For the first time, exact analytical solutions are available for some of the most interesting types of problems arising in physics and applied mathematics. Hydrodynamics of Unstable Media outlines the theory of "quasi-gaseous" unstable media, and demonstrates how the theory can be used to obtain analytical solutions. Until now, the solutions to many of the examples considered in this new book have been numerical or partial solutions. By developing a new theory of hydrodynamics for unstable media, the authors provide a means for scientists and mathematicians to solve problems exactly and analytically. Solutions to some 50 problems are provided! Hydrodynamics of Unstable Media features interdisciplinary discussions by internationally recognized authors.

This newly-translated book takes the reader from the basic principles and conservation laws of hydrodynamics to the description of general atmospheric circulation. Among the topics covered are the Kelvin, Ertel and Rossby-Obukhov invariants, quasi-geostrophic equation, thermal wind, singular Helmholtz vortices, derivation of the Navier-Stokes equation, Kolmogorov's flow, hydrodynamic stability, and geophysical boundary layers. Generalizing V. Arnold's approach to hydrodynamics, the author ingeniously brings in an analogy of Coriolis forces acting on fluid with motion of the Euler heavy top and shows how this is used in the analysis of general atmospheric circulation. This book is based on popular graduate and undergraduate courses given by F.V.Dolzhansky at the Moscow Institute of Physics and Technology, and is the result of the author's highly acclaimed work in Moscow's Laboratory of Geophysical Hydrodynamics. Each chapter is full of examples and figures, exercises and hints, motivating and illustrating both theoretical and experimental results. The exposition is comprehensive yet user-friendly in engaging and exploring the broad range of topics for students and researchers in mathematics, physics, meteorology and engineering.

Suitable for any core physics program, this classroom-tested text takes a problems-based approach to teaching continuous media. This revised and expanded edition includes a new chapter on magnetohydrodynamics as well as additional problems and more detailed solutions. Each chapter begins with a summary of the definitions and equations that are necessary to understand and tackle the problems that follow. The text also provides numerous references throughout, including Landau and Lifshitz's famous course of theoretical physics and original journal publications.

This book studies the fundamental concept of hydrodynamics as part of theoretical physics and demonstrates the connection of macroscopic approach with the description of properties of fluid motion and microscopic kinetic theory. It also presents recent investigations in instabilities and turbulence theory.

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perbaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van GuIik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Physical Nonequilibrium in Soils provides cutting-edge knowledge on physical nonequilibrium phenomena in soils, offering unique insight into the complexity of our physical world. With 18 chapters comprising the book, topics cover soil properties fluid properties mechanistic models transfer function geostatistics fractal analysis cellular-automation fluids coupling of physical and chemical nonequilibrium models confirming and quantifying physical nonequilibrium in soils analytical solutions field-scale research environmental impacts.