Point Vortex Models for Modon Dynamics

[摘要] We study the dynamics of modons in the Charney-Hasegawa-Mima equation using a point vortex model introduced by Zabusky and McWilliams. This model reduces the equation to a system of ordinary differential equations which facilitate systematic studies of several problems involving modons. These problems are relevant to the study of large-scale motions in the Earth's atmosphere as well as the study of microturbulence in tokamak plasmas. We study the possible motions of an isolated modon using the model and show by direct numerical simulation that these motions compare very well with those of actual modons. As a by-product, we discover that the path of a left-moving (westward) modon is actually unstable to small perturbations in its position or orientation. This points out that a modon may be unstable in the path sense even if it is stable in the Lyapunov sense, as was shown for left-moving modons by Laedke and Spatschek. We use the flow field generated by the model to study the flow of fluid around an isolated modom. We show that the separatrices enclosing a modon in uniform motion break and tangle in the fashion described by Poincare when the motion is nonuniform. This is established analytically by computation of a Melnikov integral and numerically by plotting invariant manifolds of stagnation points in the flow. In contrast to past assumption, we find that significant mixing occurs between the modon and the external flow when the modon is not in uniform motion. So, at least on long timescales, modons do not serve as complete atmospheric blocks. Finally, we apply the model to the study of coaxial collisions between two modons. This results in a problem for the motion of four point vortices similar to that considered by Love for point vortices in the Euler equations. The relative behavior of the two modons is described completely by a planar Hamiltonian system which we study in detail. We find a wide variety of possible interactions between the two modons and note several behaviors not previously observed in numerical simulations. An effort is made to relate these results to the fluid inside a tokamak which may contain many such modons with frequent collisions.

[发布机构] University:California Institute of Technology;Department:Engineering and Applied Science

[关键词] Applied Mathematics