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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 of a coherent
structure. 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. Barriers and Transport in Unsteady
Flows provides:* An extensive introduction and bibliography,
specifically elucidating the difficulties arising when flows are
unsteady and highlighting relevance in geophysics and
microfluidics.* Careful and rigorous development of the
mathematical theory of unsteady flow barriers within the context of
nonautonomous stable and unstable manifolds, richly complemented
with examples.* Chapters on exciting new research in the control of
flow barriers and the optimization of transport across them.
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