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Author : Nicholas C. Vlessis
Publisher :
ISBN 13 :
Total Pages : 234 pages
Book Rating : 4.:/5 (113 download)
Download or read book Nonlinear Stability of Couette Flows of Micropolar Fluids written by Nicholas C. Vlessis and published by . This book was released on 1984 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Adelina Georgescu
Publisher : World Scientific
ISBN 13 : 9814289574
Total Pages : 418 pages
Book Rating : 4.8/5 (142 download)
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.
Author : Adrian V. Coward
Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.:/5 (317 download)
Download or read book Nonlinear Stability of Oscillatory Core-annular Flow: A Generalized Kuramoto-Sivashinsky Equation with Time Periodic Coefficients written by Adrian V. Coward and published by . This book was released on 1994 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Brian Straughan
Publisher : Springer Science & Business Media
ISBN 13 : 0387217401
Total Pages : 461 pages
Book Rating : 4.3/5 (872 download)
Download or read book The Energy Method, Stability, and Nonlinear Convection written by Brian Straughan and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Six new chapters (14-19) deal with topics of current interest: multi-component convection diffusion, convection in a compressible fluid, convenction with temperature dependent viscosity and thermal conductivity, penetrative convection, nonlinear stability in ocean circulation models, and numerical solution of eigenvalue problems.
Author : Eyvind Riis
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (312 download)
Download or read book The Stability of Couette-flow in Non-stratified Viscous Fluids written by Eyvind Riis and published by . This book was released on 1962 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Trudi A. Shortis
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.:/5 (317 download)
Download or read book On the Nonlinear Stability of the Unsteady, Viscous Flow of an Incompressible Fluid in a Curved Pipe written by Trudi A. Shortis and published by . This book was released on 1995 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jyh-Chen Chen
Publisher :
ISBN 13 :
Total Pages : 348 pages
Book Rating : 4.:/5 (175 download)
Download or read book Linear and Nonlinear Stability of Unsteady Circular Couette Flow written by Jyh-Chen Chen and published by . This book was released on 1986 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alric P. Rothmayer
Publisher :
ISBN 13 :
Total Pages : 196 pages
Book Rating : 4.3/5 (91 download)
Download or read book Nonlinear Stability of Unsteady Viscous Flow written by Alric P. Rothmayer and published by . This book was released on 1995 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book ديوان النيل written by and published by . This book was released on 1980 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael Renardy
Publisher :
ISBN 13 :
Total Pages : 13 pages
Book Rating : 4.:/5 (546 download)
Download or read book Nonlinear Stability of Flows of Jeffreys Fluids at Low Weissenberg Numbers written by Michael Renardy and published by . This book was released on 1994 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "We consider the stability of steady flows of viscoelastic fluids of Jeffreys type. For sufficiently small Weissenberg numbers, but arbitrary Reynolds numbers, it is proved that the flow is stable to small disturbances if the spectrum of the linearized operator is in the left half plane."
Author : C.M. Dafermos
Publisher : Elsevier
ISBN 13 : 0080931979
Total Pages : 609 pages
Book Rating : 4.0/5 (89 download)
Download or read book Handbook of Differential Equations: Evolutionary Equations written by C.M. Dafermos and published by Elsevier. This book was released on 2008-10-06 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE’s, written by leading experts. - Review of new results in the area- Continuation of previous volumes in the handbook series covering Evolutionary PDEs- Written by leading experts
Author : C. David Andereck
Publisher : Springer Science & Business Media
ISBN 13 : 1461534380
Total Pages : 351 pages
Book Rating : 4.4/5 (615 download)
Download or read book Ordered and Turbulent Patterns in Taylor-Couette Flow written by C. David Andereck and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seldom does a physical system, particularly one as apparently simple as the flow of a Newtonian fluid between concentric rotating cylinders, retain the interest of scientists, applied mathematicians and engineers for very long. Yet, as this volume goes to press it has been nearly 70 years since G. I. Taylor's outstanding experimental and theoretical study of the linear stability of this flow was published, and a century since the first experiments were performed on rotating cylinder viscometers. Since then, the study of this system has progressed enormously, but new features of the flow patterns are still being uncovered. Interesting variations on the basic system abound. Connections with open flows are being made. More complex fluids are used in some experiments. The vigor of the research going on in this particular example of nonequilibrium systems was very apparent at the NATO Advanced Research Workshop on "Ordered and Turbulent Patterns in Taylor Couette Flow," held in Columbus, Ohio, USA May 22-24, 1991. A primary goal of this ARW was to bring together those interested in pattern formation in the classic Taylor Couette problem with those looking at variations on the basic system and with those interested in related systems, in order to better define the interesting areas for the future, the open questions, and the features common (and not common) to closed and open systems. This volume contains many of the contributions presented during the workshop.
