Mixing, entrainment and fractal dimensions of surfaces in turbulent flows

Abstract
Some basic thoughts are set down on the relation between the fractal dimension of various surfaces in turbulent flows, and the practically important processes of mixing between two streams (reacting or otherwise) separated by a convoluted surface, as well as of entrainment of irrotational flow by a turbulent stream. An expression based on heuristic arguments is derived for the flux of transportable properties (such as mass, momentum, and energy) across surfaces, and a prediction made on this basis for the fractal dimension of surfaces in fully turbulent flows is shown to be in essential agreement with measurements. It is further shown that this prediction remains robust when corrected for the non-uniform effects along the surface. A related prediction concerning the dependence of mixing on the Reynolds number and the fractal dimension of the surface is substantiated, in the developing as well as the fully developed states, by independent measurements of both the fractal dimension and the amount of mixing between reactants in a temporally evolving countercurrent shear flow.