**Contemporary Mathematics**

Volume: 283;
2001;
116 pp;
Softcover

MSC: Primary 76; 35; 37; 74;

Print ISBN: 978-0-8218-2714-7

Product Code: CONM/283

List Price: $48.00

AMS Member Price: $38.40

MAA Member Price: $43.20

**Electronic ISBN: 978-0-8218-7873-6
Product Code: CONM/283.E**

List Price: $48.00

AMS Member Price: $38.40

MAA Member Price: $43.20

# Advances in Wave Interaction and Turbulence

Share this page *Edited by *
*Paul A. Milewski; Leslie M. Smith; Fabian Waleffe; Esteban G. Tabak*

We often think of our natural environment as being composed of very many
interacting particles, undergoing individual chaotic motions, of which only
very coarse averages are perceptible at scales natural to us. However, we could
as well think of the world as being made out of individual waves. This is so
not just because the distinction between waves and particles becomes rather
blurred at the atomic level, but also because even phenomena at much larger
scales are better described in terms of waves rather than of particles: It is
rare in both fluids and solids to observe energy being carried from one region
of space to another by a given set of material particles; much more often, this
transfer occurs through chains of particles, neither of them moving much, but
each communicating with the next, and hence creating these immaterial objects
we call waves.

Waves occur at many spatial and temporal scales. Many of these waves have
small enough amplitude that they can be approximately described by linear
theory. However, the joint effect of large sets of waves is governed by
nonlinear interactions which are responsible for huge cascades of energy among
very disparate scales. Understanding these energy transfers is crucial in order
to determine the response of large systems, such as the atmosphere and the
ocean, to external forcings and dissipation mechanisms which act on scales
decades apart.

The field of wave turbulence attempts to understand the average behavior of
large ensembles of waves, subjected to forcing and dissipation at opposite ends
of their spectrum. It does so by studying individual mechanisms for energy
transfer, such as resonant triads and quartets, and attempting to draw from
them effects that should not survive averaging.

This book presents the proceedings of the AMS-IMS-SIAM Joint Summer Research
Conference on Dispersive Wave Turbulence held at Mt. Holyoke College (MA). It
drew together a group of researchers from many corners of the world, in the
context of a perceived renaissance of the field, driven by heated debate about
the fundamental mechanism of energy transfer among large sets of waves, as well
as by novel applications–and old ones revisited–to the understanding
of the natural world. These proceedings reflect the spirit that permeated the
conference, that of friendly scientific disagreement and genuine wonder at the
rich phenomenology of waves.

#### Readership

Graduate students and research mathematicians.

# Table of Contents

## Advances in Wave Interaction and Turbulence

- Contents vii8 free
- Preface ix10 free
- Strongly stratified limit of 3D primitive equations in an infinite layer 112 free
- Anomalous transport by wave turbulence 1324
- Statistical equilibrium theories for the nonlinear Schrödinger equation 2738
- Is there a 2D cascade in 3D convection? 4152
- The forced inviscid Burgers equation as a model for nonlinear interactions among dispersive waves 5162
- Traveling surface elastic waves in the half-plane 8394
- Numerical study of two-dimensional stratified turbulence 91102
- Turbulence of one-dimensional weakly nonlinear dispersive waves 107118