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Linear Stability Of Circular Couette Flow At Small Radius Ratios And The Relationship To A Cylinder Rotating In An Unbounded Fluid
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Book Synopsis Linear Stability of Circular Couette Flow at Small Radius Ratios and the Relationship to a Cylinder Rotating in an Unbounded Fluid by : Florent Petteni
Download or read book Linear Stability of Circular Couette Flow at Small Radius Ratios and the Relationship to a Cylinder Rotating in an Unbounded Fluid written by Florent Petteni and published by . This book was released on 2001 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Stability of Couette Flow Between Rotating Cylinders in the Presence of a Radial Tempearture Gradient by : Jed A. Walowit
Download or read book The Stability of Couette Flow Between Rotating Cylinders in the Presence of a Radial Tempearture Gradient written by Jed A. Walowit and published by . This book was released on 1963 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1968 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Physics Briefs written by and published by . This book was released on 1993 with total page 1288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Novel Extension to Classical Nonlinear Stability Theory of the Circular Couette Flow by : Pun Wong Yau
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.
Download or read book Science Abstracts written by and published by . This book was released on 1992 with total page 1228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Theoretical Chemical Engineering Abstracts by :
Download or read book Theoretical Chemical Engineering Abstracts written by and published by . This book was released on 1964 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Ordered and Turbulent Patterns in Taylor-Couette Flow by : C. David Andereck
Download or read book Ordered and Turbulent Patterns in Taylor-Couette Flow written by C. David Andereck and published by Springer. This book was released on 2013-11-10 with total page 357 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.
Book Synopsis On the Linear Stability of Compressible Plane Couette Flow by : Institute for Computer Applications in Science and Engineering
Download or read book On the Linear Stability of Compressible Plane Couette Flow written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1991 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Effect of Radius Ratio on the Stability of Couette Flow and Taylor Vortex Flow by : R. C. DiPrima
Download or read book The Effect of Radius Ratio on the Stability of Couette Flow and Taylor Vortex Flow written by R. C. DiPrima and published by . This book was released on 1984 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: The effect of radius ratio on the ability of Couette flow to axisymmetric and nonaxisymmetric disturbances and the stability of Taylor vortex flow to nonaxisymmetric disturbances is considered. It is assumed that the outer cylinder is at rest. As the ratio eta of the radius of the inner cylinder to the radius of the outer cylinder is decreased, it is found that the number of unstable normal modes for Couette flow at a fixed Taylor number decreases rapidly, and there is a critical value of eta equal to about 0.65, below which there is no instability of the Taylor vortex flow for the range of Taylor numbers considered here. Recent experimental observations are summarized. Additional keywords: charts, reprints. (Author).
Book Synopsis Stability of Oscillatory Two Phase Couette Flow by : Institute for Computer Applications in Science and Engineering
Download or read book Stability of Oscillatory Two Phase Couette Flow written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1993 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Linear and Nonlinear Stability of Unsteady Circular Couette Flow by : Jyh-Chen Chen
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:
Book Synopsis Two-Fluid Couette Flow Between Concentric Cylinders by : Y. Renardy
Download or read book Two-Fluid Couette Flow Between Concentric Cylinders written by Y. Renardy and published by . This book was released on 1984 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document considers the flow of two immiscible fluids lying between concentric cylinders when the outer cylinder is fixed and the inner one rotates. The interface is assumed to be concentric with the cylinders and gravitational effects are neglected. The authors present a numerical study of the effect of different viscosities, different densities and surface tension on the linear stability of the Couette flow. Their results indicate that with surface tension, a thin layer of the less viscous fluid next to either cylinder is linearly stable and that it is possible to have stability with the less dense fluid lying outside. The stable configuration with the less viscous fluid next to the inner cylinder is more stable than the one with the less viscous fluid next to the outer cylinder. The onset of Taylor instability for one-fluid flow may be delayed by the addition of a thin layer of less viscous fluid on the inner wall and promoted by a layer of more viscous fluid on the inner wall. (Author).
Book Synopsis The Stability of Couette Flow Between Rotating Cylinders in the Presence of a Radial Temperature Gradient by : Jed A. Walowit
Download or read book The Stability of Couette Flow Between Rotating Cylinders in the Presence of a Radial Temperature Gradient written by Jed A. Walowit and published by . This book was released on 1963 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Length Effects in Taylor-Couette Flow by : Craig L. Streett
Download or read book Finite Length Effects in Taylor-Couette Flow written by Craig L. Streett and published by . This book was released on 1986 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hydrodynamic Stability of Flow Between Rotating Spheres and Rotating-sliding Cylinders by : Bruce Roy Munson
Download or read book Hydrodynamic Stability of Flow Between Rotating Spheres and Rotating-sliding Cylinders written by Bruce Roy Munson and published by . This book was released on 1980 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt:
