Recent progress in experimental and computational studies of complex chaotically advected 3D flows is reviewed for the confined swirling flow in a cylindrical container with a rotating bottom and the open flow in a helical static mixer. The concept of Lagrangian averaging along particle paths, whose theoretical foundation stems from ergodic theory, is proposed as a powerful tool for constructing Poincare´ maps in numerical studies of confined flows. The same concept has also been employed to develop the first non-intrusive experimental technique for constructing Poincare´ maps in complex 3D flows. The potential of these ergodic concepts is demonstrated in computational and experimental studies for the confined swirling flow. Numerical computations for the helical mixer flow show that increasing the Reynolds number from Re = 100 to 500 leads to the appearance of unmixed islands in the flow. The mechanism that leads to the formation of such islands is shown to be linked to the growth of coherent helical vortices in the flow.

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