Navier-Stokes Equations and Turbulence (Encyclopedia of Mathematics and its Applications)

Book Description

This book presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. It is the result of many years of research by the authors to analyze turbulence using Sobolev spaces and functional analysis. In this way the authors have recovered parts of the conventional theory of turbulence, deriving rigorously from the Navier-Stokes equations that had been arrived at earlier by phenomenological arguments. Appendices give full details of the mathematical proofs and subtleties.

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This book aims to bridge the gap between practising mathematicians and the practitioners of turbulence theory. It presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. The book is the result of many years of research by the authors to analyze turbulence using Sobolev spaces and functional analysis. In this way the authors have recovered parts of the conventional theory of turbulence, deriving rigorously from the Navier-Stokes equations what had been arrived at earlier by phenomenological arguments. The mathematical technicalities are kept to a minimum within the book, enabling the language to be at a level understood by a broad audience. Each chapter is accompanied by appendices giving full details of the mathematical proofs and subtleties. This unique presentation should ensure a volume of interest to mathematicians, engineers, and physicists.

Attractors Representing Turbulent Flows (Memoirs of the American Mathematical Society)

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Attractors Representing Turbulent Flows (Memoirs of the American Mathematical Society)
P. Constantin , C. Foias , and R. Temam
Manufacturer: Amer Mathematical Society
ProductGroup: Book
Binding: Paperback

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ASIN: 0821823159

Dynamic Multilevel Methods and the Numerical Simulation of Turbulence

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Dynamic Multilevel Methods and the Numerical Simulation of Turbulence
Thierry Dubois , Frangois Jauberteau , and Roger Temam
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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This book describes the implementation of multilevel methods for the numerical simulation of turbulent flows. The general ideas for the algorithms presented stem from dynamical systems theory and are based on the decomposition of the unknown function into two or more arrays corresponding to different scales in the Fourier space. Before describing in detail the numerical algorithm, survey chapters on the mathematical theory of the Navier-Stokes equations and on the physics of the conventional theory of turbulence are included. The multilevel methods are applied here to the simulation of homogeneous isotropic turbulent flows as well as turbulent channel flows. The implementation issues are discussed in detail and numerical simulations of the flows cited above are presented and analyzed. The methods have been applied in the context of the direct numerical simulation and are therefore compared to such simulations.

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Lectures on Turbulance Theory
A. Chorin
Manufacturer: Publish or Perish
ProductGroup: Book
Binding: Paperback
ASIN: 0914098144

Mathematical Foundation of Turbulent Viscous Flows: Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 1-5, 2003 (Lecture ... Mathematics / Fondazione C.I.M.E., Firenze)

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Mathematical Foundation of Turbulent Viscous Flows: Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 1-5, 2003 (Lecture ... Mathematics / Fondazione C.I.M.E., Firenze)
Peter Constantin , Giovanni Gallavotti , Alexandre V. Kazhikhov , Yves Meyer , and Seiji Ukai
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 3540285865

Book Description

Five leading specialists reflect on different and complementary approaches to fundamental questions in the study of the Fluid Mechanics and Gas Dynamics equations. Constantin presents the Euler equations of ideal incompressible fluids and discusses the blow-up problem for the Navier-Stokes equations of viscous fluids, describing some of the major mathematical questions of turbulence theory. These questions are connected to the Caffarelli-Kohn-Nirenberg theory of singularities for the incompressible Navier-Stokes equations that is explained in Gallavotti's lectures. Kazhikhov introduces the theory of strong approximation of weak limits via the method of averaging, applied to Navier-Stokes equations. Y. Meyer focuses on several nonlinear evolution equations - in particular Navier-Stokes - and some related unexpected cancellation properties, either imposed on the initial condition, or satisfied by the solution itself, whenever it is localized in space or in time variable. Ukai presents the asymptotic analysis theory of fluid equations. He discusses the Cauchy-Kovalevskaya technique for the Boltzmann-Grad limit of the Newtonian equation, the multi-scale analysis, giving the compressible and incompressible limits of the Boltzmann equation, and the analysis of their initial layers.

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Optimal Control of Viscous Flow

Manufacturer: Society for Industrial Mathematics
ProductGroup: Book
Binding: Paperback

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ASIN: 0898714060

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Optimal control of fluid dynamics is of fundamental importance in aero/hydrodynamic vehicles, combustion control in engines, fire suppression, magnetic fusion, and ocean and atmospheric prediction. This book provides a well-crystalized theory and computational methods for this new field. It is the first and only book to provide a focused presentation of the issues concerning feedback control in viscous hydrodynamics. Engineers, physicists, and mathematicians working in the aforementioned fields will be interested in this book.

