The general area of geophysical fluid mechanics is truly interdisciplinary. Now ideas from statistical physics are being applied in novel ways to inhomogeneous complex systems such as atmospheres and oceans. In this book, the basic ideas of geophysics, probability theory, information theory, nonlinear dynamics and equilibrium statistical mechanics are introduced and applied to large time-selective decay, the effect of large scale forcing, nonlinear stability, fluid flow on a sphere and Jupiter's Great Red Spot. The book is the first to adopt this approach and it contains many recent ideas and results. Its audience ranges from graduate students and researchers in both applied mathematics and the geophysical sciences. It illustrates the richness of the interplay of mathematical analysis, qualitative models and numerical simulations which combine in the emerging area of computational science.
This book is an introductory course to the physics and chemistry of the atmosphere and to climate dynamics. It covers the basics in thermodynamics, fluid dynamics, radiation, and chemistry and explain
This book is an introductory course to the physics and chemistry of the atmosphere and to climate dynamics. It covers the basics in thermodynamics, fluid dynamics, radiation, and chemistry and explain
This three-volume series presents the ideas, models and approaches essential to understanding plasma dynamics and self-organization for researchers and graduate students in plasma physics, controlled fusion and related fields such as plasma astrophysics. Volume I develops the physical kinetics of plasma turbulence through a focus on quasi-particle models and dynamics. It discusses the essential physics concepts and theoretical methods for describing weak and strong fluid and phase space turbulence in plasma systems far from equilibrium. The book connects the traditionally 'plasma' topic of weak or wave turbulence theory to more familiar fluid turbulence theory, and extends both to the realm of collisionless phase space turbulence. This gives readers a deeper understanding of these related fields, and builds a foundation for future applications to multi-scale processes of self-organization in tokamaks and other confined plasmas. This book emphasizes the conceptual foundations and physic
This book is an introduction to the physics of suspensions of bubbles, droplets, and solid particles in both gases and fluids. Rather than treating each combination separately, a unified approach is used that permits most particle-fluid combination types to be discussed together. To do this, the book first presents a detailed discussion of the basic particle motions that small particles can sustain, paying particular attention to translations and pulsations, and to the thermal effects that occur as a result of those motions. The book then introduces the reader to the dynamics and thermodynamics of suspensions, with acoustic motions providing the main focus in the latter part of the book. The important acoustic problems of attenuation and dispersion are discussed from several fundamental perspectives. The book concludes with applications of acoustic techniques to the characterization and modification of suspensions by means of acoustic waves.
This book is an introduction to the physics of suspensions of bubbles, droplets, and solid particles in both gases and fluids. Rather than treating each combination separately, a unified approach is used that permits most particle-fluid combination types to be discussed together. To do this, the book first presents a detailed discussion of the basic particle motions that small particles can sustain, paying particular attention to translations and pulsations, and to the thermal effects that occur as a result of those motions. The book then introduces the reader to the dynamics and thermodynamics of suspensions, with acoustic motions providing the main focus in the latter part of the book. The important acoustic problems of attenuation and dispersion are discussed from several fundamental perspectives. The book concludes with applications of acoustic techniques to the characterization and modification of suspensions by means of acoustic waves.
A field is a distribution in space of physical quantities of obvious significance, such as pressure, velocity, or electromagnetic influence. This 1977 book was written for any reader who would not be content with a purely mathematical approach to the handling of fields. In letting the mathematical concepts invent themselves out of the need to describe the physical world quantitatively, Professor Shercliff shows how the same mathematical ideas may be used in a wide range of apparently different contexts including electromagnetism, fluid dynamics, nuclear reactor criticality, plasma oscillations and rotational flow. Mathematical methods are explored only far enough to give the interested reader a glimpse of activities that lie beyond, yet the unifying approach to increasingly powerful, generalised ideas at a level not reached in many books on vector analysis at the time. Special features of the book are a wealth of examples of physical interest, and a thorough appendix.
