The Discrimination and Interaction of Hydrodynamical Waves of Different Types

Abstract

In this chapter the main features of hydrodynamic waves are described and the basic ideas of this book are introduced with examples taken from hydrodynamics and gas dynamics. The fundamental notions of elementary interacting modes and quasisolitons (approximate stable solutions) for long waves are discussed in the framework of the nonsingular perturbation theory. The corresponding small parameters are defined in terms of initial (boundary) conditions (Sects. 2.1–4) and some simple estimations of perturbation terms are given in Sect. 2.5. The form of the projection operators to the subspaces of elementary modes is given in Sect. 2.3. The theory of the coupled KdV systems as a basic tool for long waves in waveguides is developed in Sects. 2.5–6. The special case of closed waveguide propagation of Rossby waves is analyzed in Sect. 2.7.