Hostname: page-component-84b7d79bbc-7nlkj Total loading time: 0 Render date: 2024-07-28T23:03:51.205Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent transport of a high-Schmidt-number scalar near an air–water interface

Published online by Cambridge University Press:  14 August 2013

Evan A. Variano  and
Edwin A. Cowen
Evan A. Variano*
Affiliation:
UC Berkeley, Civil and Environmental Engineering, Berkeley, CA 94720, USA
Edwin A. Cowen
Affiliation:
Cornell University, Civil and Environmental Engineering, 220 Hollister Hall, Ithaca, NY 14850, USA
*
†Email address for correspondence: variano@ce.berkeley.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We measure solute transport near a turbulent air–water interface at which there is zero mean shear. The interface is stirred by high-Reynolds-number homogeneous isotropic turbulence generated far below the surface, and solute transport into the water is driven by an imposed concentration gradient. The air–water interface is held at a constant concentration much higher than that in the bulk of the water by maintaining pure ${\mathrm{CO} }_{2} $ gas above a water tank that has been initially purged of dissolved ${\mathrm{CO} }_{2} $. We measure velocity and concentration fluctuations below the air–water interface, from the viscous sublayer to the middle of the ‘source region’ where the effects of the surface are first felt. Our laboratory measurement technique uses quantitative imaging to collect simultaneous concentration and velocity fields, which are measured at a resolution that reveals the dynamics in the turbulent inertial subrange. Two-point statistics reveal the spatial structure of velocity and concentration fluctuations, and are examined as a function of depth beneath the air–water interface. There is a clear dominance of large scales at all depths for all quantities, but the relative importance of scales changes markedly with proximity to the interface. Quadrant analysis of the turbulent scalar flux shows a four-way balance of flux components far from the interface, which near the interface evolves into a two-way balance between motions that are raising and lowering parcels of low-concentration fluid.

JFM classification

Geophysical and Geological Flows: Air/sea interactions Mixing: Mixing Turbulent Flows: Turbulent Flows Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 731 , 25 September 2013 , pp. 259 - 287
Copyright
©2013 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.)

