大气阻塞Charney-De Vore准地转方程的能量稳定性

Energy stability of the Charney-DeVore quasi-geostrophic equation for atmospheric blocking

Charney和DeVore(1979)发现,由于地形的影响,β平面槽道中正压大气的准地转流动有多个平衡态.本文证明了这种流动的基本流在某个参数范围内(包括平坦地表的特殊情形)是渐近稳定的,因此排除了这一参数范围内存在多个平衡态的可能性.本文作者还发现,为了使Charney-DeVore准地转方程适定,需要补充一个平均经向力或平均经向速度的条件.本文在不同的地表起伏幅度下,采用拟弧长延拓法证实至少存在3个平衡态;还通过高精度直接数值模拟研究了这些平衡态的稳定性.

Charney and DeVore(1979)found the multiple equilibrium states as a consequence of bottom topography in their pioneering work on the quasi-geostrophic barotropic flow over topography in aβ-plane channel.In the present paper,we prove that the basic flow is asymptotically stable in a parameter region,including the flat topography situation,which excludes the existence of multiple equilibrium states therein.Moreover,we show that an additional condition on the average zonal force or the average zonal velocity is indispensable to the wellposedness of the Charney-DeVore quasi-geostrophic equation.The coexistence of at least three equilibrium states is confirmed by a pseudo-arclength continuation method for different topographic amplitudes.The stabilities of the equilibrium states are examined by high-resolution direct numerical simulations.