Internally Heated Convection and Rayleigh-Bénard Convection
Internally Heated Convection and Rayleigh-Bénard Convection

Author: David Goluskin

Publisher: Springer

Published: 2015-11-21

Total Pages: 73

ISBN-13: 3319239414

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This Brief describes six basic models of buoyancy-driven convection in a fluid layer: three configurations of internally heated convection and three configurations of Rayleigh-Bénard convection. The author discusses the main quantities that characterize heat transport in each model, along with the constraints on these quantities. This presentation is the first to place the various models in a unified framework, and similarities and differences between the cases are highlighted. Necessary and sufficient conditions for convective motion are given. For the internally heated cases only, parameter-dependent lower bounds on the mean fluid temperature are proven, and results of past simulations and laboratory experiments are summarized and reanalyzed. The author poses several open questions for future study.

Rayleigh-benard Convection: Structures And Dynamics
Rayleigh-benard Convection: Structures And Dynamics

Author: Alexander V Getling

Publisher: World Scientific

Published: 1998-03-06

Total Pages: 256

ISBN-13: 9814498971

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This invaluable book presents a concise but systematic account of the formation of spatial flow structures in a horizontal fluid layer heated from below. Flows of this type, known as Rayleigh-Bénard convection, show important features of behaviour inherent not only in various hydrodynamic-instability phenomena but also in nonlinear pattern-forming processes in other contexts. The book describes the basic methods of investigating convection patterns, and the types of two- and three-dimensional flows, pattern defects, and sequences of convection-regime changes.The author pays special attention to the question of how various factors (mainly reducible to initial and boundary conditions) determine the shapes and sizes of the structures which develop. In this way, the role of order and disorder in flow patterns, as a factor strongly affecting the character of the evolution of structures, is revealed. The presentation emphasizes the physical picture of these phenomena, without excessive mathematical detail.

Rayleigh-B‚nard Convection
Rayleigh-B‚nard Convection

Author: Alexander V. Getling

Publisher: World Scientific

Published: 1998

Total Pages: 264

ISBN-13: 9789810226572

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This invaluable book presents a concise but systematic account of the formation of spatial flow structures in a horizontal fluid layer heated from below. Flows of this type, known as Rayleigh-B‚nard convection, show important features of behaviour inherent not only in various hydrodynamic-instability phenomena but also in nonlinear pattern-forming processes in other contexts. The book describes the basic methods of investigating convection patterns, and the types of two- and three-dimensional flows, pattern defects, and sequences of convection-regime changes.The author pays special attention to the question of how various factors (mainly reducible to initial and boundary conditions) determine the shapes and sizes of the structures which develop. In this way, the role of order and disorder in flow patterns, as a factor strongly affecting the character of the evolution of structures, is revealed. The presentation emphasizes the physical picture of these phenomena, without excessive mathematical detail.

Introduction to Hydrodynamic Stability
Introduction to Hydrodynamic Stability

Author: P. G. Drazin

Publisher: Cambridge University Press

Published: 2002-09-09

Total Pages: 278

ISBN-13: 1316582876

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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.

Dynamics of Spatio-Temporal Cellular Structures
Dynamics of Spatio-Temporal Cellular Structures

Author: Innocent Mutabazi

Publisher: Springer

Published: 2010-06-14

Total Pages: 249

ISBN-13: 0387251111

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The impact of Benard's discovery on 20th century physics is crucial to any modern research area such as fluid dynamics, nonlinear dynamics, and non-equilibrium thermodynamics, just to name a few. This centenary review shows the broad scope and development including modern applications, edited and written by experts in the field.

Magnetoconvection
Magnetoconvection

Author: N. O. Weiss

Publisher: Cambridge University Press

Published: 2014-10-30

Total Pages: 411

ISBN-13: 052119055X

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Leading experts present the current state of knowledge of the subject of magnetoconvection from the viewpoint of applied mathematics.

Routes to Absolute Instability in Porous Media
Routes to Absolute Instability in Porous Media

Author: Antonio Barletta

Publisher: Springer

Published: 2019-01-02

Total Pages: 283

ISBN-13: 3030061949

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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.

Dissipative Structures and Weak Turbulence
Dissipative Structures and Weak Turbulence

Author:

Publisher: Academic Press

Published: 2014-06-28

Total Pages: 505

ISBN-13: 008092445X

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Dissipative Structure and Weak Turbulence provides an understanding of the emergence and evolution of structures in macroscopic systems. This book discusses the emergence of dissipative structures. Organized into 10 chapters, this book begins with an overview of the stability of a fluid layer with potentially unstable density stratification in the field of gravity. This text then explains the theoretical description of the dynamics of a given system at a formal level. Other chapters consider several examples of how such simplified models can be derived, complicating the picture progressively to account for other phenomena. This book discusses as well the theory and experiments on plain Rayleigh–Bénard convection by setting first the theoretical frame and deriving the analytical solution of the marginal stability problem. The final chapter deals with building a bridge between chaos as studied in weakly confined systems and more advanced turbulence in the most conventional sense. This book is a valuable resource for physicists.

Chaos, Complexity And Transport: Theory And Applications - Proceedings Of The Cct '07
Chaos, Complexity And Transport: Theory And Applications - Proceedings Of The Cct '07

Author: Xavier Leoncini

Publisher: World Scientific

Published: 2008-05-27

Total Pages: 378

ISBN-13: 9814470759

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This book aims to provide the readers with a wide panorama of different aspects related to Chaos, Complexity and Transport. It consists of a collection of contributions ranging from applied mathematics to experiments, presented during the CCT'07 conference (Marseilles, June 4-8, 2007). The book encompasses different traditional fields of physics and mathematics while trying to keep a common language among the fields, and targets a nonspecialized audience.

Bénard Cells and Taylor Vortices
Bénard Cells and Taylor Vortices

Author: E. L. Koschmieder

Publisher: Cambridge University Press

Published: 1993-02-26

Total Pages: 356

ISBN-13: 9780521402040

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This book describes the motions resulting from heating a fluid layer from below.