Abstract
A stochastic numerical model is developed to simulate heat and water vapor transfer from a rough surface through a boundary layer into the fully turbulent atmosphere. The so-called interfacial boundary layer is conceptualized as a semi-stagnant layer of air in the roughness cavities at the surface into which the smallest eddies penetrate to random approach distances and with random inter-arrival times, carrying away energy, molecules, or any other scalar admixture. The model makes use of the one-dimensional transient heat conduction equation where the boundary conditions are updated in time and space by random deviates from a general gamma distribution. The one-dimensional transfer equation is solved by the implicit finite difference method which allows conversion to a standard tridiagonal matrix equation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Brutsaert W (1975) A theory for local evaporation from rough and smooth surfaces at ground level, Water Resour Res 11(4): 543–550
Brutsaert W (1979) Heat and mass transfer to and from surfaces with dense vegetation or similar permeable roughness, Bnd-Layer Met. 16:365–388
Brutsaert W (1982) Evaporation into the atmosphere. Reidel Pub Co, Dordrecht, The Netherlands
Brutsaert W (1965) A model for evaporation as a molecular diffusion process into a turbulent atmosphere. J Geophys Res 70(20): 5017–5024
Harriott P (1962a) A random eddy modification of the penetration theory. Chemical Engineering Science 17:149–154.
Kolmogorov AN (1962) A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J Fluid Mech 13:82–85
Obukhov AM (1971) Turbulence in an atmosphere with a non-uniform temperature. Bnd-Layer Met. 2:7–29
Kays WM, Crawford ME (1993) Convective heat and mass transfer. McGraw-Hill, USA
Carslaw HS, Jaeger JC (1986) Conduction of Heat in Solids. Oxford University Press, UK
Trombetti F, Caporaloni M, Tampieri F (1978) Bulk transfer velocity to and from natural and artificial surfaces. Bnd-Layer Met. 14: 585–595
Kustas WP, Humes KS, Norman JM, Moran MS (1996) Single-and Dual-Source Modeling of Energy Fluxes with Radiometric Surface Temperature. J Appl Meteor 35: 110–121
Su Z (2005) Estimation of the surface energy balance. In: Encyclopedia of hydrological sciences: 5 Volumes. / ed. by M.G. Anderson and J.J. McDonnell. Chichester Wiley & Sons 2:731–752
Harriott P (1962b) A review of Mass Transfer to Interfaces. Can J Chem Eng 4:60–69
Thomas LC, Fan LT (1971) Adaptation of the surface rejuvenation model to turbulent heat and mass transfer at a solid-fluid interface. Ind Eng Chem Fundam 10(1): 135–139
Wang HF, Anderson MP (1982) Introduction to Groundwater Modeling, Finite Difference and Finite Element Methods. W.H. Freeman and Company. San Francisco, USA
Press WH, Flannery BP, Teukolsky SA, Vetterling WT (1986) Numerical Recipes, The Art of Scientific Computing. Cambridge University Press
Crago R, Hervol N, Crowley R (2005) A complementary evaporation approach to the scalar roughness length. Water Res. Res. 41: W06117
Verhoef A, De Bruin HAR, Van den Hurk BJJM (1997) Some practical notes on the parameter kB-1 for sparse vegetation. J Appl Met 36: 560
Bird RB, Stewart WE, Lightfoot EN (1960) Transport Phenomena. Wiley and Sons, USA
Owen PR, Thomson WR (1962) Heat transfer across rough surfaces. Journal Fluid Mech 15: 321–334
Chamberlain (1968) Transport of gases to and from surfaces with bluff and wave-like roughness elements. Quart J. Royal Met Soc 94: 318–332
Dipprey DF, Sabersky RH (1963) Heat and momentum transfer in smooth and rough tubes at various Prandtl numbers. Int Journal Heat Mass Transfer 6:329–353
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer
About this paper
Cite this paper
Gieske, A.S.M. (2007). Numerical modeling of heat and water vapor transport through the interfacial boundary layer into a turbulent atmosphere. In: Geurts, B.J., Clercx, H., Uijttewaal, W. (eds) Particle-Laden Flow. ERCOFTAC Series, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6218-6_6
Download citation
DOI: https://doi.org/10.1007/978-1-4020-6218-6_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-6217-9
Online ISBN: 978-1-4020-6218-6
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)