Comparisons of mixing in chaotic and turbulent flows

Abstract

Results are presented from an experimental investigation comparing geometric scaling properties created by the mixing of dynamically passive tracers in chaotic flows with those resulting at the small scales of fully developed turbulent flows. The low Reynolds number, two-dimensional, time-periodic, closed flow between eccentric rotating cylinders is taken as the archetypal chaotic flow. The turbulent flow for comparison is the high Reynolds number, three-dimensional, unsteady, open flow in the self-similar far field of a steady axisymmetric jet. For each flow, the concentration field ζ( x, t) resulting from the mixing of a conserved scalar quantity is used to measure scaling properties of the support set on which the corresponding scalar energy dissipation rate field ( ReSc) -1∇ζ·∇ζ( x, t) is concentrated. The distributions of dissipation layer separations obtained for both flows are found to be identical. Contrary to central limit arguments for multiplicative quantities, the ensemble-averaged distributions in both flows have a —3 power law scaling for all but the smallest separations; classical log-normal scaling for multiplicative processes is found only in regions having undergone extensive stretching and folding. A statistical assessment of the fractal scaling properties based on one-dimensional intersections with the dissipation support set demonstrates that the chaotic flow at this stage of development approaches a global fractal dimension only in these same regions. Unlike previous studies of the fractal scaling of scalar isosurfaces in turbulent flows, the results for the turbulent flow presented here show no strong evidence for global fractal scaling in the dissipation support set.