Turbulence in Fluid Flows: A Dynamical Systems Approach (The IMA Volumes in Mathematics and its Applications)

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Turbulence in Fluid Flows: A Dynamical Systems Approach (The IMA Volumes in Mathematics and its Applications)

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0387941134

Book Description

The articles in this volume are based on recent research on the phenomenon of turbulence in fluid flows collected by the Institute for Mathematics and its Applications. This volume looks into the dynamical properties of the solutions of the Navier-Stokes equations, the equations of motion of incompressible, viscous fluid flows, in order to better understand this phenomenon. Although it is a basic issue of science, it has implications over a wide spectrum of modern technological applications. The articles offer a variety of approaches to the Navier-Stokes problems and related issues. This book should be of interest to both applied mathematicians and engineers.

Unstable and Turbulent Motion of Fluid: Rims, Kyoto University, 26-30 October 1992

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Unstable and Turbulent Motion of Fluid: Rims, Kyoto University, 26-30 October 1992

Manufacturer: World Scientific Pub Co Inc
ProductGroup: Book
Binding: Hardcover

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Key issues in the particle method for computation of wave breaking [An article from: Coastal Engineering]

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Key issues in the particle method for computation of wave breaking [An article from: Coastal Engineering]
H. Gotoh , and T. Sakai
Manufacturer: Elsevier
ProductGroup: Book
Binding: Digital
ASIN: B000RR6M80

Book Description

This digital document is a journal article from Coastal Engineering, published by Elsevier in . The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

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The Lagrangian particle method is a superior tool for the modelling of violent behavior of the water surface, such as wave breaking and overtopping. To further develop the numerical wave flume by the particle method, there remain several issues: modelling of the sub-particle-scale turbulence, modelling of the gas-phase behavior, modelling of movable bed (sediment transport), and modelling of floating bodies. In this paper, the sub-particle-scale turbulence model, the solid-liquid and liquid-gas two-phase-flow models, and the floating-bodies model, which have been developed by the authors, are reviewed to present the performance of the particle method in a computation of wave breaking.

Modeling particle deposition and distribution in a chamber with a two-equation Reynolds-averaged Navier-Stokes model [An article from: Journal of Aerosol Science]

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Modeling particle deposition and distribution in a chamber with a two-equation Reynolds-averaged Navier-Stokes model [An article from: Journal of Aerosol Science]
A.C.K. Lai , and F. Chen
Manufacturer: Elsevier
ProductGroup: Book
Binding: Digital
ASIN: B000PC03IC

Book Description

This digital document is a journal article from Journal of Aerosol Science, published by Elsevier in 2006. The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

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A Lagrangian simulation for aerosol particle transport and deposition in a chamber is developed. The eddy interaction model (EIM) is adopted to generate the instantaneous turbulent fluctuating velocity field. It is found that a satisfactory result can be obtained only when the near-wall grid is sufficiently fine and the near-wall turbulent kinetic energy is damped effectively according to its component normal to the wall. Seven particle size groups ranging from 0.01 to 10@mm are studied. A comparison between the current numerical model and a semi-empirical expression indicates that improved deposition fraction results were obtained. The particle deposition and particle fate in the chamber are also presented.

Customer Reviews:

The Best of Shakespeare in One Book.......2003-06-19

Having a love of literature, and being an English Lit. major has given me the oportunity to read most of Shakespeare's works. Shakespeare's talent and genius has surely endured and his beautiful writings are essential to mankind not only in the classroom but throughout our lives. His tragedies speak the loudest to me, as they are charged with drama, emotion and memorable quotations. Having to choose a favorite book of all time I would say, "Othello." Yet Hamlet is my second favorite drama of Shakespeare's, and Macbeth also holds strong. I do not care for King Lear but having Shakespeare's 4 greatest and most popular tragedies in one book is a collection worth having.

best.......2000-06-24

4 of his best i strongly recomend this group of storys.

An excellent collection with great footnotes.......2000-03-14

Hamlet, Othello, King Lear, and Macbeth are Shakespeare's greatest works. These fantastic stories, coupled with strong footnotes, make for superb reading material. I would recommend this book to beginning and master Shakespeare readers.

