Myers Hill, J, Sturman, R and Wilson, MCT (2022) Exponential mixing by orthogonal non-monotonic shears. Physica D: Nonlinear Phenomena, 434. 133224. ISSN 0167-2789
Abstract
Non-monotonic velocity profiles are an inherent feature of mixing flows obeying non-slip boundary conditions. There are, however, few known models of laminar mixing which incorporate this feature and have proven mixing properties. Here we present such a model, alternating between two non-monotonic shear flows which act in orthogonal (i.e. perpendicular) directions. Each shear is defined by an independent variable, giving a two-dimensional parameter space within which we prove the mixing property over open subsets. Within these mixing windows, we use results from the billiards literature to establish exponential mixing rates. Outside of these windows, we find large parameter regions where elliptic islands persist, leading to poor mixing. Finally, we comment on the challenges of extending these mixing windows and the potential for a non-exponential mixing rate at particular parameter values.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
Keywords: | Laminar mixing; Non-uniform hyperbolicity; Deterministic chaos |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 30 Mar 2022 15:54 |
Last Modified: | 30 Mar 2022 16:01 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.physd.2022.133224 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:185220 |