Publication Abstracts
Canuto et al. 2010
, , and , 2010: An attempt to derive the ε equation from a two-point closure. J. Atmos. Sci., 67, 1678-1685, doi:10.1175/2009JAS3290.1.
The goal of this paper is to derive the equation for the turbulence dissipation rate ε for a shear driven flow. In 1961, Davydov used a one-point closure model to derive the ε equation from first principles but the final result contained undetermined terms and thus lacked predictive power. Both in 1987 (Schiestel) and in 2001 (Rubinstein and Zhou), attempts were made to derive the ε equation using a two-point closure, but their method relied on a phenomenological assumption. The standard practice has thus been to employ a heuristic form of the ε equation that contains three empirical ingredients: two constants, c1ε and c2ε, and a diffusion term Dε. In this work, a two-point closure is employed, yielding the following results: 1) the empirical constants get replaced by c1, c2, which are now functions of K and ε; 2) c1 and c2 are not independent because a general relation between the two valid that are for any K and ε are derived; 3) c1, c2 become constant with values close to the empirical values c1ε, cε2 (i.e., homogeneous flows); and 4) the empirical form of the diffusion term Dε is no longer needed because it gets substituted by the K-ε dependence of c1, c2, which plays the role of the diffusion, together with the diffusion of the turbulent kinetic energy DK, which now enters the new ε equation (i.e., inhomogeneous flows). Thus, the three empirical ingredients c1ε, cε2, Dε are substituted with a single function c1(K,ε) or c2(K,ε), plus a DK term. Three tests of the new equation for ε are presented: one concerning channel flow and two concerning the shear-driven planetary boundary layer (PBL).
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BibTeX Citation
@article{ca08220s,
author={Canuto, V. M. and Cheng, Y. and Howard, A. M.},
title={An attempt to derive the ε equation from a two-point closure},
year={2010},
journal={Journal of the Atmospheric Sciences},
volume={67},
pages={1678--1685},
doi={10.1175/2009JAS3290.1},
}
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RIS Citation
TY - JOUR ID - ca08220s AU - Canuto, V. M. AU - Cheng, Y. AU - Howard, A. M. PY - 2010 TI - An attempt to derive the ε equation from a two-point closure JA - J. Atmos. Sci. JO - Journal of the Atmospheric Sciences VL - 67 SP - 1678 EP - 1685 DO - 10.1175/2009JAS3290.1 ER -
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