β-GMA与边界层动力学特征

β-GMA and Ekman Boundary Layer Dynamics

本文研究了β平面中的地转动量近似(β-GMA)及其成立条件.利用β-GMA得到了一个描述Ekman动力学特征的动力学方程组.研究了β项和地转动量(GM)对Ekman层动力学的共同作用.结果表明,β-GMA下的解由两部分组成,一部分即为f-GMA下的解,另一部分为β项与GM的相互作用解.这样,一方面,β-GMA解由于β项存在,对一个定常纬向对称的高度场具有纬向非对称结构,而f-GMA解是纬向对称的.利用一个定常、轴对称的圆形涡旋例子计算了Ekman层的水平风速和边界层顶部的垂直速度,并与经典解、f-GMA解作了详细的分析比较.

The geostrophic momentum approximation in the β - plane (β-GMA) and the condition of its validity are studied . A dynamical system of equations that describe motions in the Ekman boundary layer incorporating the β-GMA are derived. The effects of β-term and GM on the dynamics of boundary layer are studied. The solutions of β-GMA include two parts. One results from the solutions of f-GMA. The other results from the effect of the β-term and GM. Consequently, on one hand, the dynamics of β-GMA includes the one of f-GMA. On the other hand, the solution of f-GMA is longitudinally symmetric, but the one of β- GMA is not due to the effect of β-term for a steady, longitudinally symmetric height field. An example of a steady, axisymmetnc circular vortex is used to show the characteristics of the horizontal velocity field in the Ekman layer and the vertical veolicity at the top of PBL. These results are discussed in detail by comparing with the classical solutions and that obstained under f-GMA.