Optimal perturbation for enhanced chaotic transport

Abstract

The issue of determining the best perturbation which results in optimal chaotic flux across a separatrix is addressed, using the Melnikov function and lobe dynamics. This theoretical analysis is motivated mainly through micro-fluidic devices for which this problem has become important recently. Both two- and three-dimensional flows are analysed. Utilising a Fourier transform representation, the nature of the perturbation which maximises this flux for each frequency value is obtained. The resulting optimally attainable flux is computed. A concise bound on this flux is presented in terms of the supremum norm of the normal component of the perturbing velocity, and the size of the heteroclinic manifold. In this instance where the spatial part of the perturbation is permitted to be chosen based on the frequency, it is shown that greater flux is achievable for smaller frequencies. The theory is illustrated through two examples. © 2005 Elsevier B.V. All rights reserved.