Mixing rates and symmetry breaking in two-dimensional chaotic flow

Abstract

We experimentally determine the mixing rate for a magnetically forced two-dimensional time-periodic flow exhibiting chaotic mixing. The mixing rate, defined as the rate of decay of the root-mean square concentration inhomogeneity, grows with Reynolds number, but does not increase at the onset of nonperiodic (weakly turbulent) flow. The mixing rate increases linearly with a second non-dimensional parameter, the typical path length of a fluid element in one forcing period. The breaking of time-reversal symmetry and spatial reflection symmetry substantially increases the mixing rates. A theory by Antonsen et al. that predicts mixing rates in terms of the measured Lyapunov exponents of the flow is tested and found to predict mixing rates that are too large by approximately a factor of 10; the discrepancy is traced to the fact that large scale transport rather than stretching of fluid elements is the dominant rate limiting step when the system is sufficiently large compared to the velocity correlation length. An effective diffusion model gives a good account of the measured mixing rates. Finally, the formation of persistent recurrent patterns (also called strange eigenmodes) is shown to arise from a combination of stretching and effective diffusion.