The study of hydrodynamic stability is fundamental to many subjects, ranging from geophysics and meteorology through to engineering design. This treatise covers both classical and modern aspects of the subject, systematically developing it from the simplest physical problems, then progressing to the most complex, considering linear and nonlinear situations, and analyzing temporal and spatial stability. The authors examine each problem both analytically and numerically. Many relevant fluid flows are treated, including those where the fluid may be compressible, or those from geophysics, or those that require salient geometries for description. Details of initial-value problems are explored equally with those of stability. The text includes copious illustrations and an extensive bibliography, making it suitable for courses on hydrodynamic stability or as an authoritative reference for researchers. In this second edition the opportunity has been taken to update the text and, most importantly, provide solutions to the numerous extended exercises.

A systematic account of the theory and modelling of rotating fluids that highlights the remarkable advances in the area and brings researchers and postgraduate students in atmospheres, oceanography, geophysics, astrophysics and engineering to the frontiers of research. Sufficient mathematical and numerical detail is provided in a variety of geometries such that the analysis and results can be readily reproduced, and many numerical tables are included to enable readers to compare or benchmark their own calculations. Traditionally, there are two disjointed topics in rotating fluids: convective fluid motion driven by buoyancy, discussed by Chandrasekhar (1961), and inertial waves and precession-driven flow, described by Greenspan (1968). Now, for the first time in book form, a unified theory is presented for three topics - thermal convection, inertial waves and precession-driven flow - to demonstrate that these seemingly complicated, and previously disconnected, problems become mathematically simple in the framework of an asymptotic approach that incorporates the essential characteristics of rotating fluids.

The last thirty years have seen great leaps forward in the subject of magnetoconvection. Computational techniques can now explain exotic nonlinear behaviour, transition to chaos and the formation of structures that can be observed on the surface of the Sun. Here, two leading experts present the current state of knowledge of the subject. They provide a mathematical and numerical treatment of the interactions between electrically conducting fluids and magnetic fields that lead to the complex structures and rich behaviour observed on the Sun and other stars, as well as in the interiors of planets like the Earth. The authors' combined analytical and computational approach provides a model for the study of a wide range of related problems. The discussion includes bifurcation theory, chaotic behaviour, pattern formation in two and three dimensions, and applications to geomagnetism and to the properties of sunspots and other features at the solar surface.

Interactions between waves and mean flows play a crucial role in understanding the long-term aspects of atmospheric and oceanographic modelling. Indeed, our ability to predict climate change hinges on our ability to model waves accurately. This book gives a modern account of the nonlinear interactions between waves and mean flows, such as shear flows and vortices. A detailed account of the theory of linear dispersive waves in moving media is followed by a thorough introduction to classical wave-mean interaction theory. The author then extends the scope of the classical theory and lifts its restriction to zonally symmetric mean flows. It can be used as a fundamental reference, a course text, or by geophysicists and physicists needing a first introduction. This second edition includes brand new material, including a section on Langmuir circulations and the Craik–Leibovich instability. The author has also added exercises to aid students' learning.

Turbulence pervades our world, from weather patterns to the air entering our lungs. This book describes methods that reveal its structures and dynamics. Building on the existence of coherent structures – recurrent patterns – in turbulent flows, it describes mathematical methods that reduce the governing (Navier–Stokes) equations to simpler forms that can be understood more easily. This second edition contains a new chapter on the balanced proper orthogonal decomposition: a method derived from control theory that is especially useful for flows equipped with sensors and actuators. It also reviews relevant work carried out since 1995. The book is ideal for engineering, physical science and mathematics researchers working in fluid dynamics and other areas in which coherent patterns emerge.

John G. Harris intended to explain in this book the special techniques required to model the radiation and diffraction of elastic and surface waves. Sadly, he died before he could fulfil this ambition, but his plan has been brought to fruition by a team of his distinguished collaborators. The book begins with the basic underlying equations for wave motion and then builds upon this foundation by solving a number of fundamental scattering problems. The remaining chapters provide a thorough introduction to modern techniques that have proven essential to understanding radiation and diffraction at high frequencies. Graduate students, researchers and professionals in applied mathematics, physics and engineering will find that the chapters increase in complexity, beginning with plane-wave propagation and spectral analyses. Other topics include elastic wave theory, the Wiener–Hopf technique, the effects of viscosity on acoustic diffraction, and the phenomenon of channelling of wave energy along guided structures.

Free surface problems occur in many aspects of science and of everyday life such as the waves on a beach, bubbles rising in a glass of champagne, melting ice, pouring flows from a container and sails billowing in the wind. Consequently, the effect of surface tension on gravity-capillary flows continues to be a fertile field of research in applied mathematics and engineering. Concentrating on applications arising from fluid dynamics, Vanden-Broeck draws upon his years of experience in the field to address the many challenges involved in attempting to describe such flows mathematically. Whilst careful numerical techniques are implemented to solve the basic equations, an emphasis is placed upon the reader developing a deep understanding of the structure of the resulting solutions. The author also reviews relevant concepts in fluid mechanics to help readers from other scientific fields who are interested in free boundary problems.

