Optimal mixing in three-dimensional plane Poiseuille flow at high Peclet number
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Abstract
We consider a passive zero-mean scalar field organised into two layers of different concentrations in a three-dimensional plane channel flow subjected to a constant along-stream pressure gradient. We employ a nonlinear direct-adjoint-looping method to identify the optimal initial perturbation of the velocity field with given initial energy which yields maximal' mixing by a target time horizon, where maximal mixing is defined here as the minimisation of the spatially-integrated variance of the concentration field. We verify in three-dimensional flows the conjecture by Foures et al. (J. Fluid Mech., vol. 748, 2014, pp. 241-277) that the initial perturbation which maximizes the time-averaged energy gain of the flow leads to relatively weak mixing, and is qualitatively different from the optimal initial
mixing' perturbation which exploits classical Taylor dispersion. We carry out the analysis for two different Reynolds numbers (mix-norm' of the concentration eld, i.e. a Sobolev norm of negative index in the class introduced by Mathew et al. (Physica D, vol. 211, pp. 23-46, 2005). We show that the
true' variance-based mixing strategy can be successfully and practically approximated by the mix-norm minimisation since we f ind that the mix-norm optimal initial perturbations are far less sensitive to
changes in the target time horizon than their optimal variance-minimising counterparts.
Description
Keywords
Journal Title
Conference Name
Journal ISSN
1469-7645
Volume Title
Publisher
Publisher DOI
Sponsorship
Engineering and Physical Sciences Research Council (EP/H023348/1)