Katul Gabriel G, Porporato Amilcare, Shah Stimit, Bou-Zeid Elie
Nicholas School of the Environment, Duke University, Durham, North Carolina 27708-0328, USA and Department of Civil and Environmental Engineering, Duke University, Durham, North Carolina 27708, USA.
Department of Civil and Environmental Engineering, Princeton, New Jersey 08544, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Feb;89(2):023007. doi: 10.1103/PhysRevE.89.023007. Epub 2014 Feb 12.
In stably stratified turbulent flows, the mixing efficiency associated with eddy diffusivity for heat, or equivalently the turbulent Prandtl number (Pr(t)), is fraught with complex dynamics originating from the scalewise interplay between shear generation of turbulence and its dissipation by density gradients. A large corpus of data and numerical simulations agree on a near-universal relation between Pr(t) and the Richardson number (R(i)), which encodes the relative importance of buoyancy dissipation to mechanical production of turbulent kinetic energy. The Pr(t)-R(i) relation is shown to be derivable solely from the cospectral budgets for momentum and heat fluxes if a Rotta-like return to isotropy closure for the pressure-strain effects and Kolmogorov's theory for turbulent cascade are invoked. The ratio of the Kolmogorov to the Kolmogorov-Obukhov-Corrsin phenomenological constants, and a constant associated with isotropization of the production whose value (= 3/5) has been predicted from Rapid Distortion Theory, explain all the macroscopic nonlinearities.
在稳定分层的湍流中，与热涡扩散率相关的混合效率，或者等效地说，湍流普朗特数（Pr(t)），充满了复杂的动力学，这些动力学源于湍流的剪切生成与其由密度梯度引起的耗散之间的尺度相互作用。大量的数据和数值模拟在Pr(t)与理查森数（R(i)）之间达成了近乎普遍的关系，理查森数编码了浮力耗散对湍动能机械产生的相对重要性。如果调用压力 - 应变效应的类似罗塔（Rotta）的各向同性恢复闭合以及湍流级联的科尔莫戈罗夫（Kolmogorov）理论，Pr(t) - R(i)关系被证明仅可从动量和热通量的互谱预算中推导出来。科尔莫戈罗夫现象学常数与科尔莫戈罗夫 - 奥布霍夫 - 科辛（Kolmogorov - Obukhov - Corrsin）现象学常数的比值，以及与生成各向同性相关的一个常数，其值（= 3/5）已从快速畸变理论中预测出来，解释了所有宏观非线性。
