After first reviewing historical and current difficulties in solving streamfunction and velocity potential in a limited domain, and describing recent developments in obtaining accurate solutions in a limited domain with arbitrary shape, a newly proposed approach is introduced and its application to a torrential rain event is reported. The results show that the newly developed method has advantages in capturing mesoscale information, compared with horizontal winds.
从流函数和速度势在天气和气候诊断分析、资料同化等领域的应用出发，文章首先回顾了全球流函数速度势求解的直观精确以及有限区域问题的复杂性，在简要检查已有的求解方法在数学精度和物理意义方面的优劣之后，介绍最近提出的新方法，并把它用到一次暴雨过程的检验中，发现新方法不但计算精度和效率高，还能从原始流场捕获中尺度天气信息。对历史问题的回顾和对新方法的应用，可能会让气象界意识到研究大气旋转-辐散相互作用及其维持机制的重要性。