Interfacial Solitary Waves in a Two-fluid Medium PDF Download

Author: Lloyd R. Walker
Publisher:
ISBN:
Category : Fluid dynamics
Languages : en
Pages : 9

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Author: Hu-Yun Sha
Publisher:
ISBN:
Category :
Languages : en
Pages : 178

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Author: Richard E. Meyer
Publisher: Academic Press
ISBN: 1483265145
Category : Mathematics
Languages : en
Pages : 370

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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.

Author:
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Category :
Languages : en
Pages : 32

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This paper concerns the existence of internal solitary waves moving with a constant speed at the interface of a two-layer fluid with infinite height. The fluids are immiscible, inviscid, and incompressible with constant but different densities. Assume that the height of the upper fluid is infinite and the depth of the lower fluid is finite. It has been formally derived before that under long-wave assumption the first-order approximation of the interface satisfies the Benjamin-Ono equation, which has algebraic solitary-wave solutions. This paper gives a rigorous proof of the existence of solitary-wave solutions of the exact equations governing the fluid motion, whose first-order approximations are the algebraic solitary-wave solutions of the Benjamin-Ono equation. The proof relies on estimates of integral operators using Fourier transforms in L2(R)- space and is different from the previous existence proof of solitary waves in a two-layer fluid with finite depth.

Author: Claire David
Publisher: Bentham Science Publishers
ISBN: 1608051404
Category : Science
Languages : en
Pages : 267

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Since the first description by John Scott Russel in 1834, the solitary wave phenomenon has attracted considerable interests from scientists. The most interesting discovery since then has been the ability to integrate most of the nonlinear wave equations which govern solitary waves, from the Korteweg-de Vries equation to the nonlinear Schrodinger equation, in the 1960's. From that moment, a huge amount of theoretical works can be found on solitary waves. Due to the fact that many physical phenomena can be described by a soliton model, applications have followed each other, in telecommunications

Author: David Christopher Calvo
Publisher:
ISBN:
Category :
Languages : en
Pages : 286

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(Cont.) The analysis followed in the free-surface problem is then generalized to examine the dynamics of gravity-capillary interfacial solitary waves in a layered two-fluid system. Here, the linear stability and limiting wave forms of free solitary waves are determined over a range of system parameters using the full hydrodynamic equations. Finally, a related problem of gravity-capillary envelope solitons is considered under the general situation of unequal phase and group speeds. By asymptotic and numerical techniques it is found that envelope solitons are generally nonlocal-tails are radiated owing to a resonance mechanism that is beyond the NLS equation.

Author: Arkadi Berezovski
Publisher: Springer Nature
ISBN: 3030299511
Category : Mathematics
Languages : en
Pages : 376

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This book gathers contributions on various aspects of the theory and applications of linear and nonlinear waves and associated phenomena, as well as approaches developed in a global partnership of researchers with the national Centre of Excellence in Nonlinear Studies (CENS) at the Department of Cybernetics of Tallinn University of Technology in Estonia. The papers chiefly focus on the role of mathematics in the analysis of wave phenomena. They highlight the complexity of related topics concerning wave generation, propagation, transformation and impact in solids, gases, fluids and human tissues, while also sharing insights into selected mathematical methods for the analytical and numerical treatment of complex phenomena. In addition, the contributions derive advanced mathematical models, share innovative ideas on computing, and present novel applications for a number of research fields where both linear and nonlinear wave problems play an important role. The papers are written in a tutorial style, intended for non-specialist researchers and students. The authors first describe the basics of a problem that is currently of interest in the scientific community, discuss the state of the art in related research, and then share their own experiences in tackling the problem. Each chapter highlights the importance of applied mathematics for central issues in the study of waves and associated complex phenomena in different media. The topics range from basic principles of wave mechanics up to the mathematics of Planet Earth in the broadest sense, including contemporary challenges in the mathematics of society. In turn, the areas of application range from classic ocean wave mathematics to material science, and to human nerves and tissues. All contributions describe the approaches in a straightforward manner, making them ideal material for educational purposes, e.g. for courses, master class lectures, or seminar presentations.

