|About the Book: Abstract||Wave Spectra Of Developed Seas|
This book is an outgrowth of the NSF-CBMS conference Nonlinear Waves & Weak Turbulence held at Case Western Reserve University in May 1992. The principal speaker at the conference was Professor V.E. Zakharov who delivered a series of ten lectures outlining the historical and ongoing development in the field. Some twenty other researchers also made presentations and it is their work which makes up the bulk of this text. Professor Zakharov's opening chapter serves as a general introduction to the other papers, which of the most part are concerned with the application of the theory in various fields. While the word "turbulence" is most often associated with the fluid dynamics it is in fact a dominant feature of most systems having a large or infinite number of degrees of freedom. For our purposes we might define turbulence as the chaotic behavior of systems having a large number of degrees of freedom and which are far from thermodynamic equilibrium. Work in field can be broadly divided into two areas:
... The occurrence of transition in flows such as plane Poiseuille flow at values of the Reynolds number far below criticality must be due to instability to finite amplitude disturbances. For these flows no evidence has been found for any stable secondary motions and it seems that turbulence develops directly from the base flow at a fixed Reynolds number. It is a testimony to the intractability of these strong turbulence problems that little of substance has been added to Reynolds' original suggestion after one hundred years of stability research.
The theory of weak turbulence on the other hand has seen a great deal of progress in the last twenty five years and intriguing connections have been made to many areas of mathematics and physics. These include links to Hamiltonian mechanics, nonlinear partial differential equations and integrable systems, stochastic analysis, asymptotic analysis and even the methods developed in quantum field theory. While work in the transition process is still of great interest, most of the contributions in this text aim at finding and applying the proper mathematical and statistical tools to describe fully developed turbulence.
At first sight, the goals look similar to those of statistical physics but there is a fundamental difference. Statistical physics for the most part is concerned with systems at or near equilibrium whereas any turbulence theory must deal with systems far from equilibrium. This point is illustrated by a simple example in Professor Zakharov's introduction. The role of the thermodynamic parameters such as temperature, pressure, etc. must be replaced by questions about the distribution of the energy flux across the wave number spectrum and about the evolution of those spectra. We would like to reiterate that the analytical methods that have been developed are by no means restricted to fluid dynamics problems. Indeed topics such as acoustics, optics, Jupiter's red spot, as well as traditional hydrodynamics have all found a home between the covers of this book.
These diverse applications serve to illustrate the power of a unified approach based for the most part on a Hamiltonian formulation. That more than anything else is the common thread throughout the chapters. Weak turbulence is still a fairly new topic and not at all familiar outside a relatively small group. We believe that it deserves the attention of a wider audience.
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|Editors: Fitzmaurice, N.; Gurarie D.McCaughan, F.; Woyczynski, W.A.|
|Price: $129.00 (Paperback), $169.00 (Hardcover)|