Publication Abstracts

Canuto et al. 2010

Canuto, V.M., Y. Cheng, and A.M. Howard, 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, c and c, 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 c, 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 c, 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

  author={Canuto, V. M. and Cheng, Y. and Howard, A. M.},
  title={An attempt to derive the ε equation from a two-point closure},
  journal={Journal of the Atmospheric Sciences},

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RIS Citation

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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