A Kolmogorov-Brutsaert structure function model for evaporation into a turbulent atmosphere

Katul, Gabriel; Liu, Heping

doi:10.1002/2016WR020006

Title: A Kolmogorov-Brutsaert structure function model for evaporation into a turbulent atmosphere

Journal Article · Tue Apr 11 00:00:00 EDT 2017 · Water Resources Research

DOI:https://doi.org/10.1002/2016WR020006· OSTI ID:1466034

^[1];

^[2]

Duke Univ., Durham, NC (United States)
Washington State Univ., Pullman, WA (United States)

Abstract In 1965, Brutsaert proposed a model that predicted mean evaporation rate from rough surfaces to scale with the 3/4 power law of the friction velocity ( ) and the square‐root of molecular diffusivity ( D _m ) for water vapor. In arriving at these results, a number of assumptions were made regarding the surface renewal rate describing the contact durations between eddies and the evaporating surface, the diffusional mass process from the surface into eddies, and the cascade of turbulent kinetic energy sustaining the eddy renewal process itself. The working hypothesis explored here is that is a direct outcome of the Kolmogorov scaling for inertial subrange eddies modified to include viscous cutoff thereby bypassing the need for a surface renewal assumption. It is demonstrated that Brutsaert's model for may be more general than its original derivation implied.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Duke Univ., Durham, NC (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Biological and Environmental Research (BER)

Grant/Contract Number:: SC0006967; SC0011461; DE‐SC0006967; DE‐SC0011461; NSF‐AGS‐1112938

OSTI ID:: 1466034

Alternate ID(s):: OSTI ID: 1402402

Journal Information:: Water Resources Research, Vol. 53, Issue 5; ISSN 0043-1397

Publisher:: American Geophysical Union (AGU)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 9 works

Citation information provided by
Web of Science

References (58)

