Vale, NSW 2093, Australia
Michael L. Banner
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
*
†Email address for correspondence: w.peirson@unsw.edu.au
Get access Rights & Permissions [Opens in a new window]

Abstract

A detailed laboratory investigation of the mechanical and low-solubility gas coupling between wind and water has been undertaken using a suite of microphysical measurement techniques. Under a variety of wind conditions and in the presence and absence of mechanically generated short waves, approximately fetch-independent surface conditions have been achieved over short laboratory fetches of several metres. The mechanical coupling of the surface is found to be consistent with Banner (J. Fluid Mech. vol. 211, 1990, pp. 463–495) and Banner & Peirson (J. Fluid Mech. vol. 364, 1998, pp. 115–145). Bulk observations of re-aeration are consistent with previous laboratory studies. The surface kinematical behaviour is in accordance with the observations of Peirson & Banner (J. Fluid Mech. vol. 479, 2003, pp. 1–38). Also, their predictions of a strong enhancement of low-solubility gas flux at the onset of microscale breaking is confirmed and direct observations show a concomitant onset of very thin aqueous diffusion sublayers. It is found that the development of strong parasitic capillary waves towards the incipient breaking limit does not noticeably enhance constituent transfer. Across the broad range of conditions investigated during this study, the local instantaneous constituent transfer rate remains approximately log-normally distributed with an approximately constant standard deviation of $0.62\pm 0.15({\mathrm{log}}_e(\mathrm{m}~ {\mathrm{s}}^{-1}))$. Although wind-forced water surfaces are shown to be punctuated by intense tangential stresses and local surface convergence, localized surface convergence does not appear to be the single critical factor determining exchange rate. Larger-scale orbital wave straining is found to be a significant constituent transfer process in contrast to Witting (J. Fluid Mech. vol. 50, 1971, pp. 321–334) findings for heat fluxes, but the measured effects are consistent with his model. By comparing transfer rates in the presence and absence of microscale breaking, low-solubility gas transfer was decomposed into its turbulent/capillary ripple, gravity-wave-related and microscale breaking contributions. It was found that an efficiency factor of approximately $17\, \%$ needs to be applied to Peirson & Banner’s model, which is extended to field conditions. Although bulk thermal effects were observed and thermal diffusion layers are presumed thicker than their mass diffusion counterparts, significant thermal influences were not observed in the results.

JFM classification

Geophysical and Geological Flows: Air/sea interactions Waves/Free-surface Flows: Wind-wave interactions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 743 , 25 March 2014 , pp. 399 - 447
Copyright
© 2014 Cambridge University Press 

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.)

Footnotes

‡

Present address: Sogreah Gulf – Artelia Group, PO Box 18271, Dubai, UAE.

