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

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

George Haller (Author)

9781009225175, Cambridge University Press

Hardback, published 16 March 2023

426 pages
26 x 18.2 x 2.4 cm, 1.03 kg

'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

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.

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.

Subject Areas: Mechanics of fluids [TGMF], Meteorology & climatology [RBP], Oceanography [seas RBKC], Geophysics [PHVG], Dynamics & statics [PHDT], Fluid mechanics [PHDF]