Direct numerical simulation of homogeneous turbulence with hyperviscosity Lamorgese, A. G.; Caughey, D. A.; Pope, S. B. Physics of Fluids, Vol. 17, Issue 1 https://doi.org/10.1063/1.1833415	journal	January 2005
Thermal signatures of turbulent airflows interacting with evaporating thin porous surfaces Haghighi, Erfan; Or, Dani International Journal of Heat and Mass Transfer, Vol. 87 https://doi.org/10.1016/j.ijheatmasstransfer.2015.04.026	journal	August 2015
Air-Water gas Exchange Jähne, B.; Haußecker, H. Annual Review of Fluid Mechanics, Vol. 30, Issue 1 https://doi.org/10.1146/annurev.fluid.30.1.443	journal	January 1998
Single-eddy model for random surface renewal Gon Seo, Yang; Kook Lee, Won Chemical Engineering Science, Vol. 43, Issue 6 https://doi.org/10.1016/0009-2509(88)85112-1	journal	January 1988
Reynolds flux and danckwerts surface renewal theory Thomson, G. M.; Silver, R. S. International Journal of Heat and Mass Transfer, Vol. 15, Issue 6 https://doi.org/10.1016/0017-9310(72)90194-9	journal	June 1972
Models of the scalar spectrum for turbulent advection Hill, R. J. Journal of Fluid Mechanics, Vol. 88, Issue 3 https://doi.org/10.1017/S002211207800227X	journal	October 1978
A surface renewal model to analyze infrared image sequences of the ocean surface for the study of air-sea heat and gas exchange: SURFACE RENEWAL TO ANALYZE IR IMAGES Garbe, C. S.; Schimpf, U.; Jähne, B. Journal of Geophysical Research: Oceans, Vol. 109, Issue C8 https://doi.org/10.1029/2003JC001802	journal	August 2004
The continuous phase heat and mass-transfer properties of dispersions Calderbank, P. H.; Moo-Young, M. B. Chemical Engineering Science, Vol. 16, Issue 1-2 https://doi.org/10.1016/0009-2509(61)87005-X	journal	December 1961
The Effects of Thermal Stratification on Clustering Properties of Canopy Turbulence Cava, D.; Katul, G. G. Boundary-Layer Meteorology, Vol. 130, Issue 3 https://doi.org/10.1007/s10546-008-9342-6	journal	February 2009
Spectral Theory of the Turbulent Mean-Velocity Profile Gioia, Gustavo; Guttenberg, Nicholas; Goldenfeld, Nigel Physical Review Letters, Vol. 105, Issue 18 https://doi.org/10.1103/PhysRevLett.105.184501	journal	October 2010
Real-Space Manifestations of Bottlenecks in Turbulence Spectra Frisch, Uriel; Ray, Samriddhi Sankar; Sahoo, Ganapati Physical Review Letters, Vol. 110, Issue 6 https://doi.org/10.1103/PhysRevLett.110.064501	journal	February 2013
Evaporation from porous surfaces into turbulent airflows: Coupling eddy characteristics with pore scale vapor diffusion: DIFFUSION-TURBULENCE EVAPORATION MODEL Haghighi, E.; Or, D. Water Resources Research, Vol. 49, Issue 12 https://doi.org/10.1002/2012WR013324	journal	December 2013
Analysis of the small-scale structure of turbulence on smooth and rough walls Poggi, D.; Porporato, A.; Ridolfi, L. Physics of Fluids, Vol. 15, Issue 1 https://doi.org/10.1063/1.1521728	journal	January 2003
A functional form for the energy spectrum parametrizing bottleneck and intermittency effects Meyers, Johan; Meneveau, Charles Physics of Fluids, Vol. 20, Issue 6 https://doi.org/10.1063/1.2936312	journal	June 2008
A comparative assessment of spectral closures as applied to passive scalar diffusion Herring, J. R.; Schertzer, D.; Lesieur, M. Journal of Fluid Mechanics, Vol. 124, Issue -1 https://doi.org/10.1017/S0022112082002560	journal	November 1982
The Effect of Vegetation Density on Canopy Sub-Layer Turbulence Poggi, D.; Porporato, A.; Ridolfi, L. Boundary-Layer Meteorology, Vol. 111, Issue 3 https://doi.org/10.1023/B:BOUN.0000016576.05621.73	journal	June 2004
Dissolved oxygen transfer at the sediment-water interface in a turbulent flow Hondzo, Midhat Water Resources Research, Vol. 34, Issue 12 https://doi.org/10.1029/1998WR900009	journal	December 1998
Small-scale variation of convected quantities like temperature in turbulent fluid Part 1. General discussion and the case of small conductivity Batchelor, G. K. Journal of Fluid Mechanics, Vol. 5, Issue 01 https://doi.org/10.1017/S002211205900009X	journal	January 1959
Coupled renewal model of ocean viscous sublayer, thermal skin effect and interfacial gas transfer velocity Soloviev, Alexander V. Journal of Marine Systems, Vol. 66, Issue 1-4 https://doi.org/10.1016/j.jmarsys.2006.03.024	journal	June 2007
Water vapor transfer beneath bare soil where evaporation is influenced by a turbulent surface wind Ishihara, Yasuo; Shimojima, Eiichi; Harada, Hiroshi Journal of Hydrology, Vol. 131, Issue 1-4 https://doi.org/10.1016/0022-1694(92)90213-F	journal	February 1992
Surface-renewal models in mass transfer Perlmutter, D. D. Chemical Engineering Science, Vol. 16, Issue 3-4 https://doi.org/10.1016/0009-2509(61)80039-0	journal	December 1961
On the Statistical Theory of Isotropic Turbulence de Karman, Theodore; Howarth, Leslie Proceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences, Vol. 164, Issue 917 https://doi.org/10.1098/rspa.1938.0013	journal	January 1938
Turbulent Flows Pope, Stephen B. https://doi.org/10.1017/CBO9780511840531	book	July 2012
A theory for local evaporation (or heat transfer) from rough and smooth surfaces at ground level Brutsaert, Wilfried Water Resources Research, Vol. 11, Issue 4 https://doi.org/10.1029/WR011i004p00543	journal	August 1975
Mean Velocity Profile in a Sheared and Thermally Stratified Atmospheric Boundary Layer Katul, Gabriel G.; Konings, Alexandra G.; Porporato, Amilcare Physical Review Letters, Vol. 107, Issue 26 https://doi.org/10.1103/PhysRevLett.107.268502	journal	December 2011
Statistical models for surface renewal in heat and mass transfer: Part I. Dependence of average transport coefficients on age distribution Koppel, L. B.; Patel, R. D.; Holmes, J. T. AIChE Journal, Vol. 12, Issue 5 https://doi.org/10.1002/aic.690120520	journal	September 1966
Surface age of surface renewal in turbulent interfacial transport Kermani, A.; Shen, L. Geophysical Research Letters, Vol. 36, Issue 10 https://doi.org/10.1029/2008GL037050	journal	January 2009
A phenomenological model to describe turbulent friction in permeable-wall flows: FRICTION IN PERMEABLE WALL FLOWS Manes, C.; Ridolfi, L.; Katul, G. Geophysical Research Letters, Vol. 39, Issue 14 https://doi.org/10.1029/2012GL052369	journal	July 2012
Significance of Liquid-Film Coefficients in Gas Absorption Danckwerts, P. V. Industrial & Engineering Chemistry, Vol. 43, Issue 6 https://doi.org/10.1021/ie50498a055	journal	June 1951
