点涡动力系统的Lyapunov指数

平面上理想流体的三点涡系统是可积的Hamilton系统, 但其运动仍然相当复杂, 这给研究被动微粒在三点涡系统中运动带来了很大的困难. 着眼于点涡系统的被动微粒对初始小扰动的稳定性, 通过Oseledec定理定义被动微粒的Lyapunov指数, 给出了点涡系统中被动微粒稳定性的定量刻画. 同时, 由Hamilton系统的保体积性质得到的关于Lyapunov指数的简洁表达式, 避免了计算的繁琐. 利用这个定义, 点涡系的瞬时流场可以被划分成若干区域, 被动微粒的混沌运动只能在近涡的特定区域出现.

THE LYAPUNOV EXPONENT OF VORTEX DYNAMICS

Three-vortex system in an ideal fluid in the plane satisfies Hamiltonian form and the motion equations are integrable.However,the behavior of vertices are still complex so that it is difficult to study the passive particle in three point vertices system.Our focus is on the stability of passive particle with respect to an initial small perturbation,and Lyapunov exponent is introduced by employing Oseledec theory to describe the stability of passive particle quantitatively.In order to avoid fussy calculation,...