Four Tragedies: Hamlet, Othello, King Lear, Macbeth (Bantam Classics)

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Shakespearean tragedy -Greatness is all
Tragedy!
excellent edition of great tragedies
This book needs footnotes!
for shakespeare fans

Four Tragedies: Hamlet, Othello, King Lear, Macbeth (Bantam Classics)
William Shakespeare
Manufacturer: Bantam Classics
ProductGroup: Book
Binding: Paperback

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ASIN: 0553212834
Release Date: 1988-01-01

Book Description

HAMLET
One of the most famous plays of all time, the compelling tragedy of the young prince of Denmark who must reconcile his longing for oblivion with his duty to avenge his father’s murder is one of Shakespeare’s greatest works. The ghost, Ophelia’s death and burial, the play within a play, and the breathtaking swordplay are just some of the elements that make Hamlet a masterpiece of the theater.
OTHELLO
This great tragedy of unsurpassed intensity and emotion is
played out against Renaissance splendor. The doomed marriage
of Desdemona to the Moor Othello is the focus of a storm of tension, incited by the consummately evil villain Iago, that culminates in one of the most deeply moving scenes in theatrical history.
KING LEAR
Here is the famous and moving tragedy of a king who foolishly divides his kingdom between his two wicked daughters and estranges himself from the young daughter who loves him–a theatrical spectacle of outstanding proportions.
MACBETH
No dramatist has ever seen with more frightening clarity into the heart and mind of a murderer than has Shakespeare in this brilliant and bloody tragedy of evil. Taunted into asserting his “masculinity” by his ambitious wife, Macbeth chooses to embrace the Weird Sisters’ prophecy and kill his king–and thus, seals his own doom.

Each Edition Includes:
• Comprehensive explanatory notes
• Vivid introductions and the most up-to-date scholarship
• Clear, modernized spelling and punctuation, enabling contemporary readers to understand the Elizabethan English
• Completely updated, detailed bibliographies and performance histories
• An interpretive essay on film adaptations of the play, along with an extensive filmography

Customer Reviews:

Shakespearean tragedy -Greatness is all .......2005-10-28

To have the four great tragedies together raises the question of what the essence, the real heart of Shakespearean tragedy is.
In Aristotle's definition of Greek tragedy the overweening pride of the hero(hubris) and tragic fault( hamartia ) lead to his eventual destruction. The audience watching this is in the course of this purged of pity and fear.
In Shakespearean tragedy there is as in Aristotle a hero who is larger than the ordinary man. The hero too has a great flaw and comes to a destructive end. But the doubt and hesitancy of dreaming Hamlet, the great ambition for kingship of Macbeth, the blind filial love of Lear seem more emotionally complex than that of the Greek heroes. And the language in which the story of their respective downfalls is told is too more rich, complex, and ambivalent than that of the clearer Greek earlier model.
And this in such a way that the Shakespearean tragic heroes each seem to be in themselves a kind of supreme human essence, a manifestation of character at its greatest level of intensity.
Shakespeare's greatest heroes are individuals who become in some sense the ' type' of themselves, and live in our minds as models of humanity in its extreme essence.
'Greatness is all'

Tragedy!.......2003-07-23

Hamlet
This play, of course, is perhaps the best known in all of English literature. Taking it's inspiration from lesser plays and tales of the same name, Shakespeare crafted the characters, dialogue and plot into a timeless tale of betrayal, the quest for justice, and ultimately a hollow victory. This play, in short, is a downer.

I will speak daggers to her, but use none.

Of course, it really thrilled the audiences, who, lacking the primetime violence of today, enjoyed seeing the blood, the gore, the violence, the swordplay. Those with a more subtle bent were very satisfied with the wonderful dialogues, full of double and self-reflexive meanings. So many of the monologues have become common parlance in our language.

A hit, a very palpable hit.

The 'on one foot' synopsis: Hamlet, prince of Denmark, is suspicious that his step-father killed his father and usurped the throne and his mother's bedchamber; he plots to get revenge; in the meantime his love-interest Ophelia dies; in a duel to the death at the end the mother dies, the step-father dies, the duel contender dies, and Hamlet dies. Something is rotten in the state of Denmark.

The rest is silence.

Othello
Rude I am in speech,
And little blessed with the soft phrase of peace

Surely Shakespeare was not speaking of himself here. Even his poorly-spoken characters cannot help to have an elegance and subtlety all their own. Othello is another tragedy, this one driven by jealousy. The exact cause of the jealousy can vary; Iago can be jealous of Othello, of his love for Desdemona, of Desdemona herself, or several other possibilities. The emphasis often lies in the performance, and Shakespeare's play is written broadly enough to allow for any of these to be correct interpretations.

But men are men; the best sometimes forget.

Othello satisfied the need for violence, for passion, and for intrigue. 'On one foot', Iago, servant and friend of Othello, who also hates Othello, plants the seeds of suspicion that Desdemona has been unfaithful, leading Othello down a treacherous path that leads in his ultimate murder of Desdemona.

Take note, take note, O world!
To be direct and honest is not safe.

During one performance in the American Old West, an audience member became so entranced and enraged with the actor's portrayal of Iago that he took out his pistol and shot him. The tombstone of the actor reads 'Here lies the greatest actor'.

Lear
The prince of darkness is a gentleman.

