This up-to-date and comprehensive account of theory and experiment on wave-interaction phenomena covers fluids both at rest and in their shear flows. It includes, on the one hand, water waves, internal waves, and their evolution, interaction, and associated wave-driven means flow and, on the other hand, phenomena on nonlinear hydrodynamic stability, especially those leading to the onset of turbulence. This study provide a particularly valuable bridge between these two similar, yet different, classes of phenomena. It will be of value to oceanographers, meteorologists, and those working in fluid mechanics, atmospheric and planetary physics, plasma physics, aeronautics, and geophysical and astrophysical fluid dynamics.

Wave Interactions and Fluid Flows is a coherent, up-to-date and comprehensive account of theory and experiment on wave-interaction phenomena, both in fluids at rest and in shear flows. On the one hand, this includes water waves, internal waves, their evolution and interaction and associated wave-driven mean flows; on the other, phenomena of nonlinear hydrodynamic stability, especially those leading to the onset of turbulence. Close similarities - and crucial differences - exist between these two classes of phenomena and their treatment in this single study provides a particularly valuable bridge between more specialised, but related, disciplines. As a result, this unique book will appeal to researchers and graduate students of fluid mechanics in its widest sense, including the study of wave-interaction phenomena in such diverse fields as meteorology, aeronautical and hydraulic engineering, optics, solar physics and population dynamics. Dr Craik is an active researcher of long-standing at the University of St Andrews and has wide experience in the field of fluid mechanics.

This volume explores a range of recent advances in mathematical fluid mechanics, covering theoretical topics and numerical methods. Chapters are based on the lectures given at a workshop in the summer school Waves in Flows, held in Prague from August 27-31, 2018. A broad overview of cutting edge research is presented, with a focus on mathematical modeling and numerical simulations. Readers will find a thorough analysis of numerous state-of-the-art developments presented by leading experts in their respective fields. Specific topics covered include: Chemorepulsion Compressible Navier-Stokes systems Newtonian fluids Fluid-structure interactions Waves in Flows: The 2018 Prague-Sum Workshop Lectures will appeal to post-doctoral students and scientists whose work involves fluid mechanics.

This book was published in 2004. The Interaction of Ocean Waves and Wind describes in detail the two-way interaction between wind and ocean waves and shows how ocean waves affect weather forecasting on timescales of 5 to 90 days. Winds generate ocean waves, but at the same time airflow is modified due to the loss of energy and momentum to the waves; thus, momentum loss from the atmosphere to the ocean depends on the state of the waves. This volume discusses ocean wave evolution according to the energy balance equation. An extensive overview of nonlinear transfer is given, and as a by-product the role of four-wave interactions in the generation of extreme events, such as freak waves, is discussed. Effects on ocean circulation are described. Coupled ocean-wave, atmosphere modelling gives improved weather and wave forecasts. This volume will interest ocean wave modellers, physicists and applied mathematicians, and engineers interested in shipping and coastal protection.

Interactions between waves and mean flows play a crucial role in understanding the long-term aspects of atmospheric and oceanographic modelling. Indeed, our ability to predict climate change hinges on our ability to model waves accurately. This book gives a modern account of the nonlinear interactions between waves and mean flows such as shear flows and vortices. A detailed account of the theory of linear dispersive waves in moving media is followed by a thorough introduction to classical wave–mean interaction theory. The author then extends the scope of the classical theory and lifts its restriction to zonally symmetric mean flows. The book is a fundamental reference for graduate students and researchers in fluid mechanics, and can be used as a text for advanced courses; it will also be appreciated by geophysicists and physicists who need an introduction to this important area in fundamental fluid dynamics and atmosphere-ocean science.

A comprehensive textbook in which the author describes the science of waves in liquids and gases. Drawing on a subject of enormous extent and variety, he provides his readers with a thorough analysis of the most important and representative types of waves including sound waves, shock waves, waterwaves of all kinds, and the so-called internal waves (inside atmospheres and oceans) due to intensity stratification. Emphasis throughout is on the most generally useful fundamental ideas of wave science, including the principles of how waves interact with flows. This standard work on one of the great subdivisions of the dynamics of fluids is lucidly written and will be invaluable to engineers, physicists, geophysicists, applied mathematicians or any research worker concerned with wave motions or fluid fllows. It is especially suitable as a textbook for courses at the final year undergraduate or graduate level.

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.

Mathematics Research Center Symposium: Waves on Fluid Interfaces covers the proceedings of a symposium conducted by the Mathematics Research Center of the University of Wisconsin-Madison on October 18-20, 1982. The book focuses on nonlinear instabilities of classical interfaces, physical structure of real interfaces, and the challenges these reactions pose to the understanding of fluids. The selection first elaborates on finite-amplitude interfacial waves, instability of finite-amplitude interfacial waves, and finite-amplitude water waves with surface tension. Discussions focus on reformulation as an integro-differential equation, perturbation solutions, results for interfacial waves with current jump, wave of zero height, weakly nonlinear waves, and numerical methods. The text then takes a look at generalized vortex methods for free-surface flows; a review of solution methods for viscous flow in the presence of deformable boundaries; and existence criteria for fluid interfaces in the absence of gravity. The book ponders on the endothelial interface between tissue and blood, moving contact line, rupture of thin liquid films, film waves, and interfacial instabilities caused by air flow over a thin liquid layer. Topics include stability analysis of liquid film, interpretation of film instabilities, simple film, linear stability theory, inadequacy of the usual hydrodynamic model, and marcomolecule transport across the artery wall. The selection is a valuable source of data for researchers interested in the reactions of waves on fluid interfaces.

Presents in a systematic and unified manner the ray method, in its various forms, for studying nonlinear wave propagation in situations of physical interest, essentially fluid dynamics and plasma physics.

The subject of this volume is the observation and modelling of the gravity wave field in the atmosphere. The focus is on the question of how to include the effects of small-scale gravity waves in sophisticated global climate models. The book comprises 26 chapters, including contributions from distinguished experts in observation and theory, along with results from studies of gravity wave parameterization within comprehensive climate models.