Bücher der Reihe Cambridge Monographs on Mechanics

Professor Achenbach discusses uses of reciprocity relations for the determination of elastodynamic fields, and presents a novel method to solve for wave fields by reciprocity of the actual field with a so-called virtual solution, shedding new light on the use of reciprocity relations for dynamic fields in elastic bodies.

This monograph deals with the structure, generation and stability of flames from a mathematical point of view. It uses a specific mathematical approach to provide a unified theoretical description of fundamental flame phenomena. Its importance stems from the fact that it provides the first clear evidence that combustion can be legitimately treated as a mathematical science as well as an empirical one. The book will be of interest to researchers in combustion, fluid mechanics and applied mathematics, as well as to graduate students taking advanced courses in these areas.

Written at graduate level, this 2006 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.

For graduate students, researchers and professionals in applied mathematics, physics and engineering, this book explains the special techniques required to model the radiation and diffraction of elastic and surface waves.

This 1979 book attempts to connect the known structure of the ocean volume with experimental results in long-range sound transmission through the theory of wave propagation and the path-integral approach. The book is written at the post-graduate level, but has been carefully organised to give experimenters a grasp of important results without undue mathematics.

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.

This book presents the oceanography and mathematics necessary to develop a practical system to interpret the behaviour of the oceans.

This 2001 book presents in a systematic way the field of continuum solidification theory based on instability phenomena.

This volume focuses on the development and analysis of mathematical models of fracture phenomena. It details cases involving stress waves impinging on cracks, tractions suddenly applied to the faces of cracks, and rapid crack growth and arrest.

Observations of ocean circulation have increased as a result of international field programmes and of remote sensing systems on artificial earth satellites. Professor Bennett's work explores the potential for inverse theory, emphasizing possibilities rather than expedient or rudimentary applications.

Providing a basic foundation for advanced graduate study and research in the mechanics of solids, this 2004 treatise contains a systematic development of the fundamentals of finite inelastic deformations of heterogeneous materials.

Vortex dynamics is a natural paradigm for the field of chaotic motion and modern dynamical system theory.

Imparts a sound, quantitative understanding of colloidal science, based on fundamental theory and experiments with well-characterised model systems.

This 2000 book provides a careful and critical development of the equations which describe the motion of fluid-particle mixtures.

This book describes the motions resulting from heating a fluid layer from below and the motions of a fluid layer between two concentric cylinders when the inner cylinder is rotated.

Acoustics of Fluid-Structure Interactions addresses the theory of the production and absorption of noise and vibration by fluid flow. After providing background material in fluid mechanics, acoustics, and structural vibrations, it proceeds to more advanced topics, suited to a graduate-level course on the theory of acoustics and aerodynamic sound.

Turbulent flow is a most important branch of fluid dynamics yet its complexity has tended to make it one of the least understood. This revision takes into account developments since 1955. It will be useful as an advanced text in applied mathematics, engineering, meteorology, oceanography and physics.

Astronomers have long noted that the Earth does not rotate uniformly about an axis fixed in the planet, that both the length-of-day and the direction of the rotation axis vary periodically and irregularly by small amounts. These variations are an immediate consequence of the Earth not being a rigid body.

This monograph on generalised functions, Fourier integrals and Fourier series is intended for readers who, while accepting that a theory where each point is proved is better than one based on conjecture, nevertheless seek a treatment as elementary and free from complications as possible.

Kostrov and Das present a general theoretical model summarizing our current knowledge of fracture mechanics as applied to earthquakes and earthquake source processes.

Depending on the application, shear bands may be harmful or beneficial, but to be controlled, they must first be understood. This book establishes the mathematical setting within which shear bands may be studied and uses well established asymptotic techniques to obtain scaling laws that describe major aspects of the formation and morphology of shear bands.

Free surface problems occur in many aspects of science and of everyday life such as the waves on a beach, melting ice and bubbles rising in a glass of champagne. In this essential monograph, Vanden-Broeck addresses the many challenges involved in attempting to describe such flows mathematically.

The phenomena treated in this book all depend on the action of gravity on small density differences in a non-rotating fluid. The author gives a connected account of the various motions which can be driven or influenced by buoyancy forces in a stratified fluid, including internal waves, turbulent shear flows and buoyant convection. This excellent introduction to a rapidly developing field, first published in 1973, can be used as the basis of graduate courses in university departments of meteorology, oceanography and various branches of engineering. This edition is reprinted with corrections, and extra references have been added to allow readers to bring themselves up to date on specific topics. Professor Turner is a physicist with a special interest in laboratory modelling of small-scale geophysical processes. An important feature is the superb illustration of the text with many fine photographs of laboratory experiments and natural phenomena.

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.

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.

With an emphasis on both theory and experiment, this text describes the behaviour of homogeneous and density-stratified fluids over and around topography. The text will be a great asset to graduate and advanced undergraduate students, as well as to research professionals.

A coherent, up-to-date and comprehensive account of theory and experiment on wave-interaction phenomena, both in fluids at rest and in shear flows. This unique book will appeal to researchers and graduate students of fluid mechanics in its widest sense, including wave-interaction phenomena in meteorology, aeronautical and hydraulic engineering, optics, solar physics and population dynamics.

This paperback edition of Dr Hudson's advanced textbook presents the theory of small disturbances propagating through solids. The linearised theory of elasticity has now been replaced by a more fundamental approach based on a generalised theory of continuum mechanics. The book is of particular interest to seismologists and physicists engaged in non-destructive testing.

The analysis of the circulation of the blood is one of the most important areas of fluid mechanics research, with far-reaching medical and physiological implications.

This book gives an account of certain observed irregularities on the rotation of the Earth, both in its rate of rotation (giving a variable length of day) and in the position of its axis. These irregularities are caused by events on and within the Earth and provide a means of studying a number of geophysical problems.