References

APHA 1980 Standard Methods for the Examination of Water and Wastewater, 15th Edn. (ed. A. E. Greenberg, J. J. Connors, D. Jenkins) APHA-AWWA-WPCF.Google Scholar
ASCE 1984 Standard Measurement of Oxygen Transfer in Clean Water (ed. W. C. Boyle). ASCE.Google Scholar
Asher, W., Edson, J., McGillis, W. R., Wanninkhof, R., Ho, D. T. & Litchendorf, T. 2002 Fractional area whitecap coverage and air-sea gas transfer velocities measured during gasex-98. In Gas Transfer at Water Surfaces (ed. Donelan, M. A., Drennan, W. M., Saltzman, E. S. & Wanninkhof, R.), Geophys. Monogr. 127, pp. 199–203. AGU.Google Scholar
Banerjee, S., Lakehal, D. & Fulgosi, M. 2004 Surface divergence models for scalar exchange between turbulent streams. Int. J. Multiphase Flow 30 (7-8), 963–977.Google Scholar
Banner, M. L. 1990 The influence of wave breaking on the surface pressure distribution in wind-wave interactions. J. Fluid Mech. 211, 463–495.Google Scholar
Banner, M. L. & Peirson, W. L. 1998 Tangential stress beneath wind-driven air-water interfaces. J. Fluid Mech. 364, 115–145.Google Scholar
Banner, M. L. & Phillips, O. M. 1974 On small scale breaking waves. J. Fluid Mech. 65, 647–657.Google Scholar
Brocchini, M. & Peregrine, D. H. 2001 The dynamics of strong turbulence at free surfaces. Part 1. Description. J. Fluid Mech. 449, 225–254.Google Scholar
Cheung, T. K. & Street, R. L. 1988 The turbulent layer in the water at an air-water interface. J. Fluid Mech. 194, 133–151.CrossRefGoogle Scholar
Clymo, R. S. & Gregory, S. P. 1975 Two cheap, temperature stable battery operated devices producing a current linearly proportional to capacitance or resistance. J. Appl. Ecol. 12, 577–586.CrossRefGoogle Scholar
Coantic, M. 1986 A model of gas transfer across air-water interfaces with capillary waves. J. Geophys. Res. 91, 3,925–3,943.Google Scholar
Crapper, G. D. 1957 An exact solution for progressive capillary waves of arbitrary amplitude. J. Fluid Mech. 2, 532–540.CrossRefGoogle Scholar
CRC 2005 Handbook of Chemistry and Physics, 85th edn (ed. D. R. Lide). CRC.Google Scholar
Csanady, G.T. 1990 The role of breaking wavelets in air-sea gas transfer. J. Geophys. Res. 95, 749–759.Google Scholar
Danckwerts, P. V. 1951 Significance of liquid-film coefficients in gas absorption. Ind. Engng Chem. 43, 1460–1467.Google Scholar
Daniil, E. I. & Gulliver, J. S. 1988 Temperature dependence of liquid film coefficient for gas transfer. J. Environ. Engng 114, 1224–1229.Google Scholar
Deacon, E. L. 1977 Gas transfer to and across an air-water interface. Tellus 29, 363–374.Google Scholar
Deacon, E. L. 1981 Sea-air gas transfer: the wind speed dependence. Boundary-Layer Meteorol. 21, 31–37.CrossRefGoogle Scholar
Diorio, J. D., Liu, X. & Duncan, J. H. 2009 An experimental investigation of incipient spilling breakers. J. Fluid Mech. 633, 271–283.Google Scholar
Donelan, M. A. 1978 Whitecaps and momentum transfer. In Turbulent Fluxes through the Sea Surface, Wave Dynamics and Prediction (ed. Favre, A. & Hasselmann, K.), Plenum.Google Scholar
Donelan, M. A. 1990 Air-sea interaction. Ocean Engng Sci. 9, 239–292.Google Scholar
Donelan, M. A. & Wanninkhof, R. 2002 Gas transfer at water surfaces – concepts and issues. In Gas Transfer at Water Surfaces (ed. Donelan, M. A., Drennan, W. M., Saltzman, E. S. & Wanninkhof, R.), Geophys. Monogr. 127, pp. 1–10.Google Scholar
Downing, A. L. & Truesdale, G. A. 1955 Some factors affecting the rate of solution of oxygen in water. J. Appl. Chem. 5, 570–581.CrossRefGoogle Scholar
Duncan, J. H., Qiao, H., Philomin, V. & Wenz, A. 1999 Gentle spilling breakers: crest profile evolution. J. Fluid Mech. 379, 191–222.Google Scholar
Gemmrich, J. 2010 Strong turbulence in the wave crest region. J. Phys. Oceanogr. 40, 583–595.Google Scholar
Gemmrich, J. R., Banner, M. L. & Garrett, C. 2008 Spectrally resolved energy dissipation rate and momentum flux of breaking waves. J. Phys. Oceanogr. 38, 1296–1312.Google Scholar
Higbie, R. 1935 The rate of absorption of a pure gas into a still liquid during short periods of exposure. Trans. Am. Inst. Chem. Engrs 31, 365–389.Google Scholar
Hoover, T. E. & Berkshire, D. C. 1969 Effects of hydration on carbon dioxide exchange across an air-water interface. J. Geophys. Res. 74, 456–464.Google Scholar
