Although nonlinear waves occur in nearly all branches of physics and engi neering, there is an amazing degree of agreement about the fundamental con cepts and the basic paradigms. The underlying unity of the theory for linearized waves is already well-established, with the importance of such universal concepts as group velocity and wave superposition. For nonlinear waves the last few decades have seen the emergence of analogous unifying comcepts. The pervasiveness of the soliton concept is amply demonstrated by the ubiquity of such models as the Korteweg-de Vries equation and the nonlinear Schrodinger equation. Similarly, there is a universality in the study of wave-wave interactions, whether determin istic or statistical, and in the recent developments in the theory of wave-mean flow interactions. The aim of this text is to present the basic paradigms of weakly nonlinear waves in fluids. This book is the outcome of a CISM Summer School held at Udine from September 20-24, 2004. . Like the lectures given there the text covers asymptotic methods for the derivation of canonical evolution equations, such as the Kortew- de Vries and nonlinear Schrodinger equations, descriptions of the basic solution sets of these evolution equations, and the most relevant and compelling applica tions. These themes are interlocked, and this will be demonstrated throughout the text . The topics address any fluid flow application, but there is a bias towards geophysical fluid dynamics, reflecting for the most part the areas where many applications have been found.

The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.

Internal wave dynamics in lakes (and oceans) is an important physical component of geophysical fluid mechanics of ‘quiescent’ water bodies of the Globe. The formation of internal waves requires seasonal stratification of the water bodies and generation by (primarily) wind forces. Because they propagate in basins of variable depth, a generated wave field often experiences transformation from large basin-wide scales to smaller scales. As long as this fission is hydrodynamically stable, nothing dramatic will happen. However, if vertical density gradients and shearing of the horizontal currents in the metalimnion combine to a Richardson number sufficiently small (

The dynamics of flows in density-stratified fluids has been and remains now an important topic for scientific enquiry. Such flows arise in many contexts, ranging from industrial settings to the oceanic and atmospheric environments. It is the latter topic which is the focus of this book. Both the ocean and atmosphere are characterised by the basic vertical density stratification, and this feature can affect the dynamics on all scales ranging from the micro-scale to the planetary scale. The aim of this book is to provide a “state-of-the-art” account of stratified flows as they are relevant to the ocean and atmosphere with a primary focus on meso-scale phenomena; that is, on phenomena whose time and space scales are such that the density stratification is a dominant effect, so that frictional and diffusive effects on the one hand and the effects of the earth’s rotation on the other hand can be regarded as of less importance. This in turn leads to an emphasis on internal waves.

This review volume, the third in the series, presents the latest topics for discussion, which provides invaluable information to coastal and ocean engineers around the world. In the first paper of this volume, entitled ?Internal Solitary Waves?, Grimshaw reviews the basic theory of weakly nonlinear waves in an incompressible density-stratified fluid. The internal solitary waves solutions and effects such as friction, refraction and finite amplitude on internal solitary waves are also discussed. In the second paper entitled ?The 3/2-Power Law for Ocean Wind Waves and Its Applications?, Toba gives a thorough review on the field evidence and physical background of the 3/2-power law and the associated wind-wave energy spectra. Several wind-wave prediction models are also discussed. Goda, in his paper entitled ?Directional Wave Spectrum and Its Engineering Applications?, gives a brief historical overview of the development of directional wave spectrum. He presents several standard formulas for directional spreading function for engineering applications and discusses the effects of directional spreading on nearshore currents and wave forces on coastal structures. In a companion paper entitled ?Analysis of the Directional Wave Spectrum from Field Data?, Hashimoto describes the maximum entropy principle method, Bayesian directional spectrum estimation method and the extended maximum entropy method for estimating directional wave spectrum. Hashimoto also introduces a new developed Doppler-type directional wave meter for field measurements. Finally, in ?Reliability-Based Design of Coastal Structures?, Barcharth introduces a design procedure that makes it possible to optimize a design and/or to design to a specific failure probability level.

This review volume, the third in the series, presents the latest topics for discussion, which provides invaluable information to coastal and ocean engineers around the world. In the first paper of this volume, entitled “Internal Solitary Waves”, Grimshaw reviews the basic theory of weakly nonlinear waves in an incompressible density-stratified fluid. The internal solitary waves solutions and effects such as friction, refraction and finite amplitude on internal solitary waves are also discussed. In the second paper entitled “The 3/2-Power Law for Ocean Wind Waves and Its Applications”, Toba gives a thorough review on the field evidence and physical background of the 3/2-power law and the associated wind-wave energy spectra. Several wind-wave prediction models are also discussed. Goda, in his paper entitled “Directional Wave Spectrum and Its Engineering Applications”, gives a brief historical overview of the development of directional wave spectrum. He presents several standard formulas for directional spreading function for engineering applications and discusses the effects of directional spreading on nearshore currents and wave forces on coastal structures. In a companion paper entitled “Analysis of the Directional Wave Spectrum from Field Data”, Hashimoto describes the maximum entropy principle method, Bayesian directional spectrum estimation method and the extended maximum entropy method for estimating directional wave spectrum. Hashimoto also introduces a new developed Doppler-type directional wave meter for field measurements. Finally, in “Reliability-Based Design of Coastal Structures”, Barcharth introduces a design procedure that makes it possible to optimize a design and/or to design to a specific failure probability level.