Ageostrophic dynamics of an intense localized vortex on a β-plane
Ageostrophic dynamics of an intense localized vortex on a β-plane
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β 平面上强烈局部涡旋的地转动力学
DOI：
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发表时间：
2001
影响因子：
3.7
通讯作者：
R. Grimshaw
中科院分区：
文献类型：
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作者：
G. M. Reznik;R. Grimshaw
利用浅水模型研究了β平面上强局域涡旋的非定常动力学。在Rossby数较小、自由面高度较小但有限的情况下，建立了具有分段连续位涡的旋涡的渐近理论。类似于著名的准地转模式，涡旋平移是由涡旋附近发展的次生偶极子环流(β环流)产生的，由两部分组成。第一部分(地转β环流)与地转模式中的β环流相吻合，第二部分(非地转β环流)是由于控制方程中的非地转项所致。非地转β涡旋的时间演化分为快阶段和慢阶段。在快阶段，惯性重力波的辐射导致β回旋场从零快速发展到与快时间变量无关的偶极子场。相应地，涡旋几乎是瞬间加速的(与典型的旋转时间相比)，达到平移速度的某个限定值。在下一慢速阶段，惯性重力波辐射不明显，β涡旋随典型的旋转时间演化。地转和非地转β涡旋引起的总纬向平移速度随着时间的增加而趋于稳定平移单极的速度，超过(不超过)反气旋(气旋)的Rossby波的漂移速度。这种气旋/反气旋的不对称性推广了众所周知的发现，即相对于非稳定演化的单极的情况，反气旋的寿命比气旋更长。分析了惯性重力波对涡旋演化的影响。这些波的主要作用是为“缓慢”的涡旋演变提供“快速”调整。与地转β涡旋的能量相比，惯性重力波的能量可以忽略不计。非地转涡演变的另一个特征是位涡斑块的面积随时间变化，气旋性斑块收缩，反气旋性斑块扩张。
We consider the non-stationary dynamics of an intense localized vortex on a β-plane using a shallow-water model. An asymptotic theory for a vortex with piecewise-continuous potential vorticity is developed assuming the Rossby number to be small and the free surface elevation to be small but finite. Analogously to the well-known quasi-geostrophic model, the vortex translation is produced by a secondary dipole circulation (β-gyres) developed in the vortex vicinity and consisting of two parts. The first part (geostrophic β-gyres) coincides with the β-gyres in the geostrophic model, and the second (ageostrophic β-gyres) is due to ageostrophic terms in the governing equations. The time evolution of the ageostrophic β-gyres consists of fast and slow stages. During the fast stage the radiation of inertia–gravity waves results in the rapid development of the β-gyres from zero to a dipole field independent of the fast time variable. Correspondingly, the vortex accelerates practically instantaneously (compared to the typical swirling time) to some finite value of the translation speed. At the next slow stage the inertia–gravity wave radiation is insignificant and the β-gyres evolve with the typical swirling time. The total zonal translation speed induced by the geostrophic and ageostrophic β-gyres tends with increasing time to the speed of a steadily translating monopole exceeding (not exceeding) the drift velocity of Rossby waves for anticyclones (cyclones). This cyclone/anticyclone asymmetry generalizes the well-known finding about the greater longevity of anticyclones compared to cyclones to the case of non-stationary evolving monopoles. The influence of inertia–gravity waves upon the vortex evolution is analysed. The main role of these waves is to provide a ‘fast’ adjustment to the ‘slow’ vortex evolution. The energy of inertia–gravity waves is negligible compare to the energy of the geostrophic β-gyres. Yet another feature of the ageostrophic vortex evolution is that the area of the potential vorticity patch changes in the course of time, the cyclonic patch contracting and the anticyclonic one expanding.