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Statistics of surface renewal of passive scalars in free-surface turbulence

Published online by Cambridge University Press:  03 May 2011

ALIREZA KERMANI ,
HAMID R. KHAKPOUR ,
LIAN SHEN  and
TAKERU IGUSA
ALIREZA KERMANI
Affiliation:
Department of Civil Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
HAMID R. KHAKPOUR
Affiliation:
Department of Civil Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
LIAN SHEN*
Affiliation:
Department of Civil Engineering, Johns Hopkins University, Baltimore, MD 21218, USA Center for Environmental and Applied Fluid Mechanics, Johns Hopkins University, Baltimore, MD 21218, USA
TAKERU IGUSA
Affiliation:
Department of Civil Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
*
†Email address for correspondence: lianshen@jhu.edu
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Abstract

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We perform direct numerical simulation to study the transport of gas and heat as passive scalars in free-surface turbulence. Our analysis focuses on the surface age of surface fluid particles, i.e. the time elapsed since the last surface renewal they experienced. Using Lagrangian tracing of fluid particles combined with heat diffusion analysis, we are able to directly quantify surface age to illustrate scalar characteristics at different stages of interfacial transfer. Results show that at the early stage of surface renewal, vertical advection associated with upwellings greatly enhances surface gas flux; random surface renewal model does not apply at this stage when most of the interfacial gas transfer occurs. After a fluid particle leaves the upwelling region, it may enter a nearby downwelling region immediately, where the gas flux is sharply reduced but the variation in surface temperature is small; alternatively, the fluid particle may travel along the surface for some time before it is absorbed by a downwelling, where the surface temperature has changed significantly due to long duration of diffusion and the gas flux is also reduced. To gain further insight into the relationships between surface velocity and scalar quantities, we perform a statistical analysis of upwellings using clustering and nonlinear regression. With this analysis, we are able to provide qualitative and quantitative descriptions of the skewed probability density functions associated with the surface divergence, temperature and gas flux that support our physics-based investigation of surface renewal and surface age.

JFM classification

Waves/Free-surface Flows: Channel flow Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 678 , 10 July 2011 , pp. 379 - 416
Copyright
Copyright © Cambridge University Press 2011. The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution-NonCommercial-ShareAlike licence <http://creativecommons.org/licenses/by-nc-sa/2.5/>. The written permission of Cambridge University Press must be obtained for commercial re-use.

