Nondimensionalization of the Atmospheric Boundary-Layer System: Obukhov Length and Monin–Obukhov Similarity Theory
Nondimensionalization of the Atmospheric Boundary-Layer System: Obukhov Length and Monin–Obukhov Similarity Theory
复制标题
大气边界层系统的无量纲化：Obukhov 长度和 Monin-Obukhov 相似理论
DOI：
10.1007/s10546-021-00657-7
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发表时间：
2021
影响因子：
4.3
通讯作者：
M. Wacławczyk
中科院分区：
文献类型：
--
作者：
J. Yano;M. Wacławczyk
Obukhov长度，虽然经常被采用作为大气边界层的特征尺度，已被引入纯粹基于尺寸参数没有从控制方程的演绎推导。在这里，它的推导是追求的无量纲化的方法，以同样的方式为罗斯比变形半径和埃克曼层深度。的Obukhov长度的物理意义推断通过无量纲化的水平均匀边界层的湍流动能方程。一个无量纲化的长度尺度为一整套方程的边界层流动正式减少到奥布霍夫长度除以这个尺度的重新缩放因子。这个重新缩放因子随着边界层稳定分层的增加而增加，其中流动倾向于更水平和更温和;因此Obukhov长度逐渐失去其相关性。一个启发式的，但演绎，推导莫宁-奥布霍夫相似性理论的基础上得到的无量纲化结果也概述。
The Obukhov length, although often adopted as a characteristic scale of the atmospheric boundary layer, has been introduced purely based on a dimensional argument without a deductive derivation from the governing equations. Here, its derivation is pursued by the nondimensionalization method in the same manner as for the Rossby deformation radius and the Ekman-layer depth. Physical implications of the Obukhov length are inferred by nondimensionalizing the turbulence-kinetic-energy equation for the horizontally homogeneous boundary layer. A nondimensionalization length scale for a full set of equations for boundary-layer flow formally reduces to the Obukhov length by dividing this scale by a rescaling factor. This rescaling factor increases with increasing stable stratification of the boundary layer, in which flows tend to be more horizontal and gentler; thus the Obukhov length increasingly loses its relevance. A heuristic, but deductive, derivation of Monin–Obukhov similarity theory is also outlined based on the obtained nondimensionalization results.