Interactions between waves and mean flows play a crucial role in understanding the long-term aspects of atmospheric and oceanographic modelling. Indeed, our ability to predict climate change hinges on our ability to model waves accurately. This book gives a modern account of the nonlinear interactions between waves and mean flows such as shear flows and vortices. A detailed account of the theory of linear dispersive waves in moving media is followed by a thorough introduction to classical wave–mean interaction theory. The author then extends the scope of the classical theory and lifts its restriction to zonally symmetric mean flows. The book is a fundamental reference for graduate students and researchers in fluid mechanics, and can be used as a text for advanced courses; it will also be appreciated by geophysicists and physicists who need an introduction to this important area in fundamental fluid dynamics and atmosphere-ocean science.

The emergence of observing systems such as acoustically-tracked floats in the deep ocean, and surface drifters navigating by satellite has seen renewed interest in Lagrangian fluid dynamics. Starting from the foundations of elementary kinematics and assuming some familiarity of Eulerian fluid dynamics, this 2006 book reviews the classical and new exact solutions of the Lagrangian framework, and then addresses the general solvability of the resulting general equations of motion. A unified account of turbulent diffusion and dispersion is offered, with applications among others to plankton patchiness in the ocean. Written at graduate level, the book provides the first detailed and comprehensive analytical development of the Lagrangian formulation of fluid dynamics, of interest not only to applied mathematicians but also oceanographers, meteorologists, mechanical engineers, astrophysicists and indeed all investigators of the dynamics of fluids.

The reciprocity theorem has been used for over 100 years to establish interesting and useful relations between different loading states of a body. This book discusses current and novel uses of reciprocity relations for the determination of elastodynamic fields. The author, who is internationally distinguished for his contributions to theoretical and applied mechanics, presents a novel method to solve for wave fields, shedding new light on the use of reciprocity relations for dynamic fields in an elastic body. The material presented in the book is relevant to several fields in engineering and applied physics. Examples are ultrasonics for medical imaging and non-destructive evaluation, acoustic microscopy, seismology, exploratory geophysics, structural acoustics, and the response of structures to high-rate loads and the determination of material properties by ultrasonic techniques.

The study of hydrodynamic stability is fundamental to many subjects, ranging from geophysics and meteorology through to engineering design. This treatise covers both classical and modern aspects of the subject, systematically developing it from the simplest physical problems, then progressing chapter by chapter to the most complex, considering linear and nonlinear situations, and analysing temporal and spatial stability. The authors examine each problem both analytically and numerically: many chapters end with an appendix outlining relevant numerical techniques. All relevant fluid flows are treated, including those where the fluid may be compressible, or those from geophysics, or those that require salient geometries for description. Details of initial-value problems are explored equally with those of stability. As a result, the early transient period as well as the asymptotic fate for perturbations for a flow can be assessed. The text is enriched with many exercises, copious illustrations and an extensive bibliography and the result is a book that can be used with courses on hydrodynamic stability or as an authoritative reference for researchers.

The processes of freezing and melting were present at the beginnings of the Earth and continue to dominate the natural and industrial worlds. The solidification of a liquid or the melting of a solid involves a complex interplay of many physical effects. This 2001 book presents in a systematic way the field of continuum solidification theory based on instability phenomena. An understanding of the physics is developed by using examples of increasing complexity with the object of creating a deep physical insight applicable to more complex problems. Applied mathematicians, engineers, physicists, and materials scientists will all find this volume of interest.

The combustion of fossil fuels remains a key technology for the foreseeable future. It is therefore important that we understand the mechanisms of combustion and, in particular, the role of turbulence within this process. Combustion always takes place within a turbulent flow field for two reasons: turbulence increases the mixing process and enhances combustion, but at the same time combustion releases heat which generates flow instability through buoyancy, thus enhancing the transition to turbulence. The four chapters of this book present a thorough introduction to the field of turbulent combustion. After an overview of modeling approaches, the three remaining chapters consider the three distinct cases of premixed, non-premixed, and partially premixed combustion, respectively. This book will be of value to researchers and students of engineering and applied mathematics by demonstrating the current theories of turbulent combustion within a unified presentation of the field.

Acoustics of Fluid-Structure Interactions addresses an increasingly important branch of fluid mechanics - the absorption of noise and vibration by fluid flow. This subject, which offers numerous challenges to conventional areas of acoustics, is of growing concern in places where the environment is adversely affected by sound. Howe presents useful background material on fluid mechanics and the elementary concepts of classical acoustics and structural vibrations. Using examples, many of which include complete worked solutions, he vividly illustrates the theoretical concepts involved. He provides the basis for all calculations necessary for the determination of sound generation by aircraft, ships, general ventilation and combustion systems, as well as musical instruments. Both a graduate textbook and a reference for researchers, Acoustics of Fluid-Structure Interactions is an important synthesis of information in this field. It will also aid engineers in the theory and practice of noise control.

