LAGRANGIAN CHAOS, EULERIAN CHAOS, AND MIXING ENHANCEMENT IN CONVERGING-DIVERGING CHANNEL FLOWS

A study of Lagrangian chaos, Eulerian chaos, and mixing enhancement in converging-diverging channel flows, using spectral element direct num erical simulations, is presented. The time-dependent, incompressible N avier-Stokes and continuity equations are solved for laminar, transiti onal, and chaotic flow regimes for 100 less than or equal to Re less t han or equal to 850. Classical fluid dynamics representations and dyna mical system techniques characterize Eulerian flows, whereas Lagrangia n trajectories and finite-time Lagrangian Lyapunov exponents identify Lagrangian chaotic flow regimes and quantify mixing enhancement. Class ical representations demonstrate that the flow evolution to an aperiod ic chaotic regime occurs through a sequence of instabilities, leading to three successive supercritical Hopf bifurcations. Poincare sections and Eulerian Lyapunov exponent evaluations verify the first Hopf bifu rcation at 125<Re<150 and the onset of Eulerian chaos at Re approximat e to 550. Lagrangian trajectories and finite-time Lagrangian Lyapunov exponents reveal the onset of Lagrangian chaos, its relation with the appearance of the first Hopf bifurcation, the interplay between Lagran gian and Eulerian chaos, and the coexistence of Lagrangian chaotic flo ws with Eulerian nonchaotic velocity fields. Last, Lagrangian and Eule rian Lyapunov exponents are used to demonstrate that the onset of Eule rian chaos coincides with the spreading of a strong Lagrangian chaotic regime from the vortex region to the whole fluid domain. (C) 1996 Ame rican Institute of Physics.