Chaotic response of the 2D semi-geostrophic and 3D quasi-geostrophic equations to gentle periodic forcing
نویسندگان
چکیده
Symmetries and Hamiltonian structure are combined with Melnikov’s method to show a set of exact solutions to the 2D semi-geostrophic equations in an elliptical tank respond chaotically to gentle periodic forcing of the domain eccentricity (or of the potential vorticity, for that matter) which are sinusoidal in time with nearly any period. A similar approach confirms the chaotic response of the quasi-geostrophic equations to gentle periodic forcing by an external shearing field. Our approach simplifies and strengthens the proof by Bertozzi (upon which it is based) concerning the chaotic response of Kirchoff elliptical vortex patches to gentle shearing in the 2D Euler equations.
منابع مشابه
Averaging Principle for Quasi-geostrophic Motions under Rapidly Oscillating Forcing
In this paper, the averaging principle for quasi-geostrophic motions with rapidly oscillating forcing is proved, both on nite but large time intervals and on the entire time axis. This includes comparison estimate, stability estimate, and convergence result between quasi-geostrophic motions and its averaged motions. Furthermore, the existence of almost periodic quasi-geostrophic motions and att...
متن کاملAveraging Principle for Quasi - Geostrophic
In this paper, the averaging principle for quasi-geostrophic motions with rapidly oscillating forcing is proved, both on nite but large time intervals and on the entire time axis. This includes comparison estimate, stability estimate, and convergence result between quasi-geostrophic motions and its averaged motions. Furthermore, the existence of almost periodic quasi-geostrophic motions and att...
متن کاملChaos in symmetric Hamiltonians applied to some exact solutions of the semi-geostrophic approximation of 2D Incompressible Euler equations
Certain symmetry properties of Hamiltonian systems possessing hyperbolic fixed points with homoclinic and heteroclinic saddle connections are exploited to conclude chaotic dynamics are present under time periodic perturbations. Specifically, the theorems are applied to a set of exact solutions to the semi-geostrophic equations in an elliptical elliptical tank. Introduction We start this paper o...
متن کاملOn the a priori estimates for the Euler, the Navier-Stokes and the quasi-geostrophic equations
We prove new a priori estimates for the 3D Euler, the 3D NavierStokes and the 2D quasi-geostrophic equations by the method of similarity transforms. ∗This research was supported partially by KRF Grant(MOEHRD, Basic Research Promotion Fund); (†) permanent address. AMS 2000 Mathematics Subject Classification: 35Q30, 76B03, 76D05.
متن کاملHigher Regularity for the Critical and Super-critical Dissipative Quasi-geostrophic Equations
We study the critical and super-critical dissipative quasi-geostrophic equations in R or T. Higher regularity of mild solutions with arbitrary initial data in Ḣ is proved. As a corollary, we obtain a global existence result for the critical 2D quasigeostrophic equations with periodic Ḣ data. Some decay in time estimates are also provided.
متن کامل