For turbulent flows at relatively low speeds there exists an excellent mathematical model in the incompressible Navier–Stokes equations. Why then is the 'problem of turbulence' so difficult? One reason is that these nonlinear partial differential equations appear to be insoluble, except through numerical simulations, which offer useful approximations but little direct understanding. Three recent developments offer new hope. First, the discovery by experimentalists of coherent structures in certain turbulent flows. Secondly, the suggestion that strange attractors and other ideas from finite-dimensional dynamical systems theory might play a role in the analysis of the governing equations. And, finally, the introduction of the Karhunen-Loève or proper orthogonal decomposition. This book introduces these developments and describes how they may be combined to create low-dimensional models of turbulence, resolving only the coherent structures. This book will interest engineers, especially in the aerospace, chemical, civil, environmental and geophysical areas, as well as physicists and applied mathematicians concerned with turbulence.

The problem of ocean acoustic tomography is to infer from precise measurements of travel time, or other properties of acoustic propagation, the state of the ocean traversed by a sound field. Tomography takes advantage of two facts: that travel time and other measurable acoustic parameters are functions of temperature, water velocity, and other parameters of oceanographic interest, and can be interpreted to provide information about the intervening ocean using inverse methods; and that the ocean is virtually transparent to low-frequency sound, so that signals can be transmitted over distances of many thousands of kilometres. It is therefore possible to prepare a practical system of transmitters and receivers to interpret the behaviour of the oceans. This book gives a comprehensive presentation of the underlying oceanography and mathematics necessary to understand and develop such a system. It covers the forward and inverse tomography problem, as well as numerous models for data interpretation. Also included is an epilogue outlining the history of tomographic techniques. It should prove a valuable resource to oceanographers and climatologists, as well as applied mathematicians and engineers interested in applications of fluid mechanics tools.

The discovery of coherent structures in turbulence has fostered the hope that the study of vortices will lead to models and an understanding of turbulent flow, thereby solving or at least making less mysterious one of the great unsolved problems of classical physics. Vortex dynamics is a natural paradigm for the field of chaotic motion and modern dynamical system theory. The emphasis in this monograph is on the classical theory of inviscid incompressible fluids containing finite regions of vorticity. The effects of viscosity, compressibility, inhomogeneity and stratification are enormously important in many fields of application, from hypersonic flight to global environmental fluid mechanics. However, this volume focuses on those aspects of fluid motion which are primarily controlled by the vorticity and are such that the effects of the other fluid properties are secondary.

Observations of ocean circulation have increased as a result of international field programmes and of remote sensing systems on artificial earth satellites. Oceanographers are increasingly turning to inverse methods for combining these observations with numerical models of ocean circulation. Professor Bennett's work explores the potential for inverse theory, emphasizing possibilities rather than expedient or rudimentary applications. In addition to interpolating the data and adding realism to the model solutions, the methods can yield estimates for unobserved flow variables, forcing fields, and model parameters. Inverse formulations can resolve ill-posed modelling problems, lead to design criteria for oceanic observing systems, and enable the testing of models as scientific hypothesis. Exercises of varying difficulty rehearse technical skills and supplement the central theoretical development. Thus this book will be invaluable for environmental scientists and engineers, advanced undergraduates in applied mathematics, and graduate students in physical oceanography.

This book reviews and interrelates a large number of theoretical and experimental contributions to the research on finite plastic deformation of single crystals and polycrystalline metals. An overall theoretical framework for investigation of large strains in crystalline materials is presented that enables the blending of contemporary and earlier experimental research with modern concepts in solid mechanics. Professor Havner has provided a historical perspective throughout, including accurate attribution of ideas and emphasis on pioneering studies, beginning with G. I. Taylor and the German researchers in the 1920s. Early chapters deal with single crystals, including extensive analyses of particular experimental configurations. Then connections between single crystals and polycrystalline material behaviour are considered. Necessary background to the most general theoretical sections is presented in an appendix and approximately 200 references to the primary scientific literature are included. Engineering scientists, applied mathematicians and physical metallurgists will find this volume an invaluable guide to the development of finite plastic deformation theory.

This volume emphasizes fundamental concepts, both on the development of mathematical models of fracture phenomena and on the analysis of these models. Cases involving stress waves impinging on cracks, tractions suddenly applied to the faces of cracks, and rapid crack growth and arrest are considered in detail. Most of the work is concerned with the behavior of nominally elastic materials, but available results on elastic-plastic and elastic-viscoplastic materials are included. Connections to experimental results and to applications in structural mechanics, seismology, and materials science are noted whenever possible.