Effect of the Entrainment Flux Ratio on the Relationship between Entrainment Rate and Convective Richardson Number |
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| Authors: | Jianning Sun Yuan Wang |
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| Institution: | (1) Department of Atmospheric Sciences, Nanjing University, 22 HanKou Road, Nanjing, Jiangsu Province, 210093, P.R. China;(2) Key Laboratory of Mesoscale Severe Weather, Ministry of Education, 22 HanKou Road, Nanjing, Jiangsu Province, 210093, P.R. China |
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| Abstract: | The parameterization of the dimensionless entrainment rate (w
e
/w
*) versus the convective Richardson number (Ri
δθ
) is discussed in the framework of a first-order jump model (FOM). A theoretical estimation for the proportionality coefficient
in this parameterization, namely, the total entrainment flux ratio, is derived. This states that the total entrainment flux
ratio in FOM can be estimated as the ratio of the entrainment zone thickness to the mixed-layer depth, a relationship that
is supported by earlier tank experiments, and suggesting that the total entrainment flux ratio should be treated as a variable.
Analyses show that the variability of the total entrainment flux ratio is actually the effect of stratification in the free
atmosphere on the entrainment process, which should be taken into account in the parameterization. Further examination of
data from tank experiments and large-eddy simulations demonstrate that the different power laws for w
e
/w
* versus Ri
δθ
can be interpreted as the variability of the total entrainment flux ratio. These results indicate that the dimensionless
entrainment rate depends not only on the convective Richardson number but also upon the total entrainment flux ratio. |
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| Keywords: | Convective Richardson number Entrainment rate Entrainment zone thickness First-order jump model Total entrainment flux ratio |
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