This most difficult of Shakespeare plays, both for performing and for studying, is one of the true masterpieces of English (or any) literature, and yet is underperformed and underappreciated due to the power of its complexity and of its tragedy. Indeed, often the tragedy at the end has been softened by having Cordelia survive victorious. Beware these kinds of performances--they not Shakespeare's intent, however much we wish.

Lear begins with folly, and ends in tragedy, while treachery and evil seems to creep like a vine choking off first this person, then that. The fool is the only wise one; the insane are the only protected, and the nobles increasingly lose nobility of intent and action as the events progress. Gloucester and Lear are both deceived by wicked children turned against their better offspring; all ends in tragedy for most of the lot.

Lear addresses sibling rivalries, parent/child relationships, poverty and insanity, and any number of other readily accessible issues, but all interwoven so tightly that they cannot be unravelled easily, yet all the while the world for the characters are unravelling thread by thread before our very eyes. Lear points out the folly of human planning and agency. Lear was banned from performance, actually, during 1788-1820 when George III was considered insane, and the connexion between stage and royalty would be too blurred for official comfort.

Howl, howl, howl, howl! O! you are men of stones!

Macbeth
The witches, the blood-stained hands, the play whose name must not be mentioned in a theatre lest bad luck befall the actor or production. Macbeth is all of these, and more. Loosely based upon a real historical character, the tragedy here is one of ambition.

Fair is foul, and foul is fair:
Hover through the fog and filthy air

Did Macbeth really see the ghost of Banquo at the banquet, or was it indigestion because of the haggis? Macbeth can be played with or without a conscience, which makes for differing character development, but both options are available in Shakespeare's flexible playwriting.

Hear it not, Duncan; for it is a knell
That summons thee to heaven or to hell

Macbeth is driven by his ambition, but also by the ambition of his wife, Lady Macbeth, as treacherous a villain in many respects as any male character in Shakespeare. Macbeth has an overgrown sense of invincibility, convinced by prophecies that his course will be successful, and ordinarily it is (until it all goes awry); it is a successful struggle to the throne, but never secure, and in the end, all is lost.

Macbeth may be the bloodiest of Shakespeare's plays, a thrill for Elizabethan audiences, and a wonder to behold as the scenes get ever more desperate and darker.

This edition
There are so many editions of Shakespeare available, and many have merits. This particular volume of the four major tragic plays provides commentary by David Bevington which is insightful and accessible; it also gives photographs of performances and stagings by the New York Shakespeare Festivals, modernised spelling and concordance listings of major passages. Not short by any means (nearly 1000 pages), this will nonetheless give a good study to the plays, with visual aids, and supportive material, all in one volume.

excellent edition of great tragedies.......2002-12-14

this is an excellent 'cheap' edition of the great tragedies. besides being edited by david bevington, considered one of the foremost shakespeare scholars, the bantam edition also includes introductory essays for each play AND the source material that shakespeare used - ie, the actual short stories or plays that the bard drew on to the write his plays. wonderful stuff and a great way to get into shakespeare.

This book needs footnotes!.......2001-01-01

An integral part to any Shakespeare work is the presence of footnotes! This book has a glossary, but it does not do any good because there is not sign in the actual text itself that one can look up specific words in the glossary. While the plays themselves are very enjoyable, do not purchase this edition unless you feel very confident about your ability to read Shakespearean language.

for shakespeare fans.......2000-09-04

this is a great book for shakespeare fans. it was the first time i read shakespeare outside of class, and it was very interesting. i didn't like the prefaces much, i didn't have the patience to read them. i felt they were very of long, and harder to read and understand than the actual shakespeare. they actual plays-not stories, just to clarify- are wonderful. it would be a great book to read if you are taking a literature class and want to get a head start or if you want to expand your vocabulary. you can even relate the problems of those times to the problems of today. the plays were very fun to read once you got into them; shakespeare is just as great as he is said to be.

Four Great Tragedies: Hamlet, Othello, King Lear, Macbeth

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Four Great Tragedies: Hamlet, Othello, King Lear, Macbeth
William Shakespeare
Manufacturer: New Amer Library
ProductGroup: Book
Binding: Paperback

Shakespeare's four giants: [Hamlet, Macbeth, Othello, King Lear]

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Shakespeare's four giants: [Hamlet, Macbeth, Othello, King Lear]
Blanche Coles
Manufacturer: R.R. Smith
ProductGroup: Book
Binding: Unknown Binding

Four Tragedies: Hamlet, Othello, King Lear, Macbeth

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Four Tragedies: Hamlet, Othello, King Lear, Macbeth
William Shakespeare
Manufacturer: Penguin Classics
ProductGroup: Book
Binding: Paperback

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