References

REFERENCES

Atmane, M. A. & George, J. 2002 Gas transfer across a zero-shear surface: a local approach. In Gas Transfer at Water Surfaces (ed. Donelan, M. A., Drennan, W. M., Saltzman, E. S. & Wanninkhof, R.), pp. 255–259. American Geophysical Union.Google Scholar
Banerjee, S. 1990 Turbulence structure and transport mechanisms at interfaces. In Proc. Ninth Intl Heat Transfer Conf., pp. 395–418. Hemisphere.Google Scholar
Banerjee, S., Lakehal, D. & Fulgosi, M. 2004 Surface divergence models for scalar exchange between turbulent streams. Intl J. Multiphase Flow 30, 963–977.CrossRefGoogle Scholar
Banerjee, S., Scott, D. S. & Rhodes, E. 1968 Mass transfer to falling wavy liquid films in turbulent flow. Indust. Engng Chem. Fund. 7, 22–27.Google Scholar
Borue, V., Orszag, S. A. & Staroselsky, I. 1995 Interaction of surface waves with turbulence: direct numerical simulations of turbulent open-channel flow. J. Fluid Mech. 286, 1–23.Google Scholar
Brumley, B. H. & Jirka, G. H. 1988 Air–water transfer of slightly soluble gases: turbulence, interfacial processes and conceptual models. J. Phys.-Chem. Hydrodyn. 10, 295–319.Google Scholar
Campbell, J. A. & Hanratty, T. J. 1982 Mass transfer between a turbulent fluid and a solid boundary: Linear theory. AIChE J. 28, 988–993.Google Scholar
Campbell, J. A. & Hanratty, T. J. 1983 Mechanism of turbulent mass transfer at a solid boundary. AIChE J. 29, 221–229.Google Scholar
Chan, W. C. & Scriven, L. E. 1970 Absorption into irrotational stagnation flow. Indust. Engng Chem. Fund. 9, 114–120.Google 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 35, 1957–1968.Google Scholar
Danckwerts, P. V. 1951 Significance of liquid-film coefficients in gas absorption. Indust. Engng Chem. 43, 1460–1467.Google Scholar
Fortescue, G. E. & Pearson, J. R. A. 1967 On gas absorption into a turbulent liquid. Chem. Engng Sci. 22, 1163–1176.Google Scholar
Garbe, C. S., Schimpf, U. & Jähne, B. 2004 A surface renewal model to analyze 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., Saylor, J. R., Leighton, R. I. & Rovelstad, A. L. 1999 Transport of a passive scalar at a shear-free boundary in fully developed turbulent open channel flow. Phys. Fluids 11, 2607–2625.Google Scholar
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, 1998–2007.Google Scholar
Harriott, P. 1962 A random eddy modification of the penetration theory. Chem. Engng Sci. 17, 149–154.Google Scholar
Hasegawa, Y. & Kasagi, N. 2008 Systematic analysis of high Schmidt number turbulent mass transfer across clean, contaminated and solid interfaces. Intl J. Heat Fluid Flow 29, 765–773.Google Scholar
Hasegawa, Y. & Kasagi, N. 2009 Hybrid DNS/LES of high Schmidt number mass transfer across turbulent air–water interface. Intl J. Heat Mass Transfer 52, 1012–1022.Google Scholar
Hastie, T., Tibshirani, R. & Friedman, J. 2001 The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer.Google 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.CrossRefGoogle Scholar
Higbie, R. 1935 The rate of absorption of a pure gas into a still liquid during short periods of exposure. Trans. AIChE 31, 365–389.Google Scholar
Hunt, J. C. R. & Graham, J. M. R. 1978 Free-stream turbulence near plane boundaries. J. Fluid Mech. 84, 209–235.Google Scholar
Jähne, B. & Haußecker, H. 1998 Air–water gas exchange. Annu. Rev. Fluid. Mech. 30, 443–468.Google Scholar
Johnk, R. E. & Hanratty, T. J. 1962 Temperature profiles for turbulent flow of air in a pipe. I. The fully developed heat transfer. Chem. Engng Sci. 17, 867–879.Google Scholar
Kader, B. A. 1981 Temperature and concentration profiles in fully turbulent boundary layers. Intl J. Heat Mass Transfer 24, 1541–1544.Google Scholar
Kasagi, N., Tomita, Y. & Kuroda, A. 1992 Direct numerical simulation of passive scalar field in a turbulent channel flow. J. Heat Transfer 114, 598–606.Google Scholar
Kass, R. E. & Raftery, A. E. 1995 Bayes factors. J. Am. Stat. Assoc. 90, 773–795.Google Scholar
Kermani, A. 2010 Numerical study of turbulence and scalar transport process in free-surface and multi-phase flows. PhD thesis, Johns Hopkins University, Maryland.Google Scholar
Kermani, A. & Shen, L. 2009 Surface age of surface renewal in turbulent interfacial transport. Geophys. Res. Lett. 36, L10605.Google 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.Google Scholar
Kim, J. 1983 On the structure of wall-bounded turbulent flows. Phys. Fluids 26, 2088–2097.Google Scholar
Kim, J. 1988 Investigation of heat and momentum transport in turbulent flows via numerical simulations. In Transport Phenomena in Turbulent Flows: Theory, Experiment, and Numerical Simulation (ed. Hirata, M. & Kasagi, N.), pp. 715–729. Hemisphere.Google Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–323.Google Scholar
Komori, S., Kurose, R., Iwano, K., Ukai, T. & Suzuki, N. 2010 Direct numerical simulation of wind-driven turbulence and scalar transfer at sheared gas–liquid interfaces. J. Turbul. 11 (32), 1–20.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
Komori, S., Nagaosa, R., Murakami, Y., Chiba, S., Ishii, K. & Kuwahara, K. 1993 Direct numerical simulation of three-dimensional open-channel flow with zero-shear gas–liquid interface. Phys. Fluids A 5, 115–125.Google Scholar