References

Abraham, M. & McGowan, J. 1987 The use of characteristic volumes to measure cavity terms in reversed phase liquid-chromatography. Chromatographia 23 (4), 243–246.CrossRefGoogle Scholar
Asher, W. & Litchendorf, T. 2009 Visualizing near-surface concentration fluctuations using laser-induced fluorescence. Exp. Fluids 46 (2), 243–253.Google Scholar
Asher, W. & Wanninkhof, R. 1998 Transient tracers and air–sea gas transfer. J. Geophys. Res. 103 (C8), 958.Google Scholar
Banerjee, S., Lakehal, D. & Fulgosi, M. 2004 Surface divergence models for scalar exchange between turbulent streams. Intl J. Multiphase Flow 30 (7–8), 963–977.Google Scholar
Banerjee, S. & MacIntyre, S. 2004 The air–water interface: turbulence and scalar exchange. In PIV and Water Waves (ed. Grue, J., Liu, P. & Pedersen, G. K.). World Scientific.Google Scholar
Banner, M. L. & Peirson, W. L. 1998 Tangential stress beneath wind-driven air–water interfaces. J. Fluid Mech. 364, 115–145.CrossRefGoogle Scholar
Bird, R. B., Stewart, W. E. & Lightfoot, E. N. 2006 Transport Phenomena, revised 2nd edn. John Wiley & Sons.Google Scholar
Bodart, J., Cazalbou, J.-B. & Joly, L. 2010 Direct numerical simulation of unsheared turbulence diffusing towards a free-slip or no-slip surface. J. Turbul. 11 (48), 1–18.Google Scholar
Brumley, B. H. & Jirka, G. H. 1987 Near-surface turbulence in a grid-stirred tank. J. Fluid Mech. 183, 235–263.CrossRefGoogle Scholar
Brutsaert, W. & Jirka, G. H. (Eds) 1984 Gas Transfer at Water Surfaces. Springer.CrossRefGoogle Scholar
Calmet, I. & Magnaudet, J. 1997 Large-eddy simulation of high-Schmidt number mass transfer in a turbulent channel flow. Phys. Fluids 9 (2), 438–455.Google Scholar
Calmet, I. & Magnaudet, J. 1998 High-Schmidt number mass transfer through turbulent gas–liquid interfaces. Intl J. Heat Fluid Flow 19 (5), 522–532.CrossRefGoogle Scholar
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, 355–378.CrossRefGoogle Scholar
Campagne, G., Cazalbou, J.-B., Joly, L. & Chassaing, P. 2009 The structure of a statistically steady turbulent boundary layer near a free-slip surface. Phys. Fluids 21 (6), 065111.Google Scholar
Chang, K. & Cowen, E. A. 2002 Turbulent Prandtl number in neutrally buoyant turbulent round jet. J. Engng Mech. ASCE 128 (10), 1082–1087.CrossRefGoogle Scholar
Chu, C. R. & Jirka, G. H. 1992 Turbulent gas flux measurements below the air–water interface of a grid-stirred tank. Intl J. Heat Mass Transfer (UK) 35 (8), 1957–1968.Google Scholar
Cowen, E. A., Chang, K.-A. & Liao, Q. 2001 A single-camera coupled PTV–LIF technique. Exp. Fluids 31 (1), 63–73.CrossRefGoogle Scholar
Csanady, G. T. 1990 The role of breaking wavelets in air–sea gas transfer. J. Geophys. Res. 95 (C1), 749–759.Google Scholar
Delbos, S., Weitbrecht, V., Bleninger, T., Grand, P., Chassaing, E., Lincot, D., Kerrec, O. & Jirka, G. 2009 Homogeneous turbulence at an electrodeposition surface induced by randomly firing jet arrays. Exp. Fluids 46 (6), 1105–1114.Google Scholar
Falkenroth, A., Degreif, K. & Jahne, B. 2007 Visualization of oxygen concentration fields in the mass boundary layer by fluorescence quenching. In Transport at the Air Sea Interface – Measurements, Models and Parameterizations (ed. Garbe, C. S., Handler, R. A. & Jahne, B.). Springer.Google Scholar
Frew, N. M., Goldman, J. C., Dennett, M. R. & Johnson, A. S. 1990 Impact of phytoplankton-generated surfactants on air–sea gas exchange. J. Geophys. Res. 95 (C3), 3337–3352.CrossRefGoogle Scholar
Garbe, C. S., Schimpf, U. & Jähne, B. 2004 A surface renewal model to analyse infrared image sequences of the ocean surface for the study of air–sea heat and gas exchange. J. Geophys. Res. 109, C08S15.Google Scholar
Handler, R. A., Leighton, R. I., Smith, G. B. & Nagaosa, R. 2003 Surfactant effects on passive scalar transport in a fully developed turbulent flow. Intl J. Heat Mass Transfer 46 (12), 2219–2238.Google Scholar
Herlina, & Jirka, G. H. 2004 Application of LIF to investigate gas transfer near the air–water interface in a grid-stirred tank. Exp. Fluids 37 (3), 341–349.CrossRefGoogle Scholar
Herlina, & Jirka, G. H. 2008 Experiments on gas transfer at the air–water interface induced by oscillating grid turbulence. J. Fluid Mech. 594, 183–208.Google Scholar
Higbie, R. 1935 The rate of absorption of a pure gas into a still liquid during short periods of exposure. Trans. ASCE 31, 365–389.Google Scholar
Hunt, J. C. R. & Graham, J. M. R. 1978 Free-stream turbulence near plane boundaries. J. Fluid Mech. 84 (02), 209–235.CrossRefGoogle Scholar
Ibelings, B. & Maberly, S. 1998 Photoinhibition and the availability of inorganic carbon restrict photosynthesis by surface blooms of cyanobacteria RID B-4237-2011. Limnol. Oceanogr. 43 (3), 408–419.Google Scholar
Jähne, B. & Haußecker, H. 1998 Air–water gas exchange. Annu. Rev. Fluid Mech. 30 (1), 443–468.CrossRefGoogle Scholar
Jähne, B., Münnich, K. O., Dutzi, R. B. A., Huber, W. & Libner, P. 1987 On the parameters influencing air–water gas exchange. J. Geophys. Res. 92 (C2), 1937–1949.CrossRefGoogle Scholar
Kays, W. M. 1994 Turbulent Prandtl number – where are we? J. Heat Transfer 116 (2), 284–295.Google Scholar
Kermani, A. & Shen, L. 2009 Surface age of surface renewal in turbulent interfacial transport. Geophys. Res. Lett. 36 (10), L10605.CrossRefGoogle Scholar
