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Instability In Models Connected With Fluid Flows
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Book Synopsis Stability Criteria for Fluid Flows by : Adelina Georgescu
Download or read book Stability Criteria for Fluid Flows written by Adelina Georgescu and published by World Scientific. This book was released on 2010 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive and self-contained introduction to the mathematical problems of thermal convection. The book delineates the main ideas leading to the authors' variant of the energy method. These can be also applied to other variants of the energy method. The importance of the book lies in its focussing on the best concrete results known in the domain of fluid flows stability and in the systematic treatment of mathematical instruments used in order to reach them.
Book Synopsis Instability in Models Connected with Fluid Flows II by : Claude Bardos
Download or read book Instability in Models Connected with Fluid Flows II written by Claude Bardos and published by Springer Science & Business Media. This book was released on 2007-12-20 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a unique collection of papers, all written by leading specialists, that presents the most recent results and advances in stability theory as it relates to fluid flows. The stability property is of great interest for researchers in many fields, including mathematical analysis, theory of partial differential equations, optimal control, numerical analysis, and fluid mechanics. This text will be essential reading for many researchers working in these fields.
Book Synopsis Stability and Transition in Shear Flows by : Peter J. Schmid
Download or read book Stability and Transition in Shear Flows written by Peter J. Schmid and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed look at some of the more modern issues of hydrodynamic stability, including transient growth, eigenvalue spectra, secondary instability. It presents analytical results and numerical simulations, linear and selected nonlinear stability methods. By including classical results as well as recent developments in the field of hydrodynamic stability and transition, the book can be used as a textbook for an introductory, graduate-level course in stability theory or for a special-topics fluids course. It is equally of value as a reference for researchers in the field of hydrodynamic stability theory or with an interest in recent developments in fluid dynamics. Stability theory has seen a rapid development over the past decade, this book includes such new developments as direct numerical simulations of transition to turbulence and linear analysis based on the initial-value problem.
Book Synopsis Instability in Models Connected with Fluid Flows I by : Claude Bardos
Download or read book Instability in Models Connected with Fluid Flows I written by Claude Bardos and published by Springer Science & Business Media. This book was released on 2007-12-20 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this authoritative and comprehensive volume, Claude Bardos and Andrei Fursikov have drawn together an impressive array of international contributors to present important recent results and perspectives in this area. The main subjects that appear here relate largely to mathematical aspects of the theory but some novel schemes used in applied mathematics are also presented. Various topics from control theory, including Navier-Stokes equations, are covered.
Book Synopsis Hydrodynamics and Nonlinear Instabilities by : Claude Godrèche
Download or read book Hydrodynamics and Nonlinear Instabilities written by Claude Godrèche and published by Cambridge University Press. This book was released on 2005-07-21 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents five sets of pedagogical lectures by internationally respected researchers on nonlinear instabilities and the transition to turbulence in hydrodynamics. The book begins with a general introduction to hydrodynamics covering fluid properties, flow measurement, dimensional analysis and turbulence. Chapter two reviews the special characteristics of instabilities in open flows. Chapter three presents mathematical tools for multiscale analysis and asymptotic matching applied to the dynamics of fronts and localized nonlinear states. Chapter four gives a detailed review of pattern forming instabilities. The final chapter provides a detailed and comprehensive introduction to the instability of flames, shocks and detonations. Together, these lectures provide a thought-provoking overview of current research in this important area.