Author: Bruce R. Sutherland
Publisher: Cambridge University Press
ISBN: 1316184323
Category : Science
Languages : en
Pages : 395

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The study of internal gravity waves provides many challenges: they move along interfaces as well as in fully three-dimensional space, at relatively fast temporal and small spatial scales, making them difficult to observe and resolve in weather and climate models. Solving the equations describing their evolution poses various mathematical challenges associated with singular boundary value problems and large amplitude dynamics. This book provides the first comprehensive treatment of the theory for small and large amplitude internal gravity waves. Over 120 schematics, numerical simulations and laboratory images illustrate the theory and mathematical techniques, and 130 exercises enable the reader to apply their understanding of the theory. This is an invaluable single resource for academic researchers and graduate students studying the motion of waves within the atmosphere and ocean, and also mathematicians, physicists and engineers interested in the properties of propagating, growing and breaking waves.

Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 9

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The authors derive model equations that govern the evolution of internal gravity waves at the interface of two immiscible fluids. These models follow from the original Euler equations under the sole assumption that the waves are long compared to the undisturbed thickness of one of the fluid layers. No smallness assumption on the wave amplitude is made. Here the shallow water configuration is first considered, whereby the waves are taken to be long with respect to the total undisturbed thickness of the fluids. In part 2, the authors derive models for the configuration in which one of the two fluids has a thickness much larger than the wavelength. The fully nonlinear models contain the Korteweg-de Vries (KdV) equation and the intermediate-long-wave (ILW) equation, for shallow and deep water configurations respectively, as special cases in the limit of weak nonlinearity and unidirectional wave propagation. In particular, for a solitary wave of given amplitude, the characteristic wavelength is larger and the wave speed smaller than their counterparts for solitary wave solutions of the weakly nonlinear equations. These features are compared and found in overall good agreement with available experimental data for solitary waves of large amplitude in two-fluid systems.

Author: Stephanie Blanda
Publisher:
ISBN:
Category :
Languages : en
Pages :

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The generation of ocean waves by wind has long been a topic of interest. However, it has only been in the past 100 years or so, starting with work by Jeffreys, that significant progress has been made on this topic. Despite this progress, there is still much that is not understood. For example, the predictions of the growth rate are typically underestimates by an order of magnitude; the role of the interfacial current at the air-water interface that is set up by the wind is neglected in all studies of which we are aware; and the wind is considered to be steady in every study of which we are aware. Thus, in the formulation herein, the wind (i) is considered to be time-dependent; (ii) sets up an interfacial current; and (iii) is an exact solution to the Navier-Stokes equations. Our goal is to predict the growth rates of waves with a given wavenumber that arise as perturbations to this base flow.The problem formulation of partial differential equations for the perturbations (the waves) is simplified by setting time to be a parameter, allowing for a Fourier decomposition in time as well as in the propagation distance. The resulting ordinary differential equations are with respect to the vertical spatial variable and are of Airy-type. The differential equations are solved exactly to reduce the problem to a linear, algebraic system of 19 equations that has a vanishing determinant for nonzero waves. The result is a relationship between the complex frequency and real wavenumber. This relationship is analyzed numerically to determine the oscillation frequency corresponding to the largest growth rate for a given wavenumber. Parametric studies, in which the interfacial current, the time, and the wavenumber are varied, show that for very small times the interfacial current plays an important role in this maximum growth rate frequency. Further, a bound on time is found for which the base flow model considered here becomes inadequate.The emphasis in this dissertation is the growth rate of an instability of the interface between air flowing over water. However, the theory developed herein is generic to any two immiscible, hydrostatically stable fluids in a gravitational field and may thus be used to obtain the growth rates of interfacial waves in any system comprising fluids of arbitrary densities and viscosities.