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Please use this identifier to cite or link to this item: http://hdl.handle.net/10481/22399

Title: Scalar arguments of the mathematical functions defining molecular and turbulent transport of heat and mass in compressible fluids
Authors: Kowalski, Andrew S.
Argüeso, Daniel
Issue Date: 2011
Abstract: The advection–diffusion equations defining control volume conservation laws in micrometeorological research are analysed to resolve discrepancies in their appropriate scalar variables for heat and mass transport. A scalar variable that is conserved during vertical motions enables the interpretation of turbulent mixing as ‘diffusion’. Gas-phase heat advection is shown to depend on gradients in the potential temperature (θ), not the temperature (T). Since conduction and radiation depend on T, advection–diffusion of heat depends on gradients of both θ and T. Conservation of θ (the first Law of Thermodynamics) requires including a pressure covariance term in the definition of the turbulent heat flux. Mass advection and diffusion are universally agreed to depend directly on gradients in the gas ‘concentration’ (c), a nonetheless ambiguous term. Depending upon author, c may be defined either as a dimensionless proportion or as a dimensional density, with non-trivial differences for the gas phase. Analyses of atmospheric law, scalar conservation and similarity theory demonstrate that mass advection–diffusion in gases depends on gradients, not in density but rather in a conserved proportion. Flux-tower researchers are encouraged to respect the meteorological tradition of writing conservation equations in terms of scalar variables that are conserved through simple air motions.
Sponsorship: The authors received funding support from Andalusian regional government project GEOCARBO (P08-RNM-3721), the National Institute for Agrarian Research and Technology (INIA; SUM2006–00010-00–00), the Spanish flux-tower network CARBORED-ES (Science Ministry project CGL2010- 22193-C04–02), and the European Commission collaborative project GHG Europe (FP7/2007-2013; grant agreement 244122).
Publisher: John Wley and Sons
Keywords: Scalar
Mathematical functions
Heat
Mass
Transport
URI: http://hdl.handle.net/10481/22399
ISSN: 0280-6509
1600-0889 (online)
Rights : Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License
Citation: Kowalski, A. S.; Argüeso, D. Scalar arguments of the mathematical functions defining molecular and turbulent transport of heat and mass in compressible fluids. Tellus B 63(5): 1059-1066 (2011). [http://hdl.handle.net/10481/22399]
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