Book Synopsis Routes to Absolute Instability in Porous Media by : Antonio Barletta
Download or read book Routes to Absolute Instability in Porous Media written by Antonio Barletta and published by Springer. This book was released on 2019-01-02 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the concepts of unstable flow solutions, convective instability and absolute instability, with reference to simple (or toy) mathematical models, which are mathematically simple despite their purely abstract character. Within this paradigm, the book introduces the basic mathematical tools, Fourier transform, normal modes, wavepackets and their dynamics, before reviewing the fundamental ideas behind the mathematical modelling of fluid flow and heat transfer in porous media. The author goes on to discuss the fundamentals of the Rayleigh-Bénard instability and other thermal instabilities of convective flows in porous media, and then analyses various examples of transition from convective to absolute instability in detail, with an emphasis on the formulation, deduction of the dispersion relation and study of the numerical data regarding the threshold of absolute instability. The clear descriptions of the analytical and numerical methods needed to obtain these parametric threshold data enable readers to apply them in different or more general cases. This book is of interest to postgraduates and researchers in mechanical and thermal engineering, civil engineering, geophysics, applied mathematics, fluid mechanics, and energy technology.
Book Synopsis Reduced-Order Modelling for Flow Control by : Bernd R. Noack
Download or read book Reduced-Order Modelling for Flow Control written by Bernd R. Noack and published by Springer Science & Business Media. This book was released on 2011-05-25 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on the physical and mathematical foundations of model-based turbulence control: reduced-order modelling and control design in simulations and experiments. Leading experts provide elementary self-consistent descriptions of the main methods and outline the state of the art. Covered areas include optimization techniques, stability analysis, nonlinear reduced-order modelling, model-based control design as well as model-free and neural network approaches. The wake stabilization serves as unifying benchmark control problem.
Book Synopsis Stability Criteria For Fluid Flows by : Lidia Palese
Download or read book Stability Criteria For Fluid Flows written by Lidia Palese and published by World Scientific. This book was released on 2009-12-18 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive and self-contained introduction to the mathematical problems of thermal convection. The book delineates the main ideas leading to the authors' variant of the energy method. These can be also applied to other variants of the energy method. The importance of the book lies in its focussing on the best concrete results known in the domain of fluid flows stability and in the systematic treatment of mathematical instruments used in order to reach them.
Book Synopsis Stability Criteria for Fluid Flows by : Adelina Georgescu
Download or read book Stability Criteria for Fluid Flows written by Adelina Georgescu and published by World Scientific. This book was released on 2010 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Mathematical models governing fluid flows stability. 1.1. General mathematical models of thermodynamics. 1.2. Classical mathematical models in thermodynamics of fluids. 1.3. Classical mathematical models in thermodynamics. 1.4. Classical perturbation models. 1.5. Generalized incompressible Navier-Stokes model -- 2. Incompressible Navier-Stokes fluid. 2.1. Back to integral setting; involvement of dynamics and bifurcation. 2.2. Stability in semidynamical systems. 2.3. Perturbations; asymptotic stability; linear stability. 2.4. Linear stability. 2.5. Prodi's linearization principle. 2.6. Estimates for the spectrum of Ã. 2.7. Universal stability criteria -- 3. Elements of calculus of variations. 3.1. Generalities. 3.2. Direct and inverse problems of calculus of variations. 3.3. Symmetrization of some matricial ordinary differential operators. 3.4. Variational principles for problems (3.3.1)-(3.3.7). 3.5. Fourier series solutions for variational problems -- 4. Variants of the energy method for non-stationary equations. 4.1. Variant based on differentiation of parameters. 4.2. Variant based on simplest symmetric part of operators. 4.3. Variants based on energy splitting -- 5. Applications to linear Bénard convections. 5.1. Magnetic Bénard convection in a partially ionized fluid. 5.2. Magnetic Bénard convection for a fully ionized fluid. 5.3. Convection in a micro-polar fluid bounded by rigid walls. 5.4. Convections governed by ode's with variable coefficients -- 6. Variational methods applied to linear stability. 6.1. Magnetic Bénard problem with Hall effect. 6.2. Lyapunov method applied to the anisotropic Bénard problem. 6.3. Stability criteria for a quasi-geostrophic forced zonal flow. 6.4. Variational principle for problem (5.3.1), (5.3.2). 6.5. Taylor-Dean problem -- 7. Applications of the direct method to linear stability. 7.1. Couette flow between two cylinders subject to a magnetic field. 7.2. Soret-Dufour driven convection. 7.3. Magnetic Soret-Dufour driven convection. 7.4. Convection in a porous medium. 7.5. Convection in the presence of a dielectrophoretic force. 7.6. Convection in an anisotropic M.H.D. thermodiffusive mixture. 7.7. Inhibition of the thermal convection by a magnetic field. 7.8. Microconvection in a binary layer subject to a strong Soret effect. 7.9. Convection in the layer between the sea bed and the permafrost.
