【摘要】 本文利用MHD二维不可压模式,研究了地球磁层顶边界区剪切流引起的Kelvin-Helmholtz(K-H)不稳定性问题,得到了一个新的非线性微分方程组.理论和数值分析表明:该问题的非线性演化对初值非常敏感,而且在雷诺数和磁雷诺数给定的条件下,Alfven马赫数(M_A)对K-H不稳定性的非线性演化起决定性作用.这组方程蕴含几个吸引子,如不动点,极限环和奇异吸引子等,这体现了磁层顶非线性系统的复杂性.文中还发现背景磁场在磁层顶K-H不稳定性的非线性演化过程中起很重要的作用.更多还原

【Abstract】 A model of two-dimensional incompressibl MHD is studied in an effort to understand the nature of the nonlinear evolution of Kelvin-Helmholtz instability in the presence of shear flow fields at the magnetopause boundary layer. A new set of nonlinear differential equa-tions for describing the model has been derived by using truncated Fourier expansions.Their numerical solutions are examined, and trajected in phase space. It is found that slightly differing initial conditions can be evolve into considerable different states, and Alfven Mach number MA plays a leading role in the nonlinear evolution of the system. It is also found that the nonlinear system can exhibit a wealth of characteristic dynamical behaviors including steady state, Hopf bifurcation to periodic orbits, perio doubling bifurcations, chaotic solution (strange attractor), bifurcation from chaos to period solution and steady solution, and that compared to the intensity of the flow, the fluid becomes more stable if a strong or a weak magmetic field parallel to the flow.更多还原