?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: A Melnikov Approach?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; and chapters on exciting new research in the control of flow barriers and the optimization of transport across them.

Explore a wealth of proven mathematical methods for uncovering transport barriers in numerical, experimental and observational flow data.

This book constitutes the refereed proceedings of the First International Conference on Dynamic Data-Driven Environmental Systems Science, DyDESS 2014, held in Cambridge, MA, USA, in November 2014.The 24 revised full papers and 7 short papers were carefully reviewed and selected from 62 submissions and cover topics on sensing, imaging and retrieval for the oceans, atmosphere, space, land, earth and planets that is informed by the environmental context; algorithms for modeling and simulation, downscaling, model reduction, data assimilation, uncertainty quantification and statistical learning; methodologies for planning and control, sampling and adaptive observation, and efficient coupling of these algorithms into information-gathering and observing system designs; and applications of methodology to environmental estimation, analysis and prediction including climate, natural hazards, oceans, cryosphere, atmosphere, land, space, earth and planets.

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: A Melnikov Approach 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; and chapters on exciting new research in the control of flow barriers and the optimization of transport across them.

This book is comprised of selected research articles developed from a workshop on Ergodic Theory, Probabilistic Methods and Applications, held in April 2012 at the Banff International Research Station. It contains contributions from world leading experts in ergodic theory, numerical dynamical systems, molecular dynamics and ocean/atmosphere dynamics, nonequilibrium statistical mechanics. The volume will serve as a valuable reference for mathematicians, physicists, engineers, biologists and climate scientists, who currently use, or wish to learn how to use, probabilistic techniques to cope with dynamical models that display open or non-equilibrium behavior.

One of the priority areas of ICSU (The International Council for Science) is “Natural and Human-Induced Environmental Hazards and Disasters”. The School — held at the Institute for Mathematical Sciences, Singapore from 20 April to 2 May 2009 — on which this volume is based on was sponsored by ICSU and by its members from IUTAM (the International Union of Theoretical and Applied Mechanics) and IUGG (the International Union of Geodesy and Geophysics).This volume provides an indepth graduate-level introduction to the fluid dynamics and geophysics of hazards such as tropical cyclones, flooding, atmospheric pollution and tsunamis. It also includes discussion of the possible effects of climate change on these phenomena. Indeed, the current importance of this area is of great public concern.