EXPERIMENTAL AND COMPUTATIONAL STUDIES OF MIXING IN COMPLEX STOKES FLOWS - THE VORTEX MIXING FLOW AND MULTICELLULAR CAVITY FLOWS

A complex Stokes flow has several cells, is subject to bifurcation, an d its velocity field is, with rare exceptions, only available from num erical computations. We present experimental and computational studies of two new complex Stokes flows: a vortex mixing flow and multicell f lows in slender cavities. We develop topological relations between the geometry of the flow domain and the family of physically realizable f lows; we study bifurcations and symmetries, in particular to reveal ho w the forcing protocol's phase hides or reveals symmetries. Using a va riety of dynamical tools, comparisons of boundary integral equation nu merical computations to dye advection experiments are made throughout. Several findings challenge commonly accepted wisdom. For example, we show that higher-order periodic points can be more important than peri od-one points in establishing the advection template and extended regi ons of large stretching. We demonstrate also that a broad class of for cing functions produces the same qualitative mixing patterns. We exper imentally verify the existence of potential mixing zones for adiabatic forcing and investigate the crossover from adiabatic to non-adiabatic behaviour. Finally, we use the entire array of tools to address an op timization problem for a complex flow. We conclude that none of the dy namical tools alone can successfully fulfil the role of a merit functi on; however, the collection of tools can be applied successively as a dynamical sieve to uncover a global optimum.