Nonlinear Waves and Weak Turbulence

The classical concept of turbulence is most often associated with fluid dynamics. However, it is in fact a dominant feature of most systems having a large or infinite number of degrees of freedom. In demonstration of this fact, the current volume covers topics such as acoustics, optics, and Jupiter's red spot, as wen as traditional hydrodynamics. The emphasis of the volume is on applications of the relatively new theory of weak turbulence. 'nis theory, which has been developed largely in the last twenty five years, anows for the existence of a multiplicity of linearly unstable modes interacting in a nonlinear "soup." It makes many intriguing connections to such topics as Hamiltonian mechanics, nonlinear parties, equations and integrable systems, stochastic analysis, and methods developed in quantum field theory. Most of the contributions in this book aim at finding and applying the proper mathematical and statistical tools to describe fully developed turbulence. These diverse applications serve to illustrate the power of a unified approach based for the most part on a Hamiltonian formulation.A few chapters address a class of stochastic nonlinear nondispersive waves known as Burger:e turbulence. Set into historical context by V. E. Zakharov's opening chapter, the contributions to this book will be of interest to research workers and graduate students in pure and applied mathematics, theoretical physics, fluid mechanics, oceanography, and various areas of engineering.