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  3. Cambridge Monographs on Mechanics

This series was established in 1952 as medium for the publication of major new works of scholarship on all aspects of theoretical and applied mechanics. From its inception it has maintained a reputation for the publication of outstanding monographs, a number of which have been re-issued in paperback. The series covers such areas as wave propagation, fluid dynamics, theoretical geophysics, combustion and the mechanics of solids. Authors are encouraged to write for a wide audience, and to balance mathematical analysis with physical interpretation and experimental data, where appropriate. Whilst the research literature is expected to be a major source for the content of the book, authors should aim to synthesise new results rather than just survey them.

  • Editorial Boards: M. J. Ablowitz, University of Colorado, Boulder, S. H. Davis, Northwestern University, Illinois, J. Hinch, University of Cambridge, A. Iserles, University of Cambridge, J. Ockendon, University of Oxford, P. J. Olver, University of Minnesota

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28 results in Cambridge Monographs on Mechanics

Page 2 of 2

Turbulence, Coherent Structures, Dynamical Systems and Symmetry
  • Philip Holmes, John L. Lumley, Gal Berkooz
  • Published online:
    03 February 2010
    Print publication:
    10 October 1996
  • 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.

Theory of Solidification
  • Stephen H. Davis
  • Published online:
    20 January 2010
    Print publication:
    08 October 2001
  • 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.

Inverse Methods in Physical Oceanography
  • Andrew F. Bennett
  • Published online:
    08 January 2010
    Print publication:
    31 July 1992
  • 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.

Turbulent Combustion
  • Norbert Peters
  • Published online:
    06 January 2010
    Print publication:
    15 August 2000
  • 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.

Reciprocity in Elastodynamics
  • J. D. Achenbach
  • Published online:
    10 December 2009
    Print publication:
    26 February 2004
  • 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 Earth's Variable Rotation
  • Geophysical Causes and Consequences
  • Kurt Lambeck
  • Published online:
    06 October 2009
    Print publication:
    12 June 1980
  • 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. In this book Professor Lambeck discusses the irregular nature of this motion and the geophysical mechanisms responsible for it. A complete analysis of these causes requires a discussion of solid Earth physics, magnetohydrodynamics, oceanography and meteorology. The study of the Earth's rotation is therefore of interest not only to astronomers who wish to explain their observations, but also to many geophysicists who use the astronomers' observations to understand better the Earth's response to a variety of applied forces. The author emphasizes the important contributions made over the last 15 years, this progress being in part a consequence of the overall progress in geophysics and planetary physics and of the developments in space science and technology, which not only require that the Earth's motion be precisely known but which also have provided new and precise methods for monitoring this motion. This book is suitable for geophysicists, astronomers and geodesists who are actively engaged in research as well as for graduate students.

Dynamic Fracture Mechanics
  • L. B. Freund
  • Published online:
    03 October 2009
    Print publication:
    23 February 1990
  • 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.

Finite Plastic Deformation of Crystalline Solids
  • K. S. Havner
  • Published online:
    11 September 2009
    Print publication:
    27 March 1992
  • 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.

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