Waves On Fluid Interfaces

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.

Despite factoring in countless natural, biological, and industrial processes, fixed attention on the singular attributes and behavior of fluids near or at interfaces has not received enough attention in the surface science literature. Liquid Interfacial Systems assembles and analyzes concepts and findings as an inclusive summation of fluid-fluid interfacial phenomena. This book covers excitation, stabilization, and suppression of instability at liquid interfaces. From the influential original research and scholarship of leaders in the discipline comes a volume to impart and explain definitions, scales, governing equations, and boundary conditions used in liquid interfacial system research.

Interfacial fluid dynamics is important in areas ranging from the flight of an aircraft to the flow of blood in the heart, and an area of active research and development owing to improved analytical, experimental, and computational techniques. This book describes the latest methods and applications in the field. Written by an internationally recognized panel of experts in both theory and experimentation, coverage is organized around five topics: Benard and thermocapillary instabilities, shear and pressure induced instabilities, waves and dispersions, multiphase systems, and complex flows. This comprehensive volume will interest a broad audience of graduate students, faculty, and researchers in mechanical, aerospace, materials, and chemical engineering, as well as in applied mathematics and physics.

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, water waves 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 flows. It is especially suitable as a textbook for courses at the final-year undergraduate or graduate level.

The problem of describing two-dimensional traveling water waves is considered. The water region is of finite depth and the interface between the region and the air is given by the graph of a function. We assume the flow to be incompressible and neglect the effects of surface tension. However we assume the flow to be rotational so that the vorticity distribution is a given function depending on the values of the stream function of the flow. The presence of vorticity increases the complexity of the problem and also leads to a wider class of solutions. First we study unidirectional waves with vorticity and verify the Benjamin-Lighthill conjecture for flows whose Bernoulli constant is close to the critical one. For this purpose it is shown that every wave, whose slope is bounded by a fixed constant, is either a Stokes or a solitary wave. It is proved that the whole set of these waves is uniquely parametrised (up to translation) by the flow force which varies between its values for the supercritical and subcritical shear flows of constant depth. We also study large-amplitude unidirectional waves for which we prove bounds for the free-surface profile and for Bernoulli’s constant. Second, we consider small-amplitude waves over flows with counter currents. Such flows admit layers, where the fluid flows in different directions. In this case we prove that the initial nonlinear free-boundary problem can be reduced to a finite-dimensional Hamiltonian system with a stable equilibrium point corresponding to a uniform stream. As an application of this result, we prove the existence of non-symmetric wave profiles. Furthermore, using a different method, we prove the existence of periodic waves with an arbitrary number of crests per period.

This graduate level textbook covers the topics of sound waves, water waves and stability problems in fluids. It also touches upon the subject of chaos which is related to stability problems. It aims to lead students in an accessible and efficient way to this important subject area in fluid mechanics and applied mathematics. The emphasis is on gaining an understanding of the essential features of the subject matter, thus often ignoring complicating details which may confuse non-experts. The topics chosen also reflect the personal bias and research activity of the authors.

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.

This book constitutes a comprehensive survey of the balance equations for mass, momentum and energy for the interfaces in pure fluids and mixtures. Constitutive laws are presented for many situations in engineering science, and examples are provided, including surface viscosity effects, variable surface tension and vapor recoil. In addition, some extensions of existing theory are given: stretch effect in premixed flames, relaxation zones downstream two-phase shock waves, and effective surface tension for high gradient zones.