Hydrodynamic Instabilities

The instability of fluid flows is a key topic in classical fluid mechanics because it has huge repercussions for applied disciplines such as chemical engineering, hydraulics, aeronautics, and geophysics. This modern introduction is written for any student, researcher, or practitioner working in the area, for whom an understanding of hydrodynamic instabilities is essential. Based on a decade's experience of teaching postgraduate students in fluid dynamics, this book brings the subject to life by emphasizing the physical mechanisms involved. The theory of dynamical systems provides the basic structure of the exposition, together with asymptotic methods. Wherever possible, Charru discusses the phenomena in terms of characteristic scales and dimensional analysis. The book includes numerous experimental studies, with references to videos and multimedia material, as well as over 150 exercises which introduce the reader to new problems.

Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment, and are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography and physics as well as engineering. This is a textbook to introduce these phenomena at a level suitable for a graduate course, by modelling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized, with many figures, and in references to more still and moving pictures. The relation of chaos to transition is discussed at length. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent in linear algebra, advanced calculus, elementary theory of ordinary differential equations, complex variables and the elements of fluid mechanics. The book is aimed at graduate students but will also be very useful for specialists in other fields.

This book presents five sets of pedagogical lectures by internationally respected researchers on nonlinear instabilities and the transition to turbulence in hydrodynamics. The book begins with a general introduction to hydrodynamics covering fluid properties, flow measurement, dimensional analysis and turbulence. Chapter two reviews the special characteristics of instabilities in open flows. Chapter three presents mathematical tools for multiscale analysis and asymptotic matching applied to the dynamics of fronts and localized nonlinear states. Chapter four gives a detailed review of pattern forming instabilities. The final chapter provides a detailed and comprehensive introduction to the instability of flames, shocks and detonations. Together, these lectures provide a thought-provoking overview of current research in this important area.

Offers modern and numerical techniques for the stability of fluid flow with illustrations, an extensive bibliography, and exercises with solutions.

The first comprehensive reference guide to turbulent mixing driven by Rayleigh-Taylor, Richtmyer-Meshkov and Kelvin-Helmholtz instabilities.

This book is a complete revision of the part of Monin & Yaglom's famous two-volume work "Statistical Fluid Mechanics: Mechanics of Turbulence" that deals with the theory of laminar-flow instability and transition to turbulence. It includes the considerable advances in the subject that have been made in the last 15 years or so. It is intended as a textbook for advanced graduate courses and as a reference for research students and professional research workers. The first two Chapters are an introduction to the mathematics, and the experimental results, for the instability of laminar (or inviscid) flows to infinitesimal (in practice "small") disturbances. The third Chapter develops this linear theory in more detail and describes its application to particular problems. Chapters 4 and 5 deal with instability to finite-amplitude disturbances: much of the material has previously been available only in research papers.

This book illustrates the latest progress on the hydrodynamic instabilities induced by a shock wave, particularly RM (Richtmyer–Meshkov) instability. The hydrodynamic instabilities play crucial roles in various industrial and scientific fields, such as inertial confinement fusion, supersonic combustion, supernova explosion, etc. This book experimentally and theoretically explores the shock-driven instabilities of complex gas-gas and gas-liquid interfaces. The main difficulty in performing an experimental study on RM instability, especially in a shock-tube circumstance, lies in creating an idealized initial interface because the RM instability is extremely sensitive to the initial condition. This book introduces new experimental methods to generate shape-controllable two-dimensional gaseous interfaces, thickness-controllable gas layers, and water droplets embedded with a vapour bubble in the shock-tube experiments. It covers the latest experiments and theories on the shock-driven hydrodynamic instabilities of multi-mode, multi-layer, and multi-phase interfaces. It explores the effects of the mode-competition, interface-coupling, and phase-transition on interface evolution, respectively. This book establishes a universal nonlinear theory to predict the RM instability of a shocked multi-mode interface based on spectrum analysis. This book quantifies the effects of interface-coupling and reverberating waves on the hydrodynamic instabilities of a shocked multi-layer interface. This book provides the experimental studies of the interaction of a shock wave and a multi-phase droplet and proposes a modified Rayleigh-Plesset equation to predict the vapour bubble collapse inside a droplet.