COMPARISONS OF MIXING IN CHAOTIC AND TURBULENT FLOWS

Results are presented from an experimental investigation comparing geo metric 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-dimensio nal, time-periodic, closed flow between eccentric rotating cylinders i s taken as the archetypal chaotic flow. The turbulent flow for compari son is the high Reynolds number, three-dimensional, unsteady, open flo w in the self-similar far field of a steady axisymmetric jet. For each flow, the concentration field zeta(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 r ate field (ReSc)-1delzeta . delzeta(x,t) is concentrated. The distribu tions of dissipation layer separations obtained for both flows are fou nd to be identical. Contrary to central limit arguments for multiplica tive quantities, the ensemble-averaged distributions in both flows hav e a -3 power law scaling for all but the smallest separations; classic al log-normal scaling for multiplicative processes is found only in re gions having undergone extensive stretching and folding. A statistical assessment of the fractal scaling properties based on one-dimensional intersections with the disspation support set demonstrates that the c haotic flow at this stage of development approaches a global fractal d imension only in these same regions. Unlike previous studies of the fr actal scaling of scalar isosurfaces in turbulent flows, the results fo r the turbulent flow presented here show no strong evidence for global fractal scaling in the dissipation support set.