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Fundamental Fluid Mechanics And Magnetohydrodynamics

Author: Roger J. Hosking
Publisher: Springer
ISBN: 9812876006
Size: 47.52 MB
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This book is primarily intended to enable postgraduate research students to enhance their understanding and expertise in Fluid Mechanics and Magnetohydrodynamics (MHD), subjects no longer treated in isolation. The exercises throughout the book often serve to provide additional and quite significant knowledge or to develop selected mathematical skills, and may also fill in certain details or enhance readers’ understanding of essential concepts. A previous background or some preliminary reading in either of the two core subjects would be advantageous, and prior knowledge of multivariate calculus and differential equations is expected.

Essential Fluid Dynamics For Scientists

Author: Jonathan Braithwaite
Publisher: Morgan & Claypool Publishers
ISBN: 1681745976
Size: 58.66 MB
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The book is an introduction to the subject of fluid mechanics, essential for students and researchers in many branches of science. It illustrates its fundamental principles with a variety of examples drawn mainly from astrophysics and geophysics as well as from everyday experience. Prior familiarity with basic thermodynamics and vector calculus is assumed.

Magnetohydrodynamics And Fluid Dynamics Action Principles And Conservation Laws

Author: Gary Webb
Publisher: Springer
ISBN: 3319725114
Size: 57.19 MB
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This text focuses on conservation laws in magnetohydrodynamics, gasdynamics and hydrodynamics. A grasp of new conservation laws is essential in fusion and space plasmas, as well as in geophysical fluid dynamics; they can be used to test numerical codes, or to reveal new aspects of the underlying physics, e.g., by identifying the time history of the fluid elements as an important key to understanding fluid vorticity or in investigating the stability of steady flows. The ten Galilean Lie point symmetries of the fundamental action discussed in this book give rise to the conservation of energy, momentum, angular momentum and center of mass conservation laws via Noether’s first theorem. The advected invariants are related to fluid relabeling symmetries – so-called diffeomorphisms associated with the Lagrangian map – and are obtained by applying the Euler-Poincare approach to Noether’s second theorem. The book discusses several variants of helicity including kinetic helicity, cross helicity, magnetic helicity, Ertels’ theorem and potential vorticity, the Hollman invariant, and the Godbillon Vey invariant. The book develops the non-canonical Hamiltonian approach to MHD using the non-canonical Poisson bracket, while also refining the multisymplectic approach to ideal MHD and obtaining novel nonlocal conservation laws. It also briefly discusses Anco and Bluman’s direct method for deriving conservation laws. A range of examples is used to illustrate topological invariants in MHD and fluid dynamics, including the Hopf invariant, the Calugareanu invariant, the Taylor magnetic helicity reconnection hypothesis for magnetic fields in highly conducting plasmas, and the magnetic helicity of Alfvén simple waves, MHD topological solitons, and the Parker Archimedean spiral magnetic field. The Lagrangian map is used to obtain a class of solutions for incompressible MHD. The Aharonov-Bohm interpretation of magnetic helicity and cross helicity is discussed. In closing, examples of magnetosonic N-waves are used to illustrate the role of the wave number and group velocity concepts for MHD waves. This self-contained and pedagogical guide to the fundamentals will benefit postgraduate-level newcomers and seasoned researchers alike.

Lectures On Topological Fluid Mechanics

Author: Mitchell A. Berger
Publisher: Springer
ISBN: 3642008372
Size: 12.43 MB
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Helmholtz's seminal paper on vortex motion (1858) marks the beginning of what is now called topological fluid mechanics.After 150 years of work, the field has grown considerably. In the last several decades unexpected developments have given topological fluid mechanics new impetus, benefiting from the impressive progress in knot theory and geometric topology on the one hand, and in mathematical and computational fluid dynamics on the other. This volume contains a wide-ranging collection of up-to-date, valuable research papers written by some of the most eminent experts in the field. Topics range from fundamental aspects of mathematical fluid mechanics, including topological vortex dynamics and magnetohydrodynamics, integrability issues, Hamiltonian structures and singularity formation, to DNA tangles and knotted DNAs in sedimentation. A substantial introductory chapter on knots and links, covering elements of modern braid theory and knot polynomials, as well as more advanced topics in knot classification, provides an invaluable addition to this material.

