A point vortex dipole model of an isolated modon
A point vortex dipole model of an isolated modon
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孤立模子的点涡偶极子模型
DOI：
10.1063/1.857846
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发表时间：
1991
影响因子：
4.6
通讯作者：
D. Hobson
中科院分区：
文献类型：
--
作者：
D. Hobson
本文在Zabusky和McWilliams [Phys. Fluids 25，2175（1982）]的点涡公式的基础上，发展了一个由Charney-Hasegawa-米马（CHM）方程控制的孤立模态子的点涡偶极子模型。将模型偶极子与精确的modon解进行比较，以确定模型偶极子与modon的速度和远场行为相匹配的参数值。该模型允许一个研究非均匀运动的分析。它预测，匀速运动的右移模子应该是稳定的，因为它们的路径会响应于它们初始方向的小扰动而表现出小振幅振荡。它还预言了匀速运动的左移模子应该是不稳定的，被任意小的扰动推入有限振幅运动。这些预测证实了CHM方程下的modons演变的直接数值模拟。本文指出，尽管模态子内的涡度分布在近场区域可能是李雅普诺夫稳定的，但在近场区域内，模态子内的涡度分布可能是李雅普诺夫稳定的。
A point vortex dipole model for an isolated modon governed by the Charney–Hasegawa–Mima (CHM) equation is developed, building on the point vortex formulation of Zabusky and McWilliams [Phys. Fluids 25, 2175 (1982)]. The model dipole is compared to the exact modon solution in order to determine parameter values for which the model dipole matches the modon’s speed and far‐field behavior. The model allows one to study nonuniform motions analytically. It predicts that right‐moving modons in uniform motion should be stable in the sense that their paths exhibit small‐amplitude oscillations in response to small perturbations of their initial orientation. It also predicts that left‐moving modons in uniform motion should be unstable, being pushed into finite‐amplitude motions by arbitrarily small perturbations. These predictions are confirmed by direct numerical simulation of modons evolving under the CHM equation. It is noted that although the distribution of vorticity within modons may be Lyapunov stable in near...