The turbulent Prandtl number in a pure plume is 3/5
The turbulent Prandtl number in a pure plume is 3/5
复制标题
DOI：
10.1017/jfm.2017.259
复制
发表时间：
2017-06
影响因子：
3.7
通讯作者：
John Craske;P. Salizzoni;M. van Reeuwijk
中科院分区：
文献类型：
--
作者：
John Craske;P. Salizzoni;M. van Reeuwijk
我们推导出一个新的表达式的卷吸系数在湍流羽流使用平方平均浮力方程。所得到的表达式与以前的卷吸系数的关系的一致性意味着，在一个纯羽流的湍流普朗特数等于3/5时，速度和浮力的平均配置文件具有高斯形式的等宽。卷吸可以理解为体积通量、湍流动能的产生或主动或被动变量的标量方差的产生。这些观点的等价性表明卷吸系数和湍流普朗特和施密特数如何依赖于流的理查森数、环境分层以及速度和标量剖面的相对宽度。一般的框架是有效的自相似羽流，其特征在于由幂律缩放。对于射流和纯羽流，它表明，导出的关系是在合理的直接数值模拟和实验结果吻合。
We derive a new expression for the entrainment coefficient in a turbulent plume using an equation for the squared mean buoyancy. Consistency of the resulting expression with previous relations for the entrainment coefficient implies that the turbulent Prandtl number in a pure plume is equal to 3/5 when the mean profiles of velocity and buoyancy have a Gaussian form of equal width. Entrainment can be understood in terms of the volume flux, the production of turbulence kinetic energy or the production of scalar variance for either active or passive variables. The equivalence of these points of view indicates how the entrainment coefficient and the turbulent Prandtl and Schmidt numbers depend on the Richardson number of the flow, the ambient stratification and the relative widths of the velocity and scalar profiles. The general framework is valid for self-similar plumes, which are characterised by a power-law scaling. For jets and pure plumes it is shown that the derived relations are in reasonably good agreement with results from direct numerical simulations and experiments.