非线性垂直平流作用对大气边界层风场的影响

THE INFLUENCE OF NON-LINEAR EFFECT OF VERTICAL ADVECTION ON THE WIND FIELD IN THE PBL

本文在WuandBlumen[1]将地转动量近似引入行星边界层和TanandWu[2]-[4]将地转动量近似发展为Ekman动量近似的工作基础上，在下述三个方面作了改进：（1）在Ekman层中，用一个与实测较接近的随高度变化的二次函数代替常值的湍流粘性系数K；（2）计入非线性垂直平流惯性力的作用；（3）将平地边界层推广为山地边界层。在四力平衡下（气压梯度力、柯氏力、摩擦力、惯性力包括水平平流惯性力和垂直平流惯性力）我们求得了边界层中的风速和垂直速度分布的解析解，且以极其简单的K的复初等函数来表达。将风速、垂直速度与湍流粘性系数直接联系起来，且呈现出显函数关系，这在理论上是有一定意义的。个例计算表明，与水平平流惯性力相比，垂直平流惯性力不能任意略去，特别是在山地边界层中，后者的作用甚至超过前者，这在应用上是一重要改进。另外，山地边界层顶的垂直速度由摩擦、非线性的水平和垂直平流、地形三方面的作用来决定。我们的模式表明，摩擦和地形之间有着非线性关系，这与Pedlosky[5]的摩擦和地形作用之间互相独立的结论是不同的。

On the basis of Wu and Blumen's work (1982)on the geostrophic momentum approximation in the planetary boundary layer(PBL)and Tan and Wu (1991, 1992, 1994)on the Ekman momentum approximation in the PBL,following improvements are developed in this paper: (1)apply the eddy transfer coefficient K which is close to the usual distribution instead of a constant value in the Ekman layer,and introducing the surface layer, (2)take the effect of the vertical advective inertial force into account. (3)extend the PBL over level land to the PBL over orography. Under the condition of equilibrium among four forces(the pressure-gradient force,Coriolis force,turbulent friction force and inertial force including horizontal and vertical advective inertial forces),the analytical solutions of the distributions of the wind and the vertical velocity are obtained and expressed by a complex elementary function of K. This is of important significance,because it has connected the wind and vertical velocity with K and expressed their relation with and explicit function. The computation of individual example shows that: (1)Both the wind velocity near surface and the angle between which and the non-viscous wind are more consistent with usual observations than that of Wu and Blumen (1982); (2)comparing with the horizontal advective inertial force,the vertical advective inertial force can not be neglected, when the orography is considered,the efect of the latter is even more important than the former. The vertical velocity at the top of the PBL over orography is determined by the complex non-linear interactions among the turbulent friction, the horizontal and vertical advections of Ekman momentum and the lifting due to orography, the effect of turbulent friction is no longer independent of lifting due to orography (Pedlosky,1975). The investigation of the wind field in the PBL is profitable not only for the prediction of the PBL, but also for the parameterization of the PBL in the large-scale models and other dynamics problems