Heat And Mass Transfer Phenomena In Mhd Flow Modelling With Applications

Author: Sanjib Sengupta
Publisher: Scientific Research Publishing, Inc. USA
ISBN: 1618960679
Size: 76.52 MB
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The primary objective of the book is to provide basic idea on fluid dynamics and its related properties and help to understand research work in the field of transport phenomena in MHD flow. The fluid model describing various aspects of boundary layer flow past a vertical flat surface embedded in Darcian porous media have been studied. An asymptotic periodic transformation is used to solve the dynamical equations. The influence of several physical effects like thermal radiation, chemical reaction, magnetic field, radiation absorption,heat sink etc. have been considered on various fluid properties. In this study some significant engineering properties of interest such as skin-friction, Nusselt number and Sherwood number are also calculated and analyzed through graphs and tables. It is expected that, the governed exact closed form of solutions corresponding to different problems can be used for validating numerical treatment of certain critical flows with heat and mass transfer phenomena.

Topological Fluid Mechanics

Author: International Union of Theoretical and Applied Mechanics
Publisher: Cambridge University Press
ISBN: 9780521381451
Size: 61.37 MB
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There has been developing interest in the aspects of fluid mechanics and of magnetohydrodynamics that can be properly described as topological, rather than exclusively analytical in character. This book contains the proceedings of the IUTAM symposium on Topological Fluid Mechanics held at Cambridge UK, 13-18 August, 1989. Topics covered include the kinematic and dynamical problems in laminar and turbulent flows, as well as the range of problems that arise from the magnetohydrodynamics of highly conducting flows. The papers presented cover all approaches; theoretical, computational and experimental, and each paper has been edited by a member of the International Scientific Committee.

An Introduction To Fluid Mechanics

Author: Faith A. Morrison
Publisher: Cambridge University Press
ISBN: 1139619314
Size: 28.50 MB
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This is a modern and elegant introduction to engineering fluid mechanics enriched with numerous examples, exercises and applications. A swollen creek tumbles over rocks and through crevasses, swirling and foaming. Taffy can be stretched, reshaped and twisted in various ways. Both the water and the taffy are fluids and their motions are governed by the laws of nature. The aim of this textbook is to introduce the reader to the analysis of flows using the laws of physics and the language of mathematics. We delve deeply into the mathematical analysis of flows; knowledge of the patterns fluids form and why they are formed and also the stresses fluids generate and why they are generated is essential to designing and optimising modern systems and devices. Inventions such as helicopters and lab-on-a-chip reactors would never have been designed without the insight provided by mathematical models.

Mathematical Methods For The Magnetohydrodynamics Of Liquid Metals

Author: Jean-Frédéric Gerbeau
Publisher: Clarendon Press
ISBN: 9780191513749
Size: 13.28 MB
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This comprehensive text focuses on mathematical and numerical techniques for the simulation of magnetohydrodynamic phenomena, with an emphasis laid on the magnetohydrodynamics of liquid metals, and on a prototypical industrial application. Aimed at research mathematicians, engineers, and physicists, as well as those working in industry, and starting from a good understanding of the physics at play, the approach is a highly mathematical one, based on the rigorous analysis of the equations at hand, and a solid numerical analysis to found the simulations. At each stage of the exposition, examples of numerical simulations are provided, first on academic test cases to illustrate the approach, next on benchmarks well documented in the professional literature, and finally, whenever possible, on real industrial cases.

The Hamilton Type Principle In Fluid Dynamics

Author: Angel Fierros Palacios
Publisher: Springer Science & Business Media
ISBN: 3211343245
Size: 56.35 MB
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The book describes Fluid Dynamics, Magnetohydrodynamics, and Classical Thermodynamics as branches of Lagrange’s Analytical Mechanics. The approach presented is markedly different from the treatment given to them in traditional text books. A Hamilton-Type Variational Principle as the proper mathematical technique for the theoretical description of the dynamic state of any fluid is formulated. The scheme is completed proposing a new group of variations regarding the evolution parameter.