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Inertia-induced adiabatic structures in time-periodic laminar flows
||7th Eur. Fluid Mech. Conf. EFMC7, Manchester, 14-18 Sept. 2008.
Mixing quality in unsteady incompressible laminar flows can be greatly
by three-dimensional (3D) chaotic advection. A significant issue for mixing
applications is the response of invariant surfaces, which the
non-inertial limit (Re=0)
of such flows may admit, to fluid inertia (Re>0). We have studied
properties of a viscous incompressible time-periodic flow in a square
domain. In particular we have focused on the response of the one-action
state to the
inertial perturbations for the general two-step volume preserving maps.
investigations indicate formation of one coherent structure consisting
incomplete adiabatic surfaces and two tubes with transversal motion in
resonance-induced merger (RIM) for a specific forcing protocol (one step
x-direction followed by one step forward in y-direction)1. Here the
are remnants of perturbed invariant surfaces and tubes are centred upon
segments of periodic lines. In this study we have validated and examined the
formation of such coherent structures by RIM for any arbitrary two-step
preserving map. Fundamental topological characteristics of the general
forcing protocol (as the building block for future protocols) have been
numerically (Fig1-a) and the so called ‘RIM’ phenomena has been detected
neighborhood of parabolic borders (Fig1-b,c). Key aspects of numerical
results are validated by means of an experimental visualization method.
Furthermore the above analytical and numerical studies have been
extended to the
three-step closed loop map, i.e. bottom wall is translated while
following a triangle.
This enables infinite repetition in a laboratory set-up using finite
walls and thus
facilitates detailed experimental analysis of RIM.