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Inertia-induced adiabatic structures in time-periodic laminar flows

Författare:	Pouransari, Z., Speetjens, M., Clercx, H.
Dokumenttyp:	Konferens
Tillstånd:	Publicerad
Tidskrift:	7th Eur. Fluid Mech. Conf. EFMC7, Manchester, 14-18 Sept. 2008.
Volym:	1 274
År:	2008

Abstract

Mixing quality in unsteady incompressible laminar flows can be greatly enhanced 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 topological properties of a viscous incompressible time-periodic flow in a square cylindrical 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. Previous investigations indicate formation of one coherent structure consisting of two incomplete adiabatic surfaces and two tubes with transversal motion in between, i.e. resonance-induced merger (RIM) for a specific forcing protocol (one step forward in x-direction followed by one step forward in y-direction)1. Here the adiabatic surfaces are remnants of perturbed invariant surfaces and tubes are centred upon elliptic 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 volume preserving map. Fundamental topological characteristics of the general two-step forcing protocol (as the building block for future protocols) have been examined numerically (Fig1-a) and the so called ‘RIM’ phenomena has been detected in the neighborhood of parabolic borders (Fig1-b,c). Key aspects of numerical simulation 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.