标题： 三维混沌流场中的平流和扩散 显示英文标题

标题： Advection and diffusion in a three dimensional chaotic flow

摘要： 通过全局拉格朗日坐标变换研究了对流扩散方程。 拉格朗日坐标的度量张量严格地将动力系统理论耦合到这类偏微分方程的解中。 如果流动具有混沌流线，则扩散将在临界时间主导解，该临界时间与扩散率对数相关。 随后的快速扩散松弛在几个李雅普诺夫时间尺度内完成，并且随着扩散率的减小，它变得更加各向异性。 流动的局部李雅普诺夫时间是有限时间李雅普诺夫指数的倒数。 有限时间李雅普诺夫指数可以用两个收敛函数来表示，这两个函数负责对流和扩散输运的空间-时间复杂性。 这种复杂性在混沌区域中产生了一类新的扩散屏障，并在空间和时间上表现出类似分形的行为。 在具有剪切的可积流动中也存在快速和慢速扩散。 但与混沌流动不同的是，由于可积流动中的快速扩散严格局限于卡姆曲面上，因此可以维持标量场沿卡姆表面的大梯度。 显示英文摘要

摘要： The advection-diffusion equation is studied via a global Lagrangian coordinate transformation. The metric tensor of the Lagrangian coordinates couples the dynamical system theory rigorously into the solution of this class of partial differential equations. If the flow has chaotic streamlines, the diffusion will dominate the solution at a critical time, which scales logarithmically with the diffusivity. The subsequent rapid diffusive relaxation is completed on the order of a few Lyapunov times, and it becomes more anisotropic the smaller the diffusivity. The local Lyapunov time of the flow is the inverse of the finite time Lyapunov exponent. A finite time Lyapunov exponent can be expressed in terms of two convergence functions which are responsible for the spatio-temporal complexity of both the advective and diffusive transports. This complexity gives a new class of diffusion barrier in the chaotic region and a fractal-like behavior in both space and time. In an integrable flow with shear, there also exist fast and slow diffusion. But unlike that in a chaotic flow, a large gradient of the scalar field across the KAM surfaces can be maintained since the fast diffusion in an integrable flow is strictly confined within the KAM surfaces.