Modern Fluid Dynamics for Physics and Astrophysics

This book grew out of the need to attain a good command of modern fluid dynamics, as the majority of the bodies in the universe are made of fluids. By "modern" we mean that relatively recent discoveries, methods and techniques are included. For example, new ideas on transition to turbulence (via transiently growing stable linear modes and perhaps linear, or non-linear, secondary instabilities), new approaches to turbulence (which, however, still remains, despite intensive research efforts, to be the enigma of fluid dynamics), the use of asymptotic approximation methods, which can give analytical or semi-analytical results and complement fully numerical treatments. We also briefly discuss some important considerations, to be taken into account when one develops a numerical code in an attempt to simulate astrophysical flows on a computer (an ever increasing modern practice).§§Another special feature of this book is the focus of the text on fluid dynamics, per se. The astrophysics is mainly given in the examples and exercises. We believe that a good and broad command of fluid dynamics can be more fruitful in approaching outstanding astrophysical problems than a review of known classical problems.§§It is assumed that the students are mathematically equipped with a reasonable knowledge in analysis, including basics of ordinary and partial differential equations a good command of vector calculus and linear algebra.§§Each chapter is concluded by a "Bibliographical note," in which we discuss briefly and cite the essential literature used and give recommendations for further, deeper reading. In an effort to make this book useful as a course textbook we have included in each chapter a number of exercises, most (but not all) of them on problems relevant to astrophysics.§