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Fluid Dynamics Part 2 Asymptotic Problems Of Fluid Dynamics

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Fluid Dynamics

Fluid Dynamics Book
Author : Anatoly I. Ruban
Publisher : Oxford University Press, USA
Release : 2015
ISBN : 0199681740
File Size : 43,5 Mb
Language : En, Es, Fr and De

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Book Summary :

This is the second volume in a four-part series on fluid dynamics: Part 1. Classical Fluid Dynamics Part 2. Asymptotic Problems of Fluid Dynamics Part 3. Boundary Layers Part 4. Hydrodynamic Stability Theory The series is designed to give a comprehensive and coherent description of fluid dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture course, and then progressing through more advanced material up to the level of modern research in the field. In Part 2 the reader is introduced to asymptotic methods, and their applications to fluid dynamics. Firstly, it discusses the mathematical aspects of the asymptotic theory. This is followed by an exposition of the results of inviscid flow theory, starting with subsonic flows past thin aerofoils. This includes unsteady flow theory and the analysis of separated flows. The authors then consider supersonic flow past a thin aerofoil, where the linear approximation leads to the Ackeret formula for the pressure. They also discuss the second order Buzemann approximation, and the flow behaviour at large distances from the aerofoil. Then the properties of transonic and hypersonic flows are examined in detail. Part 2 concludes with a discussion of viscous low-Reynolds-number flows. Two classical problems of the low-Reynolds-number flow theory are considered, the flow past a sphere and the flow past a circular cylinder. In both cases the flow analysis leads to a difficulty, known as Stokes paradox. The authors show that this paradox can be resolved using the formalism of matched asymptotic expansions.

Fluid Dynamics

Fluid Dynamics Book
Author : Anatoly I. Ruban
Publisher : OUP Oxford
Release : 2015-08-20
ISBN : 0191503975
File Size : 52,6 Mb
Language : En, Es, Fr and De

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Book Summary :

This is the second volume in a four-part series on fluid dynamics: Part 1. Classical Fluid Dynamics Part 2. Asymptotic Problems of Fluid Dynamics Part 3. Boundary Layers Part 4. Hydrodynamic Stability Theory The series is designed to give a comprehensive and coherent description of fluid dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture course, and then progressing through more advanced material up to the level of modern research in the field. In Part 2 the reader is introduced to asymptotic methods, and their applications to fluid dynamics. Firstly, it discusses the mathematical aspects of the asymptotic theory. This is followed by an exposition of the results of inviscid flow theory, starting with subsonic flows past thin aerofoils. This includes unsteady flow theory and the analysis of separated flows. The authors then consider supersonic flow past a thin aerofoil, where the linear approximation leads to the Ackeret formula for the pressure. They also discuss the second order Buzemann approximation, and the flow behaviour at large distances from the aerofoil. Then the properties of transonic and hypersonic flows are examined in detail. Part 2 concludes with a discussion of viscous low-Reynolds-number flows. Two classical problems of the low-Reynolds-number flow theory are considered, the flow past a sphere and the flow past a circular cylinder. In both cases the flow analysis leads to a difficulty, known as Stokes paradox. The authors show that this paradox can be resolved using the formalism of matched asymptotic expansions.

Fluid Dynamics

Fluid Dynamics Book
Author : Anatoliĭ Ivanovich Ruban,Ruban Et Al
Publisher : Unknown
Release : 2014
ISBN : 9780191761614
File Size : 31,5 Mb
Language : En, Es, Fr and De

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Book Summary :

In this second part the reader is introduced to asymptotic methods and their applications to fluid dynamics. Discussion of the mathematical aspects is followed by an exposition of the results of inviscid flow theory, starting with subsonic flows past thin aerofoils. Supersonic flow past a thin aerofoil, where the linear approximation leads to the Ackeret formula for the pressure is then discussed. The second-order Buzemann approximation, and the flow behaviour at large distances from the aerofoil is also examined. Then the properties of transonic and hypersonic flows are discussed in detail.

Fluid Dynamics

Fluid Dynamics Book
Author : Anatoly I. Ruban
Publisher : Oxford University Press
Release : 2017-12-01
ISBN : 0191503983
File Size : 48,9 Mb
Language : En, Es, Fr and De

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Book Summary :

This is the third volume in a four-part series on Fluid Dynamics: PART 1: Classical Fluid Dynamics PART 2: Asymptotic Problems of Fluid Dynamics PART 3: Boundary Layers PART 4: Hydrodynamic Stability Theory The series is designed to give a comprehensive and coherent description of fluid dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture course, and then progressing through more advanced material up to the level of modern research in the field. The notion of the boundary layer was introduced by Prandtl (1904) to describe thin viscous layers that form on a rigid body surface in high-Reynolds-number flows. Part 3 of this series begins with the classical theory of the boundary-layer flows, including the Blasius boundary layer on a flat plate and the Falkner-Skan solutions for the boundary layer on a wedge surface. However, the main focus is on recent results of the theory that have not been presented in texbooks before. These are based on the so-called "triple-deck theory" that have proved to be invaluable in describing various fluid-dynamic phenomena, including the boundary-layer separation from a rigid body surface.

