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Barriers and Transport in Unsteady Flows

Barriers and Transport in Unsteady Flows
A Melnikov Approach


Part of Monographs on Mathematical Modeling and Computation

  • Date Published: January 2017
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial null Mathematics for availability.
  • format: Paperback
  • isbn: 9781611974577

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About the Authors
  • Fluids that mix at geophysical or microscales tend to form well-mixed areas and regions of coherent blobs. The Antarctic circumpolar vortex, which mostly retains its structure while moving unsteadily in the atmosphere, is an example. How do such structures exchange fluid with their surroundings? What is the impact on global mixing? What is the 'boundary' of the structure, and how does it move? Can these questions be answered from time-varying observational data? This book addresses these issues from the perspective of the differential equations that must be obeyed by fluid particles. In these terms, identification of the boundaries of coherent structures (i.e. 'flow barriers'), quantification of transport across them, control of the locations of these barriers, and optimization of transport across them are developed using a rigorous mathematical framework. The concepts are illustrated with an array of theoretical and applied examples that arise from oceanography and microfluidics.

    • Presents a careful and rigorous development of the mathematical theory of unsteady flow barriers within the context of nonautonomous stable and unstable manifolds
    • Theory is richly complemented with examples
    • Includes chapters on exciting new research in the control of flow barriers and the optimization of transport across them
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    Product details

    • Date Published: January 2017
    • format: Paperback
    • isbn: 9781611974577
    • length: 276 pages
    • dimensions: 255 x 178 x 18 mm
    • weight: 0.6kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial null Mathematics for availability.
  • Table of Contents

    List of figures
    1. Unsteady (nonautonomous) flows
    2. Melnikov theory for stable and unstable manifolds
    3. Quantifying transport flux across unsteady flow barriers
    4. Optimizing transport across flow barriers
    5. Controlling unsteady flow barriers

  • Author

    Sanjeeva Balasuriya, University of Adelaide
    Sanjeeva Balasuriya is an Australian Research Council Future Fellow at the School of Mathematical Sciences, University of Adelaide. He has held positions at the University of Peradeniya, Sri Lanka, Oberlin College, Ohio, Connecticut College, and the University of Sydney. His work in ordinary differential equations is inspired by many applied areas, and he has published in the Journal of Fluid Mechanics, the Journal of Theoretical Biology, the Journal of Micromechanics and Microengineering, Combustion Theory and Modeling, and Physical Review Letters, among other journals. He was the advisor to a University of Adelaide team that won the INFORMS Prize at the 2015 Mathematical Contest in Modeling and was awarded the 2006 J. H. Michell Medal for outstanding early career researcher in applied mathematics by Australian and New Zealand Industrial and Applied Mathematics (ANZIAM).

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