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Author: C. Foias
Publisher: Cambridge University Press
Published: 2001-08-27
Total Pages: 363
ISBN-13: 1139428993
DOWNLOAD EBOOK →This book presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. The mathematical technicalities are kept to a minimum within the book, enabling the language to be at a level understood by a broad audience.
Author: Wolfgang Kollmann
Publisher: Springer Nature
Published: 2024
Total Pages: 848
ISBN-13: 3031595785
DOWNLOAD EBOOK →This updated/augmented second edition retains it class-tested content and pedagogy as a core text for graduate courses in advanced fluid mechanics and applied science. The new edition adds revised sections, clarification, problems, and chapter extensions including a rewritten section on Schauder bases for turbulent pipe flow, coverage of Cantwell’s mixing length closure for turbulent pipe flow, and a section on the variational Hessian. Consisting of two parts, the first provides an introduction and general theory of fully developed turbulence, where treatment of turbulence is based on the linear functional equation derived by E. Hopf governing the characteristic functional that determines the statistical properties of a turbulent flow. In this section, Professor Kollmann explains how the theory is built on divergence free Schauder bases for the phase space of the turbulent flow and the space of argument vector fields for the characteristic functional. The second segment, presented over subsequent chapters, is devoted to mapping methods, homogeneous turbulence based upon the hypotheses of Kolmogorov and Onsager, intermittency, structural features of turbulent shear flows and their recognition. Adds section on Plancherel’s theorem and a detailed problem on analytic solution of functional differential equations; Extends chapter nine on characteristic functionals to greater explain the role of convection; Reinforces concepts with problems on the theory and particular examples of turbulent flows such as periodic pipe flow. . .
Author: R. Temam
Publisher: Springer
Published: 2006-11-14
Total Pages: 201
ISBN-13: 3540375163
DOWNLOAD EBOOK →Author: Luigi C. Berselli
Publisher: Academic Press
Published: 2021-03-10
Total Pages: 330
ISBN-13: 0128219459
DOWNLOAD EBOOK →Three-Dimensional Navier-Stokes Equations for Turbulence provides a rigorous but still accessible account of research into local and global energy dissipation, with particular emphasis on turbulence modeling. The mathematical detail is combined with coverage of physical terms such as energy balance and turbulence to make sure the reader is always in touch with the physical context. All important recent advancements in the analysis of the equations, such as rigorous bounds on structure functions and energy transfer rates in weak solutions, are addressed, and connections are made to numerical methods with many practical applications. The book is written to make this subject accessible to a range of readers, carefully tackling interdisciplinary topics where the combination of theory, numerics, and modeling can be a challenge. Includes a comprehensive survey of modern reduced-order models, including ones for data assimilation Includes a self-contained coverage of mathematical analysis of fluid flows, which will act as an ideal introduction to the book for readers without mathematical backgrounds Presents methods and techniques in a practical way so they can be rapidly applied to the reader’s own work
Author: Charles R. Doering
Publisher: Cambridge University Press
Published: 1995
Total Pages: 236
ISBN-13: 9780521445689
DOWNLOAD EBOOK →This introductory physical and mathematical presentation of the Navier-Stokes equations focuses on unresolved questions of the regularity of solutions in three spatial dimensions, and the relation of these issues to the physical phenomenon of turbulent fluid motion.
Author: Peter Constantin
Publisher: Springer
Published: 2005-11-24
Total Pages: 265
ISBN-13: 3540324542
DOWNLOAD EBOOK →Constantin presents the Euler equations of ideal incompressible fluids and the blow-up problem for the Navier-Stokes equations of viscous fluids, describing major mathematical questions of turbulence theory. These are connected to the Caffarelli-Kohn-Nirenberg theory of singularities for the incompressible Navier-Stokes equations, 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 nonlinear evolution equations and related unexpected cancellation properties, either imposed on the initial condition, or satisfied by the solution itself, localized in space or in time variable. Ukai discusses the asymptotic analysis theory of fluid equations, the Cauchy-Kovalevskaya technique for the Boltzmann-Grad limit of the Newtonian equation, the multi-scale analysis, giving compressible and incompressible limits of the Boltzmann equation, and the analysis of their initial layers.
Author: Peter Constantin
Publisher: University of Chicago Press
Published: 1988
Total Pages: 200
ISBN-13: 0226115496
DOWNLOAD EBOOK →Lecture notes of graduate courses given by the authors at Indiana University (1985-86) and the University of Chicago (1986-87). Paper edition, $14.95. Annotation copyright Book News, Inc. Portland, Or.
Author: Bjorn Birnir
Publisher: Springer Science & Business Media
Published: 2013-01-31
Total Pages: 117
ISBN-13: 1461462622
DOWNLOAD EBOOK →Turbulence is a major problem facing modern societies. It makes airline passengers return to their seats and fasten their seatbelts but it also creates drag on the aircraft that causes it to use more fuel and create more pollution. The same applies to cars, ships and the space shuttle. The mathematical theory of turbulence has been an unsolved problems for 500 years and the development of the statistical theory of the Navier-Stokes equations describes turbulent flow has been an open problem. The Kolmogorov-Obukhov Theory of Turbulence develops a statistical theory of turbulence from the stochastic Navier-Stokes equation and the physical theory, that was proposed by Kolmogorov and Obukhov in 1941. The statistical theory of turbulence shows that the noise in developed turbulence is a general form which can be used to present a mathematical model for the stochastic Navier-Stokes equation. The statistical theory of the stochastic Navier-Stokes equation is developed in a pedagogical manner and shown to imply the Kolmogorov-Obukhov statistical theory. This book looks at a new mathematical theory in turbulence which may lead to many new developments in vorticity and Lagrangian turbulence. But even more importantly it may produce a systematic way of improving direct Navier-Stokes simulations and lead to a major jump in the technology both preventing and utilizing turbulence.
Author: Viorel Barbu
Publisher: Springer Science & Business Media
Published: 2010-11-19
Total Pages: 285
ISBN-13: 0857290436
DOWNLOAD EBOOK →Stabilization of Navier–Stokes Flows presents recent notable progress in the mathematical theory of stabilization of Newtonian fluid flows. Finite-dimensional feedback controllers are used to stabilize exponentially the equilibrium solutions of Navier–Stokes equations, reducing or eliminating turbulence. Stochastic stabilization and robustness of stabilizable feedback are also discussed. The analysis developed here provides a rigorous pattern for the design of efficient stabilizable feedback controllers to meet the needs of practical problems and the conceptual controllers actually detailed will render the reader’s task of application easier still. Stabilization of Navier–Stokes Flows avoids the tedious and technical details often present in mathematical treatments of control and Navier–Stokes equations and will appeal to a sizeable audience of researchers and graduate students interested in the mathematics of flow and turbulence control and in Navier-Stokes equations in particular.
Author: R Temam
Publisher: Springer
Published: 2014-01-15
Total Pages: 208
ISBN-13: 9783662206782
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