Lucid examination of the Rayleigh-Bernard problem; clear coverage of the theory of instabilities causing convection.

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 is the fourth of six volumes collecting significant papers of the distinguished astrophysicist and Nobel laureate S. Chandrasekhar. His work is notable for its breadth as well as for its brilliance; his practice has been to change his focus from time to time to pursue new areas of research. The result has been a prolific career full of discoveries and insights, some of which are only now being fully appreciated. Chandrasekhar has selected papers that trace the development of his ideas and that present aspects of his work not fully covered in the books he has periodically published to summarize his research in each area. Volume 4 has three parts. The first, on plasma physics, includes joint work with A. N. Kaufman and K. M. Watson on the stability of the pinch, as well as a paper on Chandrasekhar's own approach to the topic of adiabatic invariants. Part 2 includes work with specific scientific applications of hydrodynamic and hydromagnetic stability not covered in his monograph on the subject. The final part contains Chandrasekhar's papers on the scientific applications of the tensor-virial theorem, in which he restores to its proper place Riemann's neglected work with ellipsoidal figures.

In this classic text, a Nobel Prize-winning astrophysicist presents the theory of stellar dynamics as a branch of classical dynamics--a discipline in the same general category as celestial mechanics. His method offers the advantages of clarifying the theory's fundamental issues and defining its underlying motivations. S. Chandrasekhar investigates two areas. The first concerns problems in which the time of relaxation of a stellar system is central. His method consists of analyzing the effects of stellar encounters in terms of the two-body problem of classical dynamics and applying this theory to the dynamics of star clusters. The second area investigates problems centering around Liouville's theorem and the solutions of the equation of continuity; here, the author discusses the dynamic implications of the existence of a field of differential motions, which appears to be the most striking kinematic feature of the galaxy and the extragalactic systems. This edition includes two papers by the author that were published after Principles of Stellar Dynamics and that have been studied and quoted extensively: "New Methods in Stellar Dynamics" (originally published in the Annals of the New York Academy of Sciences) and "Dynamical Friction" (originally published in The Astrophysical Journal).

This book by a Nobel Laureate provides the foundation for analysis of stellar atmospheres, planetary illumination, and sky radiation. Suitable for students and professionals in physics, nuclear physics, astrophysics, and atmospheric studies. 1950 edition.

An advanced textbook on AFD introducing astrophysics students to the necessary fluid dynamics, first published in 2007.

This classic presentation has never been superseded in its encyclopedic coverage of the subject, and its excellent exposition of fundamental theorems, equations, and detailed methods of solution. Topics include many aspects of the dynamics of liquids and gases and 3-dimensional problems on motion of solids through a liquid. 1932 edition.

A good working knowledge of fluid mechanics and plasma physics is essential for the modern astrophysicist. This graduate textbook provides a clear, pedagogical introduction to these core subjects. Assuming an undergraduate background in physics, this book develops fluid mechanics and plasma physics from first principles. This book is unique because it presents neutral fluids and plasmas in a unified scheme, clearly indicating both their similarities and their differences. Also, both the macroscopic (continuum) and microscopic (particle) theories are developed, establishing the connections between them. Throughout, key examples from astrophysics are used, though no previous knowledge of astronomy is assumed. Exercises are included at the end of chapters to test the reader's understanding. This textbook is aimed primarily at astrophysics graduate students. It will also be of interest to advanced students in physics and applied mathematics seeking a unified view of fluid mechanics and plasma physics, encompassing both the microscopic and macroscopic theories.

This book grew out of the need to provide students with a solid introduction to modern fluid dynamics. It offers a broad grounding in the underlying principles and techniques used, with some emphasis on applications in astrophysics and planetary science. The book comprehensively covers recent developments, methods and techniques, including, for example, new ideas on transitions to turbulence (via transiently growing stable linear modes), new approaches to turbulence (which remains the enigma of fluid dynamics), and the use of asymptotic approximation methods, which can give analytical or semi-analytical results and complement fully numerical treatments. The authors also briefly discuss some important considerations to be taken into account when developing a numerical code for computer simulation of fluid flows. Although the text is populated throughout with examples and problems from the field of astrophysics and planetary science, the text is eminently suitable as a general introduction to fluid dynamics. It is assumed that the readers are mathematically equipped with a reasonable knowledge in analysis, including basics of ordinary and partial differential equations and a good command of vector calculus and linear algebra. Each chapter concludes with bibliographical notes in which the authors briefly discuss the chapter's essential literature and give recommendations for further, deeper reading. Included in each chapter are a number of problems, some of them relevant to astrophysics and planetary science. The book is written for advanced undergraduate and graduate students, but will also prove a valuable source of reference for established researchers.

The Nobel Laureate's monumental study surveys hydrodynamic and hydromagnetic stability as a branch of experimental physics, surveying thermal instability of a layer of fluid heated from below, Benard problem, more.