Lakehal, D., Fulgosi, M., Banerjee, S. & Yadigaroglu, G. 2008 a Turbulence and heat exchange in condensing vapor–liquid flow. Phys. Fluids 20, 065101.Google Scholar
Lakehal, D., Fulgosi, M. & Yadigaroglu, G. 2008 b Direct numerical simulation of condensing stratified flow. J. Heat Transfer 130, 021501.Google Scholar
Lakehal, D., Fulgosi, M., Yadigaroglu, G. & Banerjee, S. 2003 Direct numerical simulation of turbulent heat transfer across a mobile, sheared gas–liquid interface. J. Heat Transfer 125, 1129–1139.Google Scholar
Lamont, J. C. & Scott, D. S. 1970 An eddy cell model of mass transfer into the surface of turbulent liquid. AIChE J. 16, 513–519.Google Scholar
Lin, M., Moeng, C., Tsai, W., Sullivan, P. P. & Belcher, S. E. 2008 Direct numerical simulation of wind-wave generation processes. J. Fluid Mech. 616, 1–30.Google Scholar
Liss, P. S. & Slater, P. G. 1974 Flux of gases across the air–sea interface. Nature 247, 181–184.Google Scholar
Liu, S., Kermani, A., Shen, L. & Yue, D. K. P. 2009 Investigation of coupled air–water turbulent boundary layers using direct numerical simulations. Phys. Fluids 21, 062108.Google Scholar
Lyons, S. L., Hanratty, T. J. & Mclaughlin, J. B. 1991 Direct numerical simulation of passive heat transfer in a turbulent channel flow. Intl J. Heat Mass Transfer 34, 1149–1161.Google Scholar
Magnaudet, J. & Calmet, I. 2006 Turbulent mass transfer through a flat shear-free surface. J. Fluid Mech. 553, 155–185.Google Scholar
McCready, M. J. & Hanratty, T. J. 1984 A comparison of turbulent mass transfer at gas–liquid and solid–liquid interfaces. In Gas Transfer at Water Surfaces (ed. Brutsaert, W. & Jirka, G. H.), pp. 283–292. Reidel.Google Scholar
McCready, M. J., Vassiliadou, E. & Hanratty, T. J. 1986 Computer simulation of turbulent mass transfer at a mobile interface. AIChE J. 32, 1108–1115.Google 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, 539–553.Google Scholar
Moin, P. & Mahesh, K. 1998 Direct numerical simulation: A tool in turbulence research. Annu. Rev. Fluid. Mech. 30, 539–578.Google Scholar
Münsterer, T. & Jähne, B. 1998 LIF measurements of concentration profiles in the aqueous mass boundary layer. Exp. Fluids 25, 190–196.Google Scholar
Na, Y. & Hanratty, T. J. 2000 Limiting behavior of turbulent scalar transport close to a wall. Intl J. Heat Mass Transfer 43, 1794–1758.Google Scholar
Na, Y., Papavassiliou, D. V. & Hanratty, T. J. 1999 Use of direct numerical simulation to study the effect of Prandtl number on temperature fields. Intl J. Heat Fluid Flow 20, 187–195.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, 375–394.Google Scholar
Nakajima, M., Fukui, K., Ueda, H. & Mizushina, T. 1980 Buoyancy effects on turbulent transport in combined free and forced convection between vertical parallel plates. Intl J. Heat Mass Transfer 23, 1325–1336.Google Scholar
Pan, Y. & Banerjee, S. 1995 A numerical study of free-surface turbulence in channel flow. Phys. Fluids 7, 1649–1664.Google Scholar
Perot, B. & Moin, P. 1995 Shear-free turbulent boundary layers. Part 1. Physical insight into near-wall turbulence. J. Fluid Mech. 295, 199–227.Google Scholar
Piomelli, U., Yu, Y. & Adrian, R. J. 1996 Subgrid-scale energy transfer and near-wall turbulence structure. Phys. Fluids 8, 215–224.Google Scholar
Rao, K. N., Narasimha, R. & Narayanan, M. A. B. 1971 The ‘bursting’ phenomenon in a turbulent boundary layer. J. Fluid Mech. 48, 339–352.Google Scholar
Rashidi, M., Hetsroni, G. & Banerjee, S. 1991 Mechanisms of heat and mass transport at gas–liquid interfaces. Intl J. Heat Mass Transfer 34, 1799–1810.Google Scholar
Schwertfirm, F. & Manhart, M. 2007 DNS of passive scalar transport in turbulent channel flow at high Schmidt numbers. Intl J. Heat Fluid Flow 28, 1204–1214.CrossRefGoogle Scholar
Shen, L., Triantafyllou, G. S. & Yue, D. K. P. 2001 Mixing of a passive scalar near a free surface. Phys. Fluids 13, 913–926.Google Scholar
Shen, L., Yue, D. K. P. & Triantafyllou, G. S. 2004 Effect of surfactants on free-surface turbulent flows. J. Fluid Mech. 506, 79–115.Google Scholar
Soloviev, A. V. & Schlussel, P. 1996 Evolution of cool skin and direct air–sea gas transfer coefficient during daytime. Boundary-Layer Meteorol. 77, 45–68.Google Scholar
Sugihara, Y. & Tsumori, H. 2005 Surface-renewal eddies at the air–water interface in oscillating-grid turbulence. In Environmental Hydraulics and Sustainable Water Management (ed. Lee, J. H. W. & Lam, K. M.), pp. 199–205. Taylor and Francis.Google Scholar
Tamburrino, A., Aravena, C. & Gulliver, J. S. 2007 Visualization of 2-D divergence on the free surface and its relation to gas transfer. In Transport at the Air–Sea Interface (ed. Garbe, C. S., Handler, R. A. & Jähne, B.), pp. 73–86. Springer.Google Scholar
Tamburrino, A. & Gulliver, J. S. 2002 Free-surface turbulence and mass transfer in a channel flow. AIChE J. 48, 2732–2743.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.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
Zhang, C., Shen, L. & Yue, D. K. P. 1999 The mechanism of vortex connection at a free surface. J. Fluid Mech. 384, 207–241.Google Scholar
Zhu, Y. & Antonia, R. A. 1993 Temperature dissipation measurements in a fully developed turbulent channel flow. Exp. Fluids 15, 191–199.Google Scholar