A phenomenological model for the flow resistance over submerged vegetation: MANNING'S ROUGHNESS IN VEGETATED CHANNELS Konings, Alexandra G.; Katul, Gabriel G.; Thompson, Sally E. Water Resources Research, Vol. 48, Issue 2 https://doi.org/10.1029/2011WR011000	journal	February 2012
Mechanistic Analytical Models for Long‐Distance Seed Dispersal by Wind Katul, G. G.; Porporato, A.; Nathan, R. The American Naturalist, Vol. 166, Issue 3 https://doi.org/10.1086/432589	journal	September 2005
Study of High–Reynolds Number Isotropic Turbulence by Direct Numerical Simulation Ishihara, Takashi; Gotoh, Toshiyuki; Kaneda, Yukio Annual Review of Fluid Mechanics, Vol. 41, Issue 1 https://doi.org/10.1146/annurev.fluid.010908.165203	journal	January 2009
Parameterization of the Cool Skin of the Ocean and of the Air-Ocean Gas Transfer on the Basis of Modeling Surface Renewal Soloviev, Alexander V.; Schlüssel, Peter Journal of Physical Oceanography, Vol. 24, Issue 6 https://doi.org/10.1175/1520-0485(1994)024<1339:POTCSO>2.0.CO;2	journal	June 1994
Stretched exponential distributions in nature and economy: “fat tails” with characteristic scales Laherrère, J.; Sornette, D. The European Physical Journal B, Vol. 2, Issue 4 https://doi.org/10.1007/s100510050276	journal	May 1998
An eddy cell model of mass transfer into the surface of a turbulent liquid Lamont, John C.; Scott, D. S. AIChE Journal, Vol. 16, Issue 4 https://doi.org/10.1002/aic.690160403	journal	July 1970
Conditional sampling, bursting, and the intermittent structure of sensible heat flux Katul, Gabriel G.; Albertson, John; Parlange, Marc Journal of Geophysical Research, Vol. 99, Issue D11 https://doi.org/10.1029/94JD01679	journal	January 1994
Cospectral budget of turbulence explains the bulk properties of smooth pipe flow Katul, Gabriel G.; Manes, Costantino Physical Review E, Vol. 90, Issue 6 https://doi.org/10.1103/PhysRevE.90.063008	journal	December 2014
Environmental turbulent mixing controls on air-water gas exchange in marine and aquatic systems Zappa, Christopher J.; McGillis, Wade R.; Raymond, Peter A. Geophysical Research Letters, Vol. 34, Issue 10 https://doi.org/10.1029/2006GL028790	journal	January 2007
A model for evaporation as a molecular diffusion process into a turbulent atmosphere Brutsaert, Wilfried Journal of Geophysical Research, Vol. 70, Issue 20 https://doi.org/10.1029/JZ070i020p05017	journal	October 1965
On the Spectrum of Isotropic Temperature Fluctuations in an Isotropic Turbulence Corrsin, Stanley Journal of Applied Physics, Vol. 22, Issue 4 https://doi.org/10.1063/1.1699986	journal	April 1951
Local isotropy in turbulent boundary layers at high Reynolds number Saddoughi, Seyed G.; Veeravalli, Srinivas V. Journal of Fluid Mechanics, Vol. 268 https://doi.org/10.1017/S0022112094001370	journal	June 1994
The ‘bursting’ phenomenon in a turbulent boundary layer Rao, K. Narahari; Narasimha, R.; Narayanan, M. A. Badri Journal of Fluid Mechanics, Vol. 48, Issue 2 https://doi.org/10.1017/S0022112071001605	journal	July 1971
Study of mass transfer at the air-water interface by an isotopic method Merlivat, L.; Coantic, M. Journal of Geophysical Research, Vol. 80, Issue 24 https://doi.org/10.1029/JC080i024p03455	journal	August 1975
Scaling and Similarity in Rough Channel Flows Gioia, G.; Bombardelli, F. A. Physical Review Letters, Vol. 88, Issue 1 https://doi.org/10.1103/PhysRevLett.88.014501	journal	December 2001
Mean-velocity profile of smooth channel flow explained by a cospectral budget model with wall-blockage McColl, Kaighin A.; Katul, Gabriel G.; Gentine, Pierre Physics of Fluids, Vol. 28, Issue 3 https://doi.org/10.1063/1.4943599	journal	March 2016
The role of breaking wavelets in air-sea gas transfer Csanady, G. T. Journal of Geophysical Research, Vol. 95, Issue C1 https://doi.org/10.1029/JC095iC01p00749	journal	January 1990
The bottleneck effect and the Kolmogorov constant in isotropic turbulence Donzis, D. A.; Sreenivasan, K. R. Journal of Fluid Mechanics, Vol. 657 https://doi.org/10.1017/S0022112010001400	journal	June 2010
Active Turbulence and Scalar Transport near the Forest–Atmosphere Interface Katul, Gabriel G.; Geron, Chris D.; Hsieh, Cheng-I. Journal of Applied Meteorology, Vol. 37, Issue 12 https://doi.org/10.1175/1520-0450(1998)037<1533:ATASTN>2.0.CO;2	journal	December 1998
Random eddy models for surface renewal: formulation as a stochastic process Bullin, J. A.; Dukler, A. E. Chemical Engineering Science, Vol. 27, Issue 2 https://doi.org/10.1016/0009-2509(72)85081-4	journal	February 1972
Energy-Inertial Scale Interactions for Velocity and Temperature in the Unstable Atmospheric Surface Layer Katul, Gabriel; Hsieh, Cheng-I; Sigmon, John Boundary-Layer Meteorology, Vol. 82, Issue 1 https://doi.org/10.1023/A:1000178707511	journal	January 1997
The Roughness Length for Water Vapor Sensible Heat, and Other Scalars Brutsaert, Wilfried Journal of the Atmospheric Sciences, Vol. 32, Issue 10 https://doi.org/10.1175/1520-0469(1975)032<2029:TRLFWV>2.0.CO;2	journal	October 1975
Toward a Unified Scaling Relation for Interfacial Fluxes Lorke, Andreas; Peeters, Frank Journal of Physical Oceanography, Vol. 36, Issue 5 https://doi.org/10.1175/JPO2903.1	journal	May 2006
Oxygen and Hydrogen Isotopes in the Hydrologic Cycle Gat, J. R. Annual Review of Earth and Planetary Sciences, Vol. 24, Issue 1 https://doi.org/10.1146/annurev.earth.24.1.225	journal	May 1996
The relationship between ocean surface turbulence and air-sea gas transfer velocity: An in-situ evaluation Esters, L.; Landwehr, S.; Sutherland, G. IOP Conference Series: Earth and Environmental Science, Vol. 35 https://doi.org/10.1088/1755-1315/35/1/012005	journal	May 2016
Bottlenecks in turbulent kinetic energy spectra predicted from structure function inflections using the Von Kármán-Howarth equation Katul, Gabriel G.; Manes, Costantino; Porporato, Amilcare Physical Review E, Vol. 92, Issue 3 https://doi.org/10.1103/PhysRevE.92.033009	journal	September 2015
A random eddy modification of the penetration theory Harriott, P. Chemical Engineering Science, Vol. 17, Issue 3 https://doi.org/10.1016/0009-2509(62)80026-8	journal	March 1962
A review of the molecular diffusivities of H2O, CO2, CH4, CO, O3, SO2, NH3, N2O, NO, and NO2 in air, O2 and N2 near STP Massman, W. J. Atmospheric Environment, Vol. 32, Issue 6 https://doi.org/10.1016/S1352-2310(97)00391-9	journal	March 1998
Pressure fluctuations in isotropic turbulence Batchelor, G. K. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 47, Issue 2 https://doi.org/10.1017/S0305004100026712	journal	April 1951

