Library of Oceanography Research and Abstracts
roman glazman roman glazman

Roman Glazman, circa summer 1988.

I. Baroclinic Inertia-Gravity Waves
II. Bubbles Oscillations and Adsorbed Film
III. Equatorial and Meridional Components of Rossby Solitons and Waves
IV. Long Internal Gravity Waves Dynamics and Transport
V. Magnetic Field Induced by Ocean Currents
VI. Mathematical Wave Properties of Ocean and Wind Waves
VII. Passive Scalar Transport and Fluctuation
VIII. Sea Level Measurements and Techniques
IX. Sea State Bias in Altimetry
X. Sea Surface Geometry, Fractal Properties
XI. Surface Wind and Wind Speed
XII. Spectral Analysis of Waves, Equilibrium Spectrum
XIII. Wave Turbulence and Turbulent Diffusion
XIV. Wind-Generated Gravity Waves and Surface Gravity Waves

Nonlinear Waves and Weak Turbulence

The Ocean Surface
Non-Linear Variability in Geophysics
Fractals in Natural Sciences
Nonlinear Waves and Weak Turbulence
Stochastic Models in Geosystems
About the Book: Abstract Wave Spectra Of Developed Seas
Glazman, Roman E.

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 theory of the transition from smooth laminar motion to the disordered motions characteristic of turbulence.
  • Statistical studies of fully developed turbulent systems.
  • ... 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.

    Nonlinear Waves and Weak Turbulence Table of Contents
    Year 1st published: 1992
    Editors: Fitzmaurice, N.; Gurarie D.
    McCaughan, F.; Woyczynski, W.A.
    Price: $129.00 (Paperback), $169.00 (Hardcover)
    Library of Oceanography: Support Level