A guide to computing bifurcation diagrams for fluid flows, including relevant code, with broad applicability to industrial, environmental, astrophysical flows.

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.

The main idea of the present study is to demonstrate that the qualitative theory of diffe rential equations, when applied to problems in fluid-and gasdynamics, will contribute to the understanding of qualitative aspects of fluid flows, in particular those concerned with geometrical properties of flow fields such as shape and stability of its streamline patterns. It is obvious that insight into the qualitative structure of flow fields is of great importance and appears as an ultimate aim of flow research. Qualitative insight fashions our know ledge and serves as a good guide for further quantitative investigations. Moreover, quali tative information can become very useful, especially when it is applied in close corres pondence with numerical methods, in order to interpret and value numerical results. A qualitative analysis may be crucial for the investigation of the flow in the neighbourhood of singularities where a numerical method is not reliable anymore due to discretisation er rors being unacceptable. Up till now, familiar research methods -frequently based on rigorous analyses, careful nu merical procedures and sophisticated experimental techniques -have increased considera bly our qualitative knowledge of flows, albeit that the information is often obtained indirectly by a process of a careful but cumbersome examination of quantitative data. In the past decade, new methods are under development that yield the qualitative infor mation more directly. These methods, make use of the knowledge available in the qualitative theory of differen tial equations and in the theory of bifurcations.

Instabilities of fluid flows and the associated transitions between different possible flow states provide a fascinating set of problems that have attracted researchers for over a hundred years. This book addresses state-of-the-art developments in numerical techniques for computational modelling of fluid instabilities and related bifurcation structures, as well as providing comprehensive reviews of recently solved challenging problems in the field.

This book closes the gap between standard undergraduate texts on fluid mechanics and monographical publications devoted to specific aspects of viscous fluid flows. Each chapter serves as an introduction to a special topic that will facilitate later application by readers in their research work.

The papers from this conference deal with multi-fluid flows and interfacial instabilities. Papers on multiple-layer convection, wave dynamics in viscous flows, stability of viscoelastic flows, numberical computation of bubbles, and solidification are included.