Cited By (2)

An Advanced Method Based on Surface Renewal Theory to Estimate the Friction Velocity and the Surface Heat Flux Castellví, F. Water Resources Research, Vol. 54, Issue 12 https://doi.org/10.1029/2018wr022808	journal	December 2018
Impact of phenomenological theory of turbulence on pragmatic approach to fluvial hydraulics Ali, Sk Zeeshan; Dey, Subhasish Physics of Fluids, Vol. 30, Issue 4 https://doi.org/10.1063/1.5025218	journal	April 2018

Similar Records

Theoretical analysis of non‐ G aussian heterogeneity effects on subsurface flow and transport

Journal Article · Tue Apr 11 00:00:00 EDT 2017 · Water Resources Research · OSTI ID:1466034

Riva, Monica; Guadagnini, Alberto; Neuman, Shlomo P.

The effect of plant water storage on water fluxes within the coupled soil-plant system [The role of plant water storage on water fluxes within the coupled soil-plant system]

Journal Article · Mon Nov 21 00:00:00 EST 2016 · New Phytologist · OSTI ID:1466034

Huang, Cheng -Wei; Domec, Jean -Christophe; Ward, Eric J.; +4 more

Soil–plant–atmosphere conditions regulating convective cloud formation above southeastern US pine plantations

Journal Article · Fri Mar 25 00:00:00 EDT 2016 · Global Change Biology · OSTI ID:1466034

Manoli, Gabriele; Domec, Jean‐Christophe; Novick, Kimberly; +4 more

Related Subjects

54 ENVIRONMENTAL SCIENCES
evaporation
turbulent atmosphere
surface renewal
Kolmogorov
structure function

Title: A Kolmogorov-Brutsaert structure function model for evaporation into a turbulent atmosphere

Citation Formats

References (58)

Cited By (2)

Similar Records

Related Subjects