Wave And Stability In Fluids

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Wave And Stability In Fluids

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Author : Din-Yu Hsieh
language : en
Publisher: World Scientific
Release Date : 1994

Wave And Stability In Fluids written by Din-Yu Hsieh and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Science categories.

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.

Wave Interactions And Fluid Flows

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Author : Alex D. D. Craik
language : en
Publisher: Cambridge University Press
Release Date : 1988-07-07

Wave Interactions And Fluid Flows written by Alex D. D. Craik and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-07-07 with Mathematics categories.

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.

Nonlinear Waves In Fluids Recent Advances And Modern Applications

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Author : Roger Grimshaw
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-03-23

Nonlinear Waves In Fluids Recent Advances And Modern Applications written by Roger Grimshaw and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-23 with Technology & Engineering categories.

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.

Structure And Dynamics Of Nonlinear Waves In Fluids Proceedings Of The Iutam Isimm Symposium

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Author : K Kirchgassner
language : en
Publisher: World Scientific
Release Date : 1995-08-31

Structure And Dynamics Of Nonlinear Waves In Fluids Proceedings Of The Iutam Isimm Symposium written by K Kirchgassner and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-08-31 with categories.

This symposium brought together mechanicians, physicists and applied mathematicians to discuss the interdisciplinary topic of nonlinear wave motion, which displays effects that give rise to a multitude of unanswered questions. Nonlinear waves in fluids in particular display all the prominent nonlinear phenomena such as chaos, turbulence and pattern formation. Amongst the topics emphasized in these proceedings are: travelling fronts, solitary waves and periodic waves (dissipative and conservative); temporal and spatial asymptotics of perturbations of waves; bifurcations, stability and local dynamics of waves; interaction between different waves, and between waves and the mean flow; wave breaking, nonlinear effects on focussing and diffraction; modulation and envelope equations (their derivation and validity); and numerical and experimental results.

Stability And Wave Motion In Porous Media

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Author : Brian Straughan
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-10

Stability And Wave Motion In Porous Media written by Brian Straughan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-10 with Technology & Engineering categories.

This book describes several tractable theories for fluid flow in porous media. The important mathematical quations about structural stability and spatial decay are address. Thermal convection and stability of other flows in porous media are covered. A chapter is devoted to the problem of stability of flow in a fluid overlying a porous layer. Nonlinear wave motion in porous media is analysed. In particular, waves in an elastic body with voids are investigated while acoustic waves in porous media are also analysed in some detail. A chapter is enclosed on efficient numerical methods for solving eigenvalue problems which occur in stability problems for flows in porous media. Brian Straughan is a professor at the Department of Mathemactical Sciences at Durham University, United Kingdom.

Spectral And Dynamical Stability Of Nonlinear Waves

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Author : Todd Kapitula
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-06

Spectral And Dynamical Stability Of Nonlinear Waves written by Todd Kapitula and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-06 with Mathematics categories.

This book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes fundamental ideas of the past 20+ years of research, carefully balancing theory and application. The book isolates and methodically develops key ideas by working through illustrative examples that are subsequently synthesized into general principles. Many of the seminal examples of stability theory, including orbital stability of the KdV solitary wave, and asymptotic stability of viscous shocks for scalar conservation laws, are treated in a textbook fashion for the first time. It presents spectral theory from a dynamical systems and functional analytic point of view, including essential and absolute spectra, and develops general nonlinear stability results for dissipative and Hamiltonian systems. The structure of the linear eigenvalue problem for Hamiltonian systems is carefully developed, including the Krein signature and related stability indices. The Evans function for the detection of point spectra is carefully developed through a series of frameworks of increasing complexity. Applications of the Evans function to the Orientation index, edge bifurcations, and large domain limits are developed through illustrative examples. The book is intended for first or second year graduate students in mathematics, or those with equivalent mathematical maturity. It is highly illustrated and there are many exercises scattered throughout the text that highlight and emphasize the key concepts. Upon completion of the book, the reader will be in an excellent position to understand and contribute to current research in nonlinear stability.

Lectures On The Theory Of Water Waves

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Author : Thomas J. Bridges
language : en
Publisher: Cambridge University Press
Release Date : 2016-02-04

Lectures On The Theory Of Water Waves written by Thomas J. Bridges and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-04 with Mathematics categories.

A range of experts contribute introductory-level lectures on active topics in the theory of water waves.

Stability And Transition In Shear Flows

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Author : Peter J. Schmid
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Stability And Transition In Shear Flows written by Peter J. Schmid and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

The field of hydrodynamic stability has a long history, going back to Rey nolds and Lord Rayleigh in the late 19th century. Because of its central role in many research efforts involving fluid flow, stability theory has grown into a mature discipline, firmly based on a large body of knowledge and a vast body of literature. The sheer size of this field has made it difficult for young researchers to access this exciting area of fluid dynamics. For this reason, writing a book on the subject of hydrodynamic stability theory and transition is a daunting endeavor, especially as any book on stability theory will have to follow into the footsteps of the classical treatises by Lin (1955), Betchov & Criminale (1967), Joseph (1971), and Drazin & Reid (1981). Each of these books has marked an important development in stability theory and has laid the foundation for many researchers to advance our understanding of stability and transition in shear flows.

Waves On Fluid Interfaces

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Author : Richard E. Meyer
language : en
Publisher: Academic Press
Release Date : 2014-05-10

Waves On Fluid Interfaces written by Richard E. Meyer and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

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.

Ray Methods For Nonlinear Waves In Fluids And Plasmas

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Author : Marcelo Anile
language : en
Publisher: CRC Press
Release Date : 2021-06-24

Ray Methods For Nonlinear Waves In Fluids And Plasmas written by Marcelo Anile and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-24 with Mathematics categories.

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.