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Fluid Dynamics Seminar

Monday, April 30th, 2007, 4 PM
Cullimore Lecture Hall, Room 611
New Jersey Institute of Technology

The role of resonance phenomena in chaotic mixing

Roman Grigoriev

School of Physics, Georgia Institute of Technology

Abstract

Although the field of fluid mixing via chaotic advection is relatively new, it has matured enough for us to see some common features that reappear for different geometries and different physical mechanisms used for driving the flow. In this talk I will discuss two examples of mixing in near-integrable 3D volume-preserving flows: thermocapillary-driven droplets and a Lorenz-force driven cellular flow in a channel. In both cases a small perturbation of the integrable flow leads to the destruction of the exact invariants and the emergence of an adiabatic invariant. I will then show how the adiabatic invariant can be destroyed to enable essentially complete mixing by introducing either a separatrix (for a steady flow) or a resonant surface (for a time-periodic flow). I will also explain how the volume of the mixed domain and the mixing rate can be computed analytically for the class of flows considered.