On the beta-drift of an initially circular vortex patch
On the beta-drift of an initially circular vortex patch
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关于最初圆形涡斑的 β 漂移
DOI：
10.1017/s0022112001003974
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发表时间：
2001
影响因子：
3.7
通讯作者：
D. Dritschel
中科院分区：
文献类型：
--
作者：
J. Lam;D. Dritschel
本文以前所未有的空间分辨率数值研究了在单层准地转流体和背景行星涡度梯度中涡斑的非线性无粘演化。这种演化受两个无量纲参数的控制：涡旋的初始大小（半径）与罗斯比变形半径的比较，以及涡旋的初始强度与整个涡旋中行星涡度的变化的比较。结果表明，涡旋的纬向速度随涡旋强度的增大而增大。然而，在中等涡强度下，涡速度达到最大值。大的和弱的旋涡都容易变形，常常变成椭圆形和三极形。这种变形被证明与没有行星涡度梯度β时瞬时涡度分布的不稳定性有关。所采用的极高的数值分辨率揭示了流动演化的一个显著特征，即在旋涡周围产生非常尖锐的涡度梯度，并及时向下游延伸。这些梯度的形成是因为涡旋在传播时迫使背景行星涡度轮廓偏离其路径。靠近旋涡的轮廓在旋涡周围迅速旋转并均匀化，但在某个临界距离处，旋涡不够强，相反，形成了急剧的涡度梯度。这个急剧梯度内的区域被称为“陷阱区”，尽管它会随着时间的推移缓慢收缩并泄漏。这种泄漏发生在一个狭窄的尾流中，称为“后缘”，这是另一个急剧涡度梯度的区域，延伸到涡流后面。
The nonlinear inviscid evolution of a vortex patch in a single-layer quasi-geostrophic fluid and within a background planetary vorticity gradient is examined numerically at unprecedented spatial resolution. The evolution is governed by two dimensionless parameters: the initial size (radius) of the vortex compared to the Rossby deformation radius, and the initial strength of the vortex compared to the variation of the planetary vorticity across the vortex. It is found that the zonal speed of a vortex increases with its strength. However, the meridional speed reaches a maximum at intermediate vortex strengths. Both large and weak vortices are readily deformed, often into elliptical and tripolar shapes. This deformation is shown to be related to an instability of the instantaneous vorticity distribution in the absence of the planetary vorticity gradient β. The extremely high numerical resolution employed reveals a striking feature of the flow evolution, namely the generation of very sharp vorticity gradients surrounding the vortex and extending downstream of it in time. These gradients form as the vortex forces background planetary vorticity contours out of its way as it propagates. The contours close to the vortex swirl rapidly around the vortex and homogenize, but at some critical distance the swirl is not strong enough and, instead, a sharp vorticity gradient forms. The region inside this sharp gradient is called the ‘trapped zone’, though it shrinks slowly in time and leaks. This leaking occurs in a narrow wake called the ‘trailing front’, another zone of sharp vorticity gradients, extending behind the vortex.