Asymptotic Modelling of Fluid Flow Phenomena

Asymptotic Modelling of Fluid Flow Phenomena Book
Author : Radyadour Kh. Zeytounian
Publisher : Springer Science & Business Media
Release : 2006-04-10
ISBN : 0306483866
File Size : 26,5 Mb
Language : En, Es, Fr and De

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Book Summary :

for the fluctuations around the means but rather fluctuations, and appearing in the following incompressible system of equations: on any wall; at initial time, and are assumed known. This contribution arose from discussion with J. P. Guiraud on attempts to push forward our last co-signed paper (1986) and the main idea is to put a stochastic structure on fluctuations and to identify the large eddies with a part of the probability space. The Reynolds stresses are derived from a kind of Monte-Carlo process on equations for fluctuations. Those are themselves modelled against a technique, using the Guiraud and Zeytounian (1986). The scheme consists in a set of like equations, considered as random, because they mimic the large eddy fluctuations. The Reynolds stresses are got from stochastic averaging over a family of their solutions. Asymptotics underlies the scheme, but in a rather loose hidden way. We explain this in relation with homogenizati- localization processes (described within the §3. 4 ofChapter 3). Ofcourse the mathematical well posedness of the scheme is not known and the numerics would be formidable! Whether this attempt will inspire researchers in the field of highly complex turbulent flows is not foreseeable and we have hope that the idea will prove useful.

Fluid Dynamics in Biology

Fluid Dynamics in Biology Book
Author : Angela Y. Cheer,AMS-IMS-SIAM Joint Summer Research Conference on Biofluiddynamics (1991 : Seattle),Cornelis P. Van Dam
Publisher : American Mathematical Soc.
Release : 1993
ISBN : 0821851489
File Size : 46,7 Mb
Language : En, Es, Fr and De

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Book Summary :

This book contains nearly all the papers presented at the AMS-IMS-SIAM Joint Summer Research Conference on Biofluiddynamics, held in July 1991, at the University of Washington, Seattle. The lead paper, by Sir James Lighthill, presents a comprehensive review of external flows in biology. The other papers on external and internal flows illuminate developments in the protean field of biofluiddynamics from diverse viewpoints, reflecting the field's multidisciplinary nature. For this reason, the book appeals to mathematicians, biologists, engineers, physiologists, cardiologists, and oceanographers. The papers highlight a number of problems that have remained largely unexplored due to the difficulty of addressing biological flow motions, which are often governed by large systems of nonlinear differential equations and involve complex geometries.However, recent advances in computational fluid dynamics have expanded opportunities to solve such problems. These developments have increased interest in areas such as the mechanisms of blood and air flow in humans, the dynamic ecology of the oceans, animal swimming and flight, to name a few. This volume addresses many of these flow problems.

Atmospheric and Oceanic Fluid Dynamics

Atmospheric and Oceanic Fluid Dynamics Book
Author : Geoffrey K. Vallis
Publisher : Cambridge University Press
Release : 2006-11-06
ISBN : 1139459961
File Size : 33,8 Mb
Language : En, Es, Fr and De

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Book Summary :

Fluid dynamics is fundamental to our understanding of the atmosphere and oceans. Although many of the same principles of fluid dynamics apply to both the atmosphere and oceans, textbooks tend to concentrate on the atmosphere, the ocean, or the theory of geophysical fluid dynamics (GFD). This textbook provides a comprehensive unified treatment of atmospheric and oceanic fluid dynamics. The book introduces the fundamentals of geophysical fluid dynamics, including rotation and stratification, vorticity and potential vorticity, and scaling and approximations. It discusses baroclinic and barotropic instabilities, wave-mean flow interactions and turbulence, and the general circulation of the atmosphere and ocean. Student problems and exercises are included at the end of each chapter. Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation will be an invaluable graduate textbook on advanced courses in GFD, meteorology, atmospheric science and oceanography, and an excellent review volume for researchers. Additional resources are available at www.cambridge.org/9780521849692.

Practical Asymptotics

Practical Asymptotics Book
Author : H.K. Kuiken
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 9401006989
File Size : 43,8 Mb
Language : En, Es, Fr and De

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Book Summary :

Practical Asymptotics is an effective tool for reducing the complexity of large-scale applied-mathematical models arising in engineering, physics, chemistry, and industry, without compromising their accuracy. It exploits the full potential of the dimensionless representation of these models by considering the special nature of the characteristic dimensionless quantities. It can be argued that these dimensionless quantities mostly assume extreme values, particularly for practical parameter settings. Thus, otherwise complicated models can be rendered far less complex and the numerical effort to solve them is greatly reduced. In this book the effectiveness of Practical Asymptotics is demonstrated by fifteen papers devoted to widely differing fields of applied science, such as glass-bottle production, semiconductors, surface-tension-driven flows, microwaving joining, heat generation in foodstuff production, chemical-clock reactions, low-Mach-number flows, to name a few. A strong plea is made for making asymptotics teaching an integral part of any numerics curriculum. Not only will asymptotics reduce the computational effort, it also provides a fuller understanding of the underlying problems.