This book provides an introduction to turbulence in vortex systems,
and to turbulence theory for incompressible flow described in terms
of the vorticity field. It is the author's hope that by the end of
the book the reader will believe that these subjects are identical,
and constitute a special case of fairly standard statistical
mechanics, with both equilibrium and non-equilibrium aspects. The
author's main goal is to relate turbulence to statistical
mechanics. The book is organized as follows: the first three
chapters constitute a fairly standard introduction to homogeneous
turbulence in incompressible flow; a quick review of fluid
mechanics; a summary of the appropriate Fourier theory; a summary
of Kolmogorov's theory of the inertial range. The next four
chapters present the statistical theory of vortex notion, and the
vortex dynamics of turbulence. The book ends with the major
conclusion that turbulence can no longer be viewed as
incomprehensible. This book will be appropriate for professionals
in the fields of applied mathematics, mechanical engineering, or
physics, as well as graduate students in these noted areas.
General
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