Bifurcation Analysis of Fluid Flows: Analysis beyond Simulation

A better understanding of the mechanisms leading a fluid system to exhibit turbulent behavior is one of the grand challenges of the physical and mathematical sciences. Over the last few decades, numerical bifurcation methods have been extended and applied to a number of flow problems to identify critical conditions for fluid instabilities to occur. This book provides a state-of-the-art account of these numerical methods, with much attention to modern linear systems solvers and generalized eigenvalue solvers. These methods also have a broad applicability in industrial, environmental and astrophysical flows. The book is a must-have reference for anyone working in scientific fields where fluid flow instabilities play a role. Exercises at the end of each chapter and Python code for the bifurcation analysis of canonical fluid flow problems provide practice material to get to grips with the methods and concepts presented in the book.

Henk A. Dijkstra is professor of dynamical oceanography at the Institute for Marine and Atmospheric Research Utrecht (IMAU) within the Department of Physics and Astronomy at Utrecht University, The Netherlands. Henk A. Dijkstra is professor of dynamical oceanography at the Institute for Marine and Atmospheric Research Utrecht (IMAU) within the Department of Physics and Astronomy at Utrecht University, The Netherlands. He has been a member of the Dutch Royal Academy of Arts and Sciences (KNAW) since 2002. He received the Lewis Fry Richardson medal from the European Geosciences Union in 2005, he was elected a Fellow of the Society for Industrial and Applied Mathematics (SIAM) in 2009, and he was awarded an Advanced Grant from the European Research Council in 2021. He is author of several books, including Nonlinear Physical Oceanography (Springer, 2005), Dynamical Oceanography (2008), Nonlinear Climate Dynamics (Cambridge University Press, 2013) and Networks in Climate (Cambridge University Press, 2019).

Fred W. Wubs is associate professor of numerical mathematics at the Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence within the Faculty of Science and Engineering of the University of Groningen, The Netherlands. He is the (co-)author of almost seventy publications in the areas of numerical treatment of (stochastic) partial differential equations, preconditioning of sparse linear systems, solution of large sparse eigenvalue problems and high-performance computing.