Book Synopsis Instability in Models Connected with Fluid Flows II by : Claude Bardos
Download or read book Instability in Models Connected with Fluid Flows II written by Claude Bardos and published by Springer. This book was released on 2007-12-10 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a unique collection of papers, all written by leading specialists, that presents the most recent results and advances in stability theory as it relates to fluid flows. The stability property is of great interest for researchers in many fields, including mathematical analysis, theory of partial differential equations, optimal control, numerical analysis, and fluid mechanics. This text will be essential reading for many researchers working in these fields.
Book Synopsis Introduction to Hydrodynamic Stability by : P. G. Drazin
Download or read book Introduction to Hydrodynamic Stability written by P. G. Drazin and published by Cambridge University Press. This book was released on 2002-09-09 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment, and are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography and physics as well as engineering. This is a textbook to introduce these phenomena at a level suitable for a graduate course, by modelling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized, with many figures, and in references to more still and moving pictures. The relation of chaos to transition is discussed at length. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent in linear algebra, advanced calculus, elementary theory of ordinary differential equations, complex variables and the elements of fluid mechanics. The book is aimed at graduate students but will also be very useful for specialists in other fields.
Book Synopsis Two-Fluid Model Stability, Simulation and Chaos by : Martín López de Bertodano
Download or read book Two-Fluid Model Stability, Simulation and Chaos written by Martín López de Bertodano and published by Springer. This book was released on 2016-11-09 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the linear and nonlinear two-phase stability of the one-dimensional Two-Fluid Model (TFM) material waves and the numerical methods used to solve it. The TFM fluid dynamic stability is a problem that remains open since its inception more than forty years ago. The difficulty is formidable because it involves the combined challenges of two-phase topological structure and turbulence, both nonlinear phenomena. The one dimensional approach permits the separation of the former from the latter.The authors first analyze the kinematic and Kelvin-Helmholtz instabilities with the simplified one-dimensional Fixed-Flux Model (FFM). They then analyze the density wave instability with the well-known Drift-Flux Model. They demonstrate that the Fixed-Flux and Drift-Flux assumptions are two complementary TFM simplifications that address two-phase local and global linear instabilities separately. Furthermore, they demonstrate with a well-posed FFM and a DFM two cases of nonlinear two-phase behavior that are chaotic and Lyapunov stable. On the practical side, they also assess the regularization of an ill-posed one-dimensional TFM industrial code. Furthermore, the one-dimensional stability analyses are applied to obtain well-posed CFD TFMs that are either stable (RANS) or Lyapunov stable (URANS), with the focus on numerical convergence.
Download or read book Modelling Fluid Flow written by János Vad and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modelling Fluid Flow presents invited lectures, workshop summaries and a selection of papers from a recent international conference CMFF '03 on fluid technology. The lectures follow the current evolution and the newest challenges of the computational methods and measuring techniques related to fluid flow. The workshop summaries reflect the recent trends, open questions and unsolved problems in the mutually inspiring fields of experimental and computational fluid mechanics. The papers cover a wide range of fluids engineering, including reactive flow, chemical and process engineering, environmental fluid dynamics, turbulence modelling, numerical methods, and fluid machinery.
