On the instability of geostrophic vortices
On the instability of geostrophic vortices
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论地转涡的不稳定性
DOI：
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发表时间：
1988
影响因子：
3.7
通讯作者：
G. Flierl
中科院分区：
文献类型：
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作者：
G. Flierl
本文用线性化的等值线动力学模式研究了正、斜压、准地转、f平面、圆形涡旋的不稳定性。我们使用一个圆形区域的水平均匀的位涡周围的环形均匀，但不同的，位涡的旋涡模型。我们主要集中于外半径B以外的基本状态中无环流的孤立涡。除了线性分析，我们还考虑弱非线性波。振幅方程具有三次非线性，并且根据三次项系数的符号，可以给出增长的非线性稳定或非线性增强。当外环足够窄时，正压孤立涡是不稳定的;另一方面，如果整个涡的尺度与斜压模态的变形半径相比足够小，则破裂可能优先于与涡的扭曲和倾斜相对应的深度变化扰动。随着涡旋的斜压性增强，大尺度涡旋也表现出椭圆型的斜压不稳定性，这种不稳定性对外环尺度的变化相对不敏感。当基本状态的斜压气流占主导地位时，扭转模式消失，我们只看到与环形区域足够强的剪切或与变形半径相比足够大的涡旋相关的不稳定性。有限振幅结果表明，对于足够大的涡旋，斜压不稳定模态是非线性稳定的，而在大多数情况下，另外两种不稳定模态是非线性不稳定的。
The instabilities of barotropic and baroclinic, quasi-geostrophic, f-plane, circular vortices are found using a linearized contour dynamics model. We model the vortex using a circular region of horizontally uniform potential vorticity surrounded by an annulus of uniform, but different, potential vorticity. We concentrate mostly upon isolated vortices with no circulation in the basic state outside the outer radius b. In addition to linear analyses, we also consider weakly nonlinear waves. The amplitude equation has a cubic nonlinearity and, depending upon the sign of the coefficient of the cubic term, may give nonlinear stabilization or nonlinear enhancement of the growth. Barotropic isolated eddies are unstable when the outer annulus is narrow enough; on the other hand, if the scale of the whole vortex is sufficiently small compared to the radius of deformation of a baroclinic mode, the break up may be preferentially to a depth-varying disturbance corresponding to a twisting and tilting of the vortex. As the vortex becomes more baroclinic, we find that large-scale vortices show an elliptical mode baroclinic instability as well which is relatively insensitive to the scale of the outer annulus. When the baroclinic currents in the basic state dominate, the twisting mode disappears, and we see only the instabilities associated with either strong enough shear in the annular region or sufficiently large vortices compared with the deformation radius. The finite amplitude results show that the baroclinic instability mode for large enough vortices is nonlinearly stabilized while in most cases, the other two kinds of instability are nonlinearly destabilized.