## Publication Abstracts

### Canuto et al. 2010

**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_{1ε} and c_{2ε}, and a diffusion term D_{ε}. In this work, a two-point closure is employed, yielding the following results: 1) the empirical constants get replaced by c_{1}, c_{2}, which are now functions of K and ε; 2) c_{1} and c_{2} are not independent because a general relation between the two valid that are for any K and ε are derived; 3) c_{1}, c_{2} become constant with values close to the empirical values c_{1ε}, c_{ε2} (i.e., homogeneous flows); and 4) the empirical form of the diffusion term D_{ε} is no longer needed because it gets substituted by the K-ε dependence of c_{1}, c_{2}, which plays the role of the diffusion, together with the diffusion of the turbulent kinetic energy D_{K}, which now enters the new ε equation (i.e., inhomogeneous flows). Thus, the three empirical ingredients c_{1ε}, c_{ε2}, D_{ε} are substituted with a single function c_{1}(K,ε) or c_{2}(K,ε), plus a D_{K} 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={J. Atmos. Sci.}, 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. VL - 67 SP - 1678 EP - 1685 DO - 10.1175/2009JAS3290.1 ER -

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