Transport Barriers and Coherent Structures in Flow Data: Advective, Diffusive, Stochastic and Active Methods

by George Haller

Overview

Transport barriers are observed inhibitors of the spread of substances in flows. The collection of such barriers offers a powerful geometric template that frames the main pathways, or lack thereof, in any transport process. This book surveys effective and mathematically grounded methods for defining, locating and leveraging transport barriers in numerical simulations, laboratory experiments, technological processes and nature. It provides a unified treatment of material developed over the past two decades, focusing on the methods that have a solid foundation and broad applicability to data sets beyond simple model flows. The intended audience ranges from advanced undergraduates to researchers in the areas of turbulence, geophysical flows, aerodynamics, chemical engineering, environmental engineering, flow visualization, computational mathematics and dynamical systems. Detailed open-source implementations of the numerical methods are provided in an accompanying collection of Jupyter notebooks linked from the electronic version of the book.

Product Details

ISBN-13:	9781009225175
Publisher:	Cambridge University Press
Publication date:	03/16/2023
Pages:	426
Product dimensions:	7.17(w) x 10.24(h) x 0.94(d)

About the Author

George Haller holds the Chair in Nonlinear Dynamics at the Institute of Mechanical Systems of ETH Zürich. Previously, he held tenured faculty positions at Brown University, McGill University and MIT. For his research in nonlinear dynamical systems, he has received numerous recognitions including a Sloan Fellowship, an ASME T. Hughes Young Investigator award, a Manning Assistant Professorship at Brown and a Faculty of Engineering Distinguished Professorship at McGill. He is an elected fellow of the SIAM, APS, ASME and an external member of the Hungarian Academy of Science. He is the author of more than 150 publications.

Table of Contents

1. Introduction; 2. Eulerian and Lagrangian fundamentals; 3. Objectivity of transport barriers; 4. Barriers to chaotic advection; 5. Lagrangian and objective Eulerian coherent structures; 6. Flow separation and attachment surfaces as transport barriers; 7. Inertial LCSs: Transport barriers in finite-size particle motion; 8. Passive barriers to diffusive and stochastic transport; 9. Dynamically active barriers to transport; Appendix; References; Index.

Editorial Reviews

‘This is a must read for anyone interested in data-driven fluid mechanics. Coherent structures are central to how we understand fluids, and Haller has been a pioneer in this field for decades. This book covers an exciting range of topics from introductory to advanced material, complete with beautiful graphics and illustrations.' Steven L. Brunton, University of Washington

‘George Haller has written a clear, well-illustrated text that step-by-step explains the mathematics needed to understand and quantify fluid motions that cause mixing and describes and identifies the corresponding transport barriers to mixing processes. The ideas are introduced in a systematic way, with examples that highlight analytical features, software available via github, and interpretations to help the reader build intuition for the mathematical concepts and their application to physical processes.' Howard A. Stone, Princeton University

‘Dynamical systems theory was developed in the 1980s, but for fluid dynamics has not played the prominent role it deserves. The present insightful and well-written book ‘Transport Barriers and Coherent Structure in Flow Data’ by George Haller now bridges this gap between modern fluid dynamics and dynamical systems theory. It is based on mathematically grounded and solid methods, which are then applied to fluid dynamical problems and data sets. It also includes the usage of modern data-driven methods. The book is complemented by clickable links to a library of numerical implementations of transport barrier detection methods. It is a wonderful textbook for Turbulence and Advanced Fluid Mechanics classes for students in Applied Mathematics, Physics, and Mechanical and Chemical Engineering alike and unmissable for scientists working at the interface between dynamical systems theory and fluid dynamics.’ Detlef Lohse, University of Twente

‘… essential reading in areas related to chemical engineering, geophysical flows, and aerodynamics, to name a few of its applications. … Highly recommended.’ R. N. Laoulache, Choice

From the Publisher