Abstract
It is important to investigate the mechanism of fluid transportations, for example, in order to estimate the diffusion of contaminants in the environment or to efficiently mix up different kinds of liquid in a chemical plant. On the other hand, it is known that fluid particles are transported chaotically in Lagrangian description even when the flow is seen to be stable in Eulerian description. In this paper, we investigate such a chaotic mixing of the two-dimensional Rayleigh-Benard convection with some periodic perturbations in Lagrangian description by focusing on the invariant structures such as KAM tori and Lagrangian coherent structures (LCSs). We numerically show that the topological structure of LCSs comes to resemble that of Poincare maps when the integration time for LCS is large enough, though they do not have a clear relationship when the integration time is small enough. In addition, we show that the fluid particles at the center of KAM tori are transported periodically inside the convection. In particular, we illustrate that the quasi-periodic regions themselves rotate around the center of KAM tori and are transported periodically, even though each particle inside quasi-periodic regions is transported quasi-periodically. This implies that KAM tori have a twisted structure in state space. Finally we clarify the bifurcation diagram of the periodic orbits at the center of KAM tori by varying the amplitude of the perturbation of the convection.
