再论地转流的正压不稳定

Barotropic Instability of Geostrophic Flow:The Problem Revisited

本文研究了考虑地转约束的情况下,正压不稳定的必要条件,并基于能量学和位涡动力学理论,对正压不稳定的必要条件的物理含义进行了诠释。对于满足地转平衡的基本流,瑞利—郭晓岚定理[(Rayleigh,1880)、Kuo(1949,1973)]修正为:若地转流可能出现不稳定,其位涡梯度需在某个纬度取极值。Fjortoft定理(Fjortoft,1950)相应地成为:若地转流可能出现不稳定,需满足Q_(y)(位涡的经向梯度)与U-U_(s)(地转流速度与Q_(y)为零处的地转流速度之差)同号。即由原结论中的绝对涡度修正为位涡,这是地转约束也是位涡约束的结果。研究指出满足能量关系是正压不稳定可能出现的能量学要求,瑞利—郭晓岚定理是正压不稳定可能出现的位涡动力学条件,而Fjortoft定理则是能量学与位涡动力学两种要求的协调,能量关系、瑞利—郭晓岚定理和Fjortoft定理三者均须满足,正压不稳定才有可能发生。

Rayleigh-Kuo and Fjørtoft theorems provide the necessary conditions for barotropic instability of a geophysical fluid flow.This instability corresponds to a geostrophic flow is crucial for the geophysical flow;therefore,this paper modifies two necessary conditions for this instability.The implication of the necessary conditions for barotropic instability is explained based on the energetics and potential vorticity dynamic theories.Rayleigh-Kuo theorem for the geostrophic flow is revised as follows:As a necessary condition for the barotropic instability of the geostrophic flow,the potential flow vorticity should have an extreme point.The Fjørtoft theorem(Fjørtoft,1950)correspondingly changes to the following:As a necessary condition for the barotropic instability of the geostrophic flow,Q_(y)(U-U_(s))>0 in the geostrophic flow field,where ys is a point at which Q_(y)=0 and U(ys)=Us.These modified conditions indicate that the absolute vorticity in the original theorems is modified to potential vorticity,which is a consequence of the geostrophic and potential vorticity constraints.The energy relation exhibits the energetics requirement for the potential barotropic instability.Rayleigh-Kuo theorem is a potential vorticity dynamic condition for the possible barotropic instability,and the Fjørtoft theorem is the coordination of two requirements corresponding to energetics and potential vorticity dynamics.All these three requirements must be met for the barotropic instability.