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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.
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 mathematical background to the topic of asymptotic
approximation methods for the solution of ordinary and partial
differential equations is given first. These methods are then
applied to several examples of problems from astrophysical fluid
(and magneto-fluid) dynamics. An entire chapter is devoted to each
topic and among them are - accretion disk boundary layers, fronts
in thermally bistable interstellar medium; ideas from geophysics
(shallow water theory) applied to modeling accretion disks; the
discovery of transient perturbation growth in accretion disks, a
growth than may reasonably give rise to secondary instabilities
which, in turn, can be instrumental in driving angular momentum
transport in these objects. Finally a critical nonlinear analysis
of the magnetic Taylor-Couette-flow is given. It is found that for
the latter, the magneto-rotational instability, whose importance
for driving accretion disk turbulence had been considered
paramount, actually saturates at an amplitude that goes with the
magnetic Prandtl number, a fact that would imply that this
instability, per- se, cannot cause sufficient angular momentum
transport to induce accretion.
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