Hung, L.-P. & Tsai, W.-T. 2009 The formation of parasitic capillary ripples on gravity–capillary waves and the underlying vortical structures. J. Phys. Oceanogr. 39, 263–289.Google Scholar
Jähne, B. & Haußecker, H. 1998 Air-water gas exchange. Annu. Rev. Fluid Mech. 30, 444–468.Google Scholar
Jähne, B., Munnich, K. O., Bosinger, R., Dutzi, A., Huber, W. & Libner, P. 1987 On the parameters influencing air-water gas exchange. J. Geophys. Res. 92, 1937–1949.Google Scholar
Jessup, A. T. 1996 The infrared signature of breaking waves. In The Air-Sea Interface: Radio and Acoustic Sensing, Turbulence and Wave Dynamics (ed. Donelan, M. A., Hui, W. H. & Plant, W. J.), Rosenstiel School of Marine and Atmospheric Science, University of Miami.Google Scholar
Jessup, A. T. & Phadnis, K. R. 2005 Measurement of the geometric and kinematic properties of microscale breaking waves from infrared imagery using a PIV algorithm. Meas. Sci. Technol. 16, 1961–1969.Google Scholar
Jessup, A. T. & Zappa, C. J. 1997 Defining and quantifying microscale wave breaking with infrared imagery. J. Geophys. Res. 102 (C10), 23145–23153.CrossRefGoogle Scholar
Jirka, G. H. & Ho, A. H. W. 1990 Measurements of gas concentration fluctuations at a water surface. J. Hydraul. Engng. 116, 835–847.Google Scholar
Kawamura, H., Okuda, K., Kawai, S. & Toba, Y. 1981 Structure of turbulent boundary layer over wind waves in a wind tunnel. Tohoku Geophys. J. 28, 69–86.Google Scholar
Kleiss, J. M. & Melville, W. K. 2010 Observations of wave-breaking kinematics in fetch-limited seas. J. Phys. Oceanogr. 40, 2575–2604.Google Scholar
Komori, S., Nagaoa, R. & Murakami, Y. 1993 Turbulence structure and mass transfer across a sheared air-water interface in wind-driven turbulence. J. Fluid Mech. 249, 161–183.Google Scholar
Ledwell, J. J. 1984 The variation of the gas transfer coefficient with molecular diffusivity. In Gas Transfer at Water Surfaces (ed. Brutsaert, W. & Jirka, G. H.), pp. 293–302. Springer.CrossRefGoogle Scholar
Lewis, W. K. & Whitman, W. G. 1924 Principles of gas absorption. Ind. Engng Chem. 16, 1215–1220.Google Scholar
Liss, P. S. 1973 Processes of gas exchange across an air-water interface. Deep-Sea Res. 20, 221–238.Google Scholar
Liss, P. S. & Merlivat, L. 1986 Air-sea gas exchange rates: introduction and synthesis. In The Role of Air-Sea Exchange in Geo-chemical Cycling (ed. Buat-Menard, P.), pp. 113–129. Springer.Google Scholar
Longuet-Higgins, M. S. 1953 Mass transport in water waves. Phil. Trans. R. Soc. Lond. A 245, 535–581.Google Scholar
Longuet-Higgins, M. S. 1992 Capillary rollers and bores. J. Fluid Mech. 240, 659–679.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1995 Parasitic capillary waves: a direct calculation. J. Fluid Mech. 301, 79–107.Google Scholar
MacIntyre, F. 1971 Enhancement of gas transfer by interfacial ripples. Phys. Fluids 14, 181–184.Google Scholar
McKenna, S. P. & McGillis, W. R. 2004 The role of free-surface turbulence and surfactants in air-water gas transfer. Int J. Heat Mass Transfer 47 (3), 539–553.CrossRefGoogle Scholar
McCready, M. J., Vassiliadou, E. & Hanratty, T. J. 1986 Computer simulation of turbulent mass transfer at a mobile interface. AIChE Journal 32 (7), 1108–1115.Google Scholar
Melville, W. K. & Matusov, P. 2002 Distribution of breaking waves at the ocean surface. Nature 417, 58–63.Google Scholar
Mitsuyasu, H. 2009 Looking Closely at Ocean Waves: From Their Birth to Death. Terrapub.Google Scholar
Münsterer, T. & Jähne, B. 1998 LIF measurements of concentration profiles in the aqueous mass boundary layer. Exp. Fluids 25, 190–196.CrossRefGoogle Scholar
Peirson, W. L. 1997 Measurement of surface velocities and shears at a wavy air-water interface using particle image velocimetry. Exp. Fluids 23, 427–437.Google Scholar
Peirson, W. L. & Banner, M. L. 2003 Aqueous surface layer flows induced by microscale breaking wind waves. J. Fluid Mech. 479, 1–38.CrossRefGoogle Scholar
Peirson, W. L. & Garcia, A. W. 2008 On the wind-induced growth of slow water waves of finite steepness. J. Fluid Mech. 608, 243–274.Google Scholar
Peirson, W. L., Walker, J. W., Welch, C. H. & Banner, M. L. 2007 Defining the enhancement of air-water interfacial oxygen exchange rate due to wind-forced microscale waves. In Transport at the Air Sea Interface – Measurements, Models and Parameterizations (ed. Garbe, C. S., Handler, R. A. & Jähne, B.), Springer.Google Scholar
