On the relative importance between chaotic mixing and diffusion

Abstract

In this paper, we discuss the concepts of mixing, transport and chaotic mixing and transport from the fluid mechanics view point and show that in the chaotic regions the mixing and transport is dominated by the chaotic mixing and transport process and in the weak chaotic region or regular region the mixing and transport is dominated by the diffusion process. The characteristic length scale and time scale to determine the relative importance between the two processes are derived through a scaling argument in terms of Lyapunov exponent and diffusivity. Using parameter values in the troposphere, we find a good agreement between the theoretic predictions here and our early experiment results. We speculate that for dynamically active field-like vorticity the chaotic mixing can act as agent for cascading motion into small scales and on the other hand these generated small scale motions can cascade into large scale motion indirectly.