Dual length scale two-equation modelling of the canopy turbulent kinetic energy wake budget

Christophe Sanz; Gabriel G. Katul

doi:10.1016/j.crme.2007.07.005

Dual length scale two-equation modelling of the canopy turbulent kinetic energy wake budget
[Modélisation à 2 équations et 2 échelles de longueur de l'énergie cinétique turbulente dans la canopée]

Présenté par : Sébastien Candel

Christophe Sanz ¹ ; Gabriel G. Katul ²

¹ 3, rue du Mont Louvet, 91640 Fontenay lès Briis, France
² Nicholas School of the Environment and Earth Sciences, Duke University, Durham, NC 27708, USA

Comptes Rendus. Mécanique, Volume 335 (2007) no. 11, pp. 685-690.

Résumé
Abstract

Dans la canopée, la modélisation du bilan de sillage de l'énergie cinétique turbulente (k) repose principalement sur des termes source additionnels. Nous avons déterminé la relation entre les coefficients des modèles usuels de termes source et le rapport sans dimension (λ) entre l'échelle de longueur du transport turbulent ( $l_{m}$ ) et celle de la relation de Kolmogorov ( $l_{ε}$ ). Nous avons généralisé les modèles de termes source par analyse dimensionnelle et nous avons déterminé l'ordre de grandeur de la variation des différents termes. Lorsque λ est une constante, le modèle de terme source généralisé présente une constante de similitude ( $C_{ε 4}$ ) indépendante du modèle de termes source, ce qui tend à confirmer la conjecture de Seginer.

Within vegetation canopies, the turbulent kinetic energy (k) budget is mainly modelled through source terms added to the free-air state formulation. The dependence of the modelled source term coefficients upon a dimensionless ratio (λ) between the mixing length for turbulent transport ( $l_{m}$ ) and the relaxation length scale ( $l_{ε}$ ) of Kolmogorov's relation is proposed. Using dimensional analysis, the order of magnitude variation of the terms involved in the newly proposed model for the coefficients of these source terms are derived. When λ is a constant, this generalized model results in a similarity constant ( $C_{ε 4}$ ) independent of the source term model, lending support to an earlier conjecture by Seginer.

Reçu le : 2006-05-01
Accepté le : 2007-07-18
Publié le : 2007-09-14

DOI : 10.1016/j.crme.2007.07.005

Keywords: Turbulence, Dissipation, Turbid medium, Turbulence model, Vegetation canopy, Wakes
Mot clés : Turbulence, Dissipation, Couvert végétal, Milieu turbide, Modèle de turbulence, Sillages

Affiliations des auteurs :

Christophe Sanz ¹ ; Gabriel G. Katul ²

¹ 3, rue du Mont Louvet, 91640 Fontenay lès Briis, France
² Nicholas School of the Environment and Earth Sciences, Duke University, Durham, NC 27708, USA

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     author = {Christophe Sanz and Gabriel G. Katul},
     title = {Dual length scale two-equation modelling of the canopy turbulent kinetic energy wake budget},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {685--690},
     publisher = {Elsevier},
     volume = {335},
     number = {11},
     year = {2007},
     doi = {10.1016/j.crme.2007.07.005},
     language = {en},
}

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Christophe Sanz; Gabriel G. Katul. Dual length scale two-equation modelling of the canopy turbulent kinetic energy wake budget. Comptes Rendus. Mécanique, Volume 335 (2007) no. 11, pp. 685-690. doi : 10.1016/j.crme.2007.07.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.07.005/

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