Book Synopsis Geophysical Fluid Dynamics II by : Emin Özsoy
Download or read book Geophysical Fluid Dynamics II written by Emin Özsoy and published by Springer Nature. This book was released on 2021-08-13 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops a fundamental understanding of geophysical fluid dynamics based on a mathematical description of the flows of inhomogeneous fluids. It covers these topics: 1. development of the equations of motion for an inhomogeneous fluid 2. review of thermodynamics 3. thermodynamic and kinetic energy equations 4. equations of state for the atmosphere and the ocean, salt, and moisture effects 5. concepts of potential temperature and potential density 6. Boussinesq and quasi-geostrophic approximations 7. conservation equations for vorticity, mechanical and thermal energy instability theories, internal waves, mixing, convection, double-diffusion, stratified turbulence, fronts, intrusions, gravity currents Graduate students will be able to learn and apply the basic theory of geophysical fluid dynamics of inhomogeneous fluids on a rotating earth, including: 1. derivation of the governing equations for a stratified fluid starting from basic principles of physics 2. review of thermodynamics, equations of state, isothermal, adiabatic, isentropic changes 3. scaling of the equations, Boussinesq approximation, applied to the ocean and the atmosphere 4. examples of stratified flows at geophysical scales, steady and unsteady motions, inertia-gravity internal waves, quasi-geostrophic theory 5. vorticity and energy conservation in stratified fluids 6.boundary layer convection in stratified containers and basins
Book Synopsis Unsteady Combustor Physics by : Tim C. Lieuwen
Download or read book Unsteady Combustor Physics written by Tim C. Lieuwen and published by Cambridge University Press. This book was released on 2012-08-27 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developing clean, sustainable energy systems is a pre-eminent issue of our time. Most projections indicate that combustion-based energy conversion systems will continue to be the predominant approach for the majority of our energy usage. Unsteady combustor issues present the key challenge associated with the development of clean, high-efficiency combustion systems such as those used for power generation, heating or propulsion applications. This comprehensive study is unique, treating the subject in a systematic manner. Although this book focuses on unsteady combusting flows, it places particular emphasis on the system dynamics that occur at the intersection of the combustion, fluid mechanics and acoustic disciplines. Individuals with a background in fluid mechanics and combustion will find this book to be an incomparable study that synthesises these fields into a coherent understanding of the intrinsically unsteady processes in combustors.
Book Synopsis Mathematical Fluid Mechanics by : Jiri Neustupa
Download or read book Mathematical Fluid Mechanics written by Jiri Neustupa and published by Birkhäuser. This book was released on 2012-12-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical modeling and numerical simulation in fluid mechanics are topics of great importance both in theory and technical applications. The present book attempts to describe the current status in various areas of research. The 10 chapters, mostly survey articles, are written by internationally renowned specialists and offer a range of approaches to and views of the essential questions and problems. In particular, the theories of incompressible and compressible Navier-Stokes equations are considered, as well as stability theory and numerical methods in fluid mechanics. Although the book is primarily written for researchers in the field, it will also serve as a valuable source of information to graduate students.
Book Synopsis Dynamic Mode Decomposition by : J. Nathan Kutz
Download or read book Dynamic Mode Decomposition written by J. Nathan Kutz and published by SIAM. This book was released on 2016-11-23 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data-driven dynamical systems is a burgeoning field?it connects how measurements of nonlinear dynamical systems and/or complex systems can be used with well-established methods in dynamical systems theory. This is a critically important new direction because the governing equations of many problems under consideration by practitioners in various scientific fields are not typically known. Thus, using data alone to help derive, in an optimal sense, the best dynamical system representation of a given application allows for important new insights. The recently developed dynamic mode decomposition (DMD) is an innovative tool for integrating data with dynamical systems theory. The DMD has deep connections with traditional dynamical systems theory and many recent innovations in compressed sensing and machine learning. Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems, the first book to address the DMD algorithm, presents a pedagogical and comprehensive approach to all aspects of DMD currently developed or under development; blends theoretical development, example codes, and applications to showcase the theory and its many innovations and uses; highlights the numerous innovations around the DMD algorithm and demonstrates its efficacy using example problems from engineering and the physical and biological sciences; and provides extensive MATLAB code, data for intuitive examples of key methods, and graphical presentations.
