期刊
PHYSICA D-NONLINEAR PHENOMENA
卷 211, 期 1-2, 页码 23-46出版社
ELSEVIER
DOI: 10.1016/j.physd.2005.07.017
关键词
mixing; chaotic advection
We present a multiscale measure for mixing that is based on the concept of weak convergence and averages the mixedness of an advected scalar field at various scales. This new measure, referred to as the Mix-Norm, resolves the inability of the L 2 variance of the scalar density field to capture small-scale variations when advected by chaotic maps or flows. In addition, the Mix-Norm succeeds in capturing the efficiency of a mixing protocol in the context of a particular initial scalar field, wherein Lyapunov-exponent based measures fail to do so. We relate the Mix-Norm to the classical ergodic theoretic notion of mixing and present its formulation in terms of the power spectrum of the scalar field. We demonstrate the utility of the Mix-Norm by showing how it measures the efficiency of mixing due to various discrete dynamical systems and to diffusion. In particular, we show that the Mix-Norm can capture known exponential and algebraic mixing properties of certain maps. We also analyze numerically the behaviour of scalar fields evolved by the Standard Map using the Mix-Norm. (c) 2005 Elsevier B.V. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据