Khakpour, H. R., Shen, L. & Yue, D. K. P. 2011 Transport of passive scalar in turbulent shear flow under a clean or surfactant-contaminated free surface. J. Fluid Mech. 670, 527–557.CrossRefGoogle Scholar
King, A. T., Tinoco, R. O. & Cowen, E. A. 2012 A $k{\unicode{x2013}} \varepsilon $ turbulence model based on the scales of vertical shear and stem wakes valid for emergent and submerged vegetated flows. J. Fluid Mech. 701, 1–39.Google Scholar
Komori, S., McGillis, W. & Kurose, R. (Eds) 2011 Gas Transfer at Water Surfaces 2010. Kyoto University Press.Google Scholar
Komori, S., Murakami, Y. & Ueda, H. 1989 The relationship between surface-renewal and bursting motions in an open-channel flow. J. Fluid Mech. 203, 103–123.Google Scholar
Kumar, S., Gupta, R. & Banerjee, S. 1998 An experimental investigation of the characteristics of free-surface turbulence in channel flow. Phys. Fluids 10 (2), 437–456.Google Scholar
Lamont, J. C. & Scott, D. S. 1970 An eddy cell model of mass transfer into the surface of a turbulent liquid. AIChE J. 16 (4), 513–519.CrossRefGoogle Scholar
Law, C. & Khoo, B. 2002 Transport across a turbulent air–water interface. AIChE J. 48 (9), 1856–1868.CrossRefGoogle Scholar
Lumley, J. L. 1967 Similarity and the turbulent energy spectrum. Phys. Fluids 10 (4), 855–858.Google Scholar
Magnaudet, J. 2003 High-Reynolds-number turbulence in a shear-free boundary layer: revisiting the Hunt–Graham theory. J. Fluid Mech. 484, 167–196.CrossRefGoogle Scholar
Magnaudet, J. & Calmet, I. 2006 Turbulent mass transfer through a flat shear-free surface. J. Fluid Mech. 553, 155–185.CrossRefGoogle Scholar
McCready, M. J. & Hanratty, T. J. 1984 Concentration fluctuations close to a gas–liquid interface. AIChE J. 30 (5), 816–817.CrossRefGoogle Scholar
McKenna, S. P. & McGillis, W. R. 2004 The role of free-surface turbulence and surfactants in air–water gas transfer. Intl J. Heat Mass Transfer 47 (3), 539–553.Google Scholar
Monismith, S. G. 2007 Hydrodynamics of coral reefs. Annu. Rev. Fluid Mech. 39 (1), 37–55.CrossRefGoogle Scholar
Moog, D. & Jirka, G. 1999 Air–water gas transfer in uniform channel flow. J. Hydraul. Engng 125 (1), 3–10.Google Scholar
Munsterer, T. & Jähne, B. 1998 LIF measurements of concentration profiles in the aqueous mass boundary layer. Exp. Fluids 25 (3), 190–196.CrossRefGoogle Scholar
Mydlarski, L. & Warhaft, Z. 1998 Passive scalar statistics in high-Péclet-number grid turbulence. J. Fluid Mech. 358, 135–175.Google Scholar
Nagaosa, R. & Handler, R. A. 2003 Statistical analysis of coherent vortices near a free surface in a fully developed turbulence. Phys. Fluids 15 (2), 375–394.Google Scholar
O’Gorman, P. A. & Pullin, D. I. 2005 Effect of Schmidt number on the velocity-scalar cospectrum in isotropic turbulence with a mean scalar gradient. J. Fluid Mech. 532, 111–140.Google Scholar
Perot, B. & Moin, P. 1995 Shear-free turbulent boundary layers. Part 1. Physical insights into near-wall turbulence. J. Fluid Mech. 295, 199–227.Google Scholar
Petrášek, Z. & Schwille, P. 2008 Precise measurement of diffusion coefficients using scanning fluorescence correlation spectroscopy. Biophys. J. 94 (4), 1437–1448.CrossRefGoogle ScholarPubMed
Pope, S. B. 2000 Turbulent Flows, 1st edn. Cambridge University Press.CrossRefGoogle Scholar
Rashidi, M., Hetsroni, G. & Banerjee, S. 1991 Mechanisms of heat and mass-transport at gas–liquid interfaces. Intl J. Heat Mass Transfer 34 (7), 1799–1810.CrossRefGoogle Scholar
Savelsberg, R. & van de Water, W. 2008 Turbulence of a Free Surface. Phys. Rev. Lett. 100 (3), 034501.Google Scholar
Tamburrino, A. & Gulliver, J. 2002 Free-surface turbulence and mass transfer in a channel flow. AIChE J. 48 (12), 2732–2743.CrossRefGoogle Scholar
Teixeira, M. A. C. & Belcher, S. E. 2000 Dissipation of shear-free turbulence near boundaries. J. Fluid Mech. 422, 167–191.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. The MIT Press.Google Scholar
Thomas, N. H. & Hancock, P. E. 1977 Grid turbulence near a moving wall. J. Fluid Mech. 82 (03), 481–496.Google Scholar
Turney, D. & Banerjee, S. 2011 Near surface turbulence and its relationship to air–water gas transfer rates. In Gas Transfer at Water Surfaces 2010 (ed. Komori, S., McGillis, W. & Kurose, R.). Kyoto University 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. Lett. 32, L04607.CrossRefGoogle Scholar
Uzkan, T. & Reynolds, W. C. 1967 A shear-free turbulent boundary layer. J. Fluid Mech. 28 (04), 803–821.CrossRefGoogle Scholar
Variano, E. A. 2007 measurements of gas transfer and turbulence at a shear-free turbulent air–water interface, PhD Thesis, Cornell University, Ithaca, NY, USA.Google Scholar
Variano, E. A. & Cowen, E. A. 2008 A random-jet-stirred turbulence tank. J. Fluid Mech. 604, 1–32.CrossRefGoogle Scholar
Walker, D. T., Leighton, R. I. & Garza-Rios, L. O. 1996 Shear-free turbulence near a flat free surface. J. Fluid Mech. 320, 19–51.Google Scholar
Woodrow, P. & Duke, S. 2002 LIF measurements of oxygen concentration gradients along flat and wavy air–water interfaces. In Gas Transfer at Water Surfaces (ed. Donelan, M., Drennan, W., Saltzman, E. & Wanninkhof, R.). pp. 83–88. American Geophysical Union.Google Scholar