This book discusses the properties of quantized vortex lines in superfluid helium-4 in the light of research on vortices in modern fluid mechanics, and gives the first comprehensive treatment of the problem. The author begins with a review of the knowledge of classical fluid dynamics which is relevant to the main topics of the book. This is followed by a presentation of basic material on helium II and quantized vortices. The following chapters deal with various different aspects of the subject, and the book concludes with substantial introductions to two currently active topics, namely superfluid turbulence and the nucleation of quantized vortices. Both quantum tunnelling and thermal activation nucleation processes are also discussed, including the Kosterlitz-Thouless transition in thin films. The author's comprehensive approach will make this book invaluable for students taking advanced undergraduate or graduate courses, and for all those involved in research on classical and quantum
This book discusses the properties of quantized vortex lines in superfluid helium-4 in the light of research on vortices in modern fluid mechanics, and gives the first comprehensive treatment of the problem. The author begins with a review of the knowledge of classical fluid dynamics which is relevant to the main topics of the book. This is followed by a presentation of basic material on helium II and quantized vortices. The following chapters deal with various different aspects of the subject, and the book concludes with substantial introductions to two currently active topics, namely superfluid turbulence and the nucleation of quantized vortices. Both quantum tunnelling and thermal activation nucleation processes are also discussed, including the Kosterlitz-Thouless transition in thin films. The author's comprehensive approach will make this book invaluable for students taking advanced undergraduate or graduate courses, and for all those involved in research on classical and quantum
Continuum mechanics underlies many geological and geophysical phenomena, from earthquakes and faults to the fluid dynamics of the Earth. This interdisciplinary book provides geoscientists, physicists and applied mathematicians with a class-tested, accessible overview of continuum mechanics. Starting from thermodynamic principles and geometrical insights, the book surveys solid, fluid and gas dynamics. In later review chapters, it explores new aspects of the field emerging from nonlinearity and dynamical complexity and provides a brief introduction to computational modeling. Simple, yet rigorous, derivations are used to review the essential mathematics. The author emphasizes the full three-dimensional geometries of real-world examples, enabling students to apply this in deconstructing solid earth and planet-related problems. Problem sets and worked examples are provided, making this a practical resource for graduate students in geophysics, planetary physics and geology and a beneficial
Lattice Boltzmann method (LBM) is a relatively new simulation technique for the modeling of complex fluid systems and has attracted interest from researchers in computational physics. Unlike the tradi
This book is an introduction to the applications in nonequilibrium statistical mechanics of chaotic dynamics, and also to the use of techniques in statistical mechanics important for an understanding of the chaotic behaviour of fluid systems. The fundamental concepts of dynamical systems theory are reviewed and simple examples are given. Advanced topics including SRB and Gibbs measures, unstable periodic orbit expansions, and applications to billiard-ball systems, are then explained. The text emphasises the connections between transport coefficients, needed to describe macroscopic properties of fluid flows, and quantities, such as Lyapunov exponents and Kolmogorov-Sinai entropies, which describe the microscopic, chaotic behaviour of the fluid. Later chapters consider the roles of the expanding and contracting manifolds of hyperbolic dynamical systems and the large number of particles in macroscopic systems. Exercises, detailed references and suggestions for further reading are included
There is a resurgence of applications in which the calculus of variations has direct relevance. In addition to application to solid mechanics and dynamics, it is now being applied in a variety of numerical methods, numerical grid generation, modern physics, various optimization settings and fluid dynamics. Many applications, such as nonlinear optimal control theory applied to continuous systems, have only recently become tractable computationally, with the advent of advanced algorithms and large computer systems. This book reflects the strong connection between calculus of variations and the applications for which variational methods form the fundamental foundation. The mathematical fundamentals of calculus of variations (at least those necessary to pursue applications) is rather compact and is contained in a single chapter of the book. The majority of the text consists of applications of variational calculus for a variety of fields.
Combustion is a fascinating phenomenon coupling complex chemistry to transport mechanisms and nonlinear fluid dynamics. This book provides an up-to-date and comprehensive presentation of the nonlinear dynamics of combustion waves and other non-equilibrium energetic systems. The major advances in this field have resulted from analytical studies of simplified models performed in close relation with carefully controlled laboratory experiments. The key to understanding the complex phenomena is a systematic reduction of the complexity of the basic equations. Focusing on this fundamental approach, the book is split into three parts. Part I provides physical insights for physics-oriented readers, Part II presents detailed technical analysis using perturbation methods for theoreticians, and Part III recalls the necessary background knowledge in physics, chemistry and fluid dynamics. This structure makes the content accessible to newcomers to the physics of unstable fronts in flows, whilst also
Vector analysis provides the language that is needed for a precise quantitative statement of the general laws and relationships governing such branches of physics as electromagnetism and fluid dynamics. The account of the subject is aimed principally at physicists but the presentation is equally appropriate for engineers. The justification for adding to the available textbooks on vector analysis stems from Professor Kemmer's novel presentation of the subject developed through many years of teaching, and in relating the mathematics to physical models. While maintaining mathematical precision, the methodology of presentation relies greatly on the visual, geometric aspects of the subject and is supported throughout the text by many beautiful illustrations that are more than just schematic. A unification of the whole body of results developed in the book - from the simple ideas of differentiation and integration of vector fields to the theory of orthogonal curvilinear coordinates and to th
The contributions in this volume discuss numerous hot topics of interdisciplinary interest in plasma physics, astrophysics, and fluid dynamics. It collects the articles presented at a Workshop that ha
At the University of Surrey in 1995 an EPSRC Spring School was held in Applied Nonlinear Mathematics for postgraduate students in mathematics, engineering, physics or biology; this volume contains the bulk of the lectures given there, by a team of internationally distinguished scientists. The aim of the school was to introduce students to current topics of research interest at an appropriate level. The majority of the courses are in the area of nonlinear dynamics with application to fluid mechanics, boundary layer transition, driven oscillators and waves. However, there are also lectures considering problems in nonlinear elasticity and mathematical biology. The articles have all been edited so that the book forms a coherent and accessible account of recent advances in nonlinear mathematics.
At the University of Surrey in 1995 an EPSRC Spring School was held in Applied Nonlinear Mathematics for postgraduate students in mathematics, engineering, physics or biology; this volume contains the bulk of the lectures given there, by a team of internationally distinguished scientists. The aim of the school was to introduce students to current topics of research interest at an appropriate level. The majority of the courses are in the area of nonlinear dynamics with application to fluid mechanics, boundary layer transition, driven oscillators and waves. However, there are also lectures considering problems in nonlinear elasticity and mathematical biology. The articles have all been edited so that the book forms a coherent and accessible account of recent advances in nonlinear mathematics.
The book reports on selected projects on the High Performance Computer in Bavaria (HLRB). The projects originate from the fields of fluid dynamics, astrophysics and cosmology, computational physics in
Finite volume methods are used for various applications in fluid dynamics, magnetohydrodynamics, structural analysis or nuclear physics. A closer look reveals many interesting phenomena and mathematic