Phillips, O. M. 1985 Spectral and statistical properties of the equilibrium range in wind-generated gravity-waves. J. Fluid Mech. 156, 505–531.Google Scholar
Qiao, H. & Duncan, J. H. 2001 Gentle spilling breakers: crest flow-field evolution. J. Fluid Mech. 439, 57–85.Google Scholar
Saylor, J. R. & Handler, R. A. 1999 Capillary wave gas exchange in the presence of surfactants. Exp. Fluids 27, 332–338.Google Scholar
Scriven, L. E. & Pigford, R. L. 1958 On phase equilibrium at the gas-liquid interface during absorption. AIChE J. 4, 439–444.Google Scholar
Siddiqui, M. K. H. & Loewen, M. R. 2007 Characteristics of the wind drift layer and microscale breaking waves. J. Fluid Mech. 573, 417–456.Google Scholar
Skjelbreia, L. & Hendrickson, J. 1961 Fifth order gravity wave theory. In Proc. 7th Int. Conf. Coastal Engng pp. 184–196. ASCE.Google Scholar
Szeri, A. J. 1997 Capillary waves and air-sea gas transfer. J. Fluid Mech. 332, 341–358.Google Scholar
Takehara, K. & Etoh, G. T. 2002 A direct visualization method for $\mathrm{CO}_2$ gas transfer at water surface driven by wind waves. In Gas Transfer at Water Surfaces (ed. Donelan, M. A., Drennan, W. M., Saltzman, E. S. & Wanninkhof, R.), Geophys. Monogr. 127, pp. 89–95.Google Scholar
Thorpe, S. A. 2005 The Turbulent Ocean. Cambridge University Press.Google Scholar
Toba, Y. & Kawamura, H. 1996 Wind-wave coupled downward-bursting boundary layer beneath the sea surface. J. Phys. Oceanogr. 52, 409–419.Google Scholar
Tsai, W.-T. & Hung, L.-P. 2011 Characteristics of gas-flux density distribution at the water surfaces. In Gas Transfer at Water Surfaces (ed. Komori, S. & McGillis, W.), Kyoto University Press, (in press).Google Scholar
Turney, D. E., Smith, W. C. & Banerjee, S. 2005 A measure of near-surface fluid motions that predicts air-water gas transfer in a wide range of conditions. Geophys. Res. Let. 32, L04607.Google Scholar
Veron, F., Melville, W.K. & Lenain, L. 2008 Wave-coherent air-sea heat flux. J. Phys. Oceanogr. 38, 788–802.Google Scholar
Veron, F., Saxena, G. & Misra, S. K. 2007 Measurements of the viscous tangential stress in the airflow above wind waves. Geophys. Res. Lett. 34, L19603.Google Scholar
Walker, J. W.2009 The exchange of oxygen at the surface of open waters under wind forcing. PhD thesis. School of Civil and Environmental Engineering, The University of New South Wales.Google Scholar
Walker, J. W. & Peirson, W. L. 2008 Measurement of gas transfer across wind-forced wavy air-water interfaces using laser-induced fluorescence. Exp. Fluids 44, 249–259.Google Scholar
Wanninkhof, R. 1992 Relationship between gas exchange and wind speed over the ocean. J. Geophys. Res. 97, 7373–7381.Google Scholar
Wanninkhof, R., Asher, W. E., Ho, David T., Sweeney, Colm & Wade R., McGillis 2009 Advances in quantifying air-sea gas exchange and environmental forcing. Annu. Rev. Mar. Sci. 1, 213–244.Google Scholar
Wanninkhof, R. H. & Bliven, L. F. 1991 Relationship between gas exchange, wind speed, and radar backscattar in a large wind wave tank. J. Geophys. Res. 96, 2785–2796.Google Scholar
Wanninkhof, R. & McGillis, W. R. 1999 A cubic relationship between gas transfer and wind speed. Geophys. Res. Lett. 26, 1889–1892.Google Scholar
Witting, J. 1971 Effects of plane progressive irrotational waves on thermal boundary layers. J. Fluid Mech. 50, 321–334.Google Scholar
Wolff, L. M. & Hanratty, T. J. 1994 Instantaneous concentration profiles of oxygen absorption in a stratified flow. Exp. Fluids 16, 385–392.Google Scholar
Woodrow, P. T. & Duke, S. R. 2001 Laser-induced fluorescence studies of oxygen transfer across unsheared flat and wavy air-water interfaces. Ind. Engng Chem. Res. 40, 1985–1995.Google Scholar
Yan, X., Peirson, W. L., Walker, J. W. & Banner, M. L. 2011 On transitions in the Schmidt number dependency of low solubility gas transfer across air-water interfaces. In Gas Transfer at Water Surfaces (ed. Komori, S. & McGillis, W.), pp. 355–365. Kyoto University Press.Google Scholar
Zappa, C. J., Asher, W. E. & Jessup, A. T. 2001 Microscale wave breaking and air-water gas transfer. J. Geophys. Res. 106 (C05), 9385–9391.Google Scholar
Zappa, C. J., Asher, W. E., Jessup, A. T., Klinke, J. & Long, S. R. 2004 Microbreaking and the enhancement of air-water transfer velocity. J. Geophys. Res. 109, C08S16.Google Scholar