Author : Pun Wong Yau
Publisher :
ISBN 13 :
Total Pages : 145 pages
Book Rating : 4.:/5 (14 download)
Download or read book A Novel Extension to Classical Nonlinear Stability Theory of the Circular Couette Flow written by Pun Wong Yau and published by . This book was released on 2016 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: A nonlinear stability analysis of the viscous circular Couette flow to axisymmetric finite amplitude perturbations under axial periodic boundary conditions is developed. The analysis is based on investigating the properties of a reduced Arnol’d energy Casimir functional Ard of Wang (2009) [75]. A weighted kinetic energy integral of the perturbation, which has a form of Ard, the difference between the reduced Arnol’d functional and its base flow value, is used as a Lyapunov functional. We show that all the inviscid flow effects as well as all the viscous dependent terms that are related to the flow boundaries vanish. The time evolution of Ard depends only on the viscous effects of the perturbation’s dynamics inside the flow domain. The requirement for the temporal decay of Ard leads to two novel sufficient conditions for the nonlinear stability of the circular Couette flow in response to axisymmetric viscous perturbations. The linearized version of these conditions for infinitesimally small perturbations recovers the recent linear stability results by Kloosterziel (2010) [39]. By examining the nonlinear stability conditions, we establish a definite operational region of the viscous circular Couette flow that is independent of the fluid viscosity. In this region of operation, the flow is nonlinearly stable in response to perturbations of any size, provided that the initial total circulation function is above a minimum level determined by the operational conditions of the base flow. Comparisons with historical studies show that our results shed light on the experimental measurements of Wendt (1933) [76], and extend the classical nonlinear stability results of Serrin (1959) [62] and Joseph & Hung (1971) [35]. When the flow is nonlinearly stable and evolves axisymmetrically for all time, then it always decays asymptotically in time to the circular Couette flow determined uniquely by the setup of the rotating cylinders. Finally, we derive upper bound estimates on the decay rate of finite amplitude perturbations for the solid body rotation flow between two co-axial rotating cylinders and for the circular Couette flow. We demonstrate via numerical simulations that the respective analytical upper bounds are relevant to the dynamics of various axisymmetric perturbations tested, where they are strictly obeyed in both examples. This present study provides specific parameter regions for which the circular Couette flow is nonlinearly stable for all Reynolds numbers.
Author : Robert Betchov
Publisher :
ISBN 13 :
Total Pages : 356 pages
Book Rating : 4.3/5 (91 download)
Download or read book Stability of Parallel Flows written by Robert Betchov and published by . This book was released on 1967 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : U. A. Al-Mubaiyedh
Publisher :
ISBN 13 :
Total Pages : 2 pages
Book Rating : 4.:/5 (432 download)
Download or read book Nonlinear Stability Analyses of Non-Isothermal Viscoelastic Taylor-Couette Flow written by U. A. Al-Mubaiyedh and published by . This book was released on 1999 with total page 2 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Grzegorz Lukaszewicz
Publisher : Springer Science & Business Media
ISBN 13 : 1461206413
Total Pages : 262 pages
Book Rating : 4.4/5 (612 download)
Download or read book Micropolar Fluids written by Grzegorz Lukaszewicz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Micropolar fluids are fluids with microstructure. They belong to a class of fluids with nonsymmetric stress tensor that we shall call polar fluids, and include, as a special case, the well-established Navier-Stokes model of classical fluids that we shall call ordinary fluids. Physically, micropolar fluids may represent fluids consisting of rigid, randomly oriented (or spherical) particles suspended in a viscous medium, where the deformation of fluid particles is ignored. The model of micropolar fluids introduced in [65] by C. A. Eringen is worth studying as a very well balanced one. First, it is a well-founded and significant generalization of the classical Navier-Stokes model, covering, both in theory and applications, many more phenomena than the classical one. Moreover, it is elegant and not too complicated, in other words, man ageable to both mathematicians who study its theory and physicists and engineers who apply it. The main aim of this book is to present the theory of micropolar fluids, in particular its mathematical theory, to a wide range of readers. The book also presents two applications of micropolar fluids, one in the theory of lubrication and the other in the theory of porous media, as well as several exact solutions of particular problems and a numerical method. We took pains to make the presentation both clear and uniform.
Author : Francis John Edward Reid
Publisher :
ISBN 13 :
Total Pages : 182 pages
Book Rating : 4.:/5 (768 download)
Download or read book The Weakly Nonlinear Stability of an Oscillatory Fluid Flow written by Francis John Edward Reid and published by . This book was released on 2006 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
