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E-grāmata: Fundamental Fluid Mechanics and Magnetohydrodynamics

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  • Formāts: PDF+DRM
  • Izdošanas datums: 19-Oct-2015
  • Izdevniecība: Springer Verlag, Singapore
  • Valoda: eng
  • ISBN-13: 9789812876003
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Fundamental Fluid Mechanics and MagnetohydrodynamicsPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 19-Oct-2015
  • Izdevniecība: Springer Verlag, Singapore
  • Valoda: eng
  • ISBN-13: 9789812876003
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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.

Recenzijas

The authors broach a wide range of topics in fluid mechanics and magnetohydrodynamics (MHD) including basic theory, wave propagation, shock wave theory, singular perturbation and boundary layer theory, magnetohydrostatics and MHD stability. this excellent book seems to fully meet the intention of the authors of enabling graduate research studies of fluid mechanics and MHD to enhance their understanding and expertise in the area. (Mark Thompson, Mathematical Reviews, June, 2017)









This book is intended for the use of postgraduate research students. The main purpose is to enhance the understanding of this double research subject, which is in continuous development. it is remarkable that the concept of fluid (and magnetofluid) is treated to cover both the domains of rarefied and dense plasmas. (Ivįn Abonyi, zbMATH 1332.76001, 2016)

1 Vectors and Tensors
1(36)
1.1 Introduction
1(2)
1.2 Vector Representations
3(4)
1.3 Dyadics
7(1)
1.4 Dyadic Representations
8(3)
1.5 Vector Differential Operator
11(2)
1.6 Orthogonal Curvilinear Coordinates
13(3)
1.7 Stokes Theorem
16(4)
1.8 Divergence Theorem
20(3)
1.9 Green Identities
23(1)
1.10 Heaviside Step and Dirac Delta Functions
24(7)
1.11 Green Functions
31(6)
Bibliography
35(2)
2 Fundamental Equations
37(34)
2.1 Conservation Equations
37(2)
2.2 Fluid Pressure Tensor
39(3)
2.3 Gravity
42(1)
2.4 Eulerian and Lagrangian Descriptions
43(3)
2.5 Rates of Change of Material Integrals
46(2)
2.6 Equations of Change
48(6)
2.7 Classical Macroscopic Equations
54(1)
2.8 Extended Macroscopic Models
55(2)
2.9 Plasma Pressure Tensor
57(4)
2.9.1 Invariant Form for the Traceless Component
57(2)
2.9.2 Parallel, Cross and Perpendicular Components
59(2)
2.10 Parallel Viscosity in an Ion-Electron Plasma
61(4)
2.11 Heat Flux*
65(2)
2.12 Magnetic Induction
67(4)
Bibliography
69(2)
3 Basic Fluid Dynamics
71(42)
3.1 Fundamental Model
71(2)
3.2 Ideal Fluid Model
73(4)
3.3 Vorticity and Irrotational Flow
77(3)
3.4 Subsonic Flow and the Incompressible Approximation
80(2)
3.5 Potential Flow
82(2)
3.6 Solving the Laplace Equation
84(4)
3.7 Pressure Variation in Ideal Subsonic Flow
88(2)
3.8 Boundary Layers
90(3)
3.9 Vortices
93(4)
3.10 Stokes Flow Past a Sphere
97(3)
3.11 Exact Viscous Flow Solutions
100(1)
3.12 Singular Perturbation Theory
101(1)
3.13 The Oseen Correction
102(5)
3.14 Dynamical Meteorology and Oceanography*
107(6)
Bibliography
110(3)
4 Waves in Fluids
113(44)
4.1 Introduction
113(3)
4.2 Short-Wavelength Approximation
116(2)
4.3 Sound Waves on a Slowly Varying Background Flow
118(2)
4.4 The Sonic Wake from a Point Source
120(4)
4.5 Water Waves
124(4)
4.6 Floating Flexible Plates and Surface Tension
128(8)
4.7 An Interface Between Two Fluids
136(2)
4.8 Local Averaging
138(4)
4.9 Wave Reaction on a Background Mean Flow
142(3)
4.10 Oscillation-Centre (OC) Description
145(4)
4.11 Shock Waves
149(3)
4.12 Shock Structure
152(5)
Bibliography
154(3)
5 Magnetohydrodynamics (MHD)
157(46)
5.1 Introduction
157(1)
5.2 Maxwell Equations
158(1)
5.3 Pre-Maxwell Equations
159(1)
5.4 Galilean Invariance
160(2)
5.5 Conducting Liquids
162(2)
5.6 Plasma MHD
164(1)
5.7 Ideal MHD Model
165(4)
5.8 "Frozen-In" Magnetic Field
169(2)
5.9 Ideal MHD Waves
171(4)
5.10 MHD Equilibria (Magnetohydrostatics)
175(5)
5.10.1 Magnetically Confined Plasma Equilibria
176(2)
5.10.2 Force-Free Equilibria
178(1)
5.10.3 Variational Principles for MHD Equilibrium
179(1)
5.11 Magnetic Coordinates
180(4)
5.12 Advected Ideal MHD Discontinuities
184(6)
5.13 Vacuum Fields
190(4)
5.14 Resistive MHD Model
194(1)
5.15 Hall MHD Model
195(2)
5.16 Advected Non-ideal MHD Discontinuities*
197(6)
Bibliography
200(3)
6 MHD Stability Theory
203(65)
6.1 Introduction
203(3)
6.2 Normal Modes in a Plasma Slab
206(1)
6.3 Ideal Gravitational Interchange Instabilities
207(2)
6.4 Magnetic Field Shear and Slab Modes
209(2)
6.5 Ideal MHD Variational Principle
211(8)
6.5.1 Linearised Equation of Motion
211(1)
6.5.2 Identification of Δ W and Self-adjointness
212(4)
6.5.3 Heuristic Form of Δ W
216(1)
6.5.4 Physical Interpretation of Terms in the Plasma Contribution
217(2)
6.5.5 Brief Note on the Eigenvalue Spectrum
219(1)
6.6 Ideal Instabilities in Cylindrical Geometry
219(7)
6.7 Ideal Instabilities in Toroidal Geometry
226(11)
6.7.1 Reduced K and Δ W in the Generalised Flute Ordering
228(2)
6.7.2 2-Field Reduction: Elimination of Χ
230(1)
6.7.3 1-Field Reduction: Elimination of ξ
231(1)
6.7.4 Ballooning Equation
232(4)
6.7.5 Geometric Interpretations
236(1)
6.8 Magnetorotational Theory
237(8)
6.8.1 Planar Short-Wavelength Self-gravitational Modes in a Thin Disc
239(4)
6.8.2 Magnetorotational Instabilities in a Keplerian Disc
243(2)
6.9 Resistive-g Instabilities
245(4)
6.9.1 Uniform Magnetic Field
246(1)
6.9.2 Sheared Magnetic Field
246(3)
6.10 Resistive Tearing Instabilities
249(4)
6.11 Effect of Plasma Viscosity on Stability
253(6)
6.11.1 Magnetoviscous Stabilisation of Ideal and Resistive Instabilities
254(3)
6.11.2 Enhanced Energy Release in Magnetic Reconnexion
257(2)
6.12 Hall Instability
259(9)
6.12.1 Gravitational Interchange Instability in Ion-Electron Plasma
260(4)
6.12.2 Hall Effect in Kepler Disc Dynamics
264(3)
6.12.3 Hall Reconnexion
267(1)
Bibliography 268(3)
Glossary 271(4)
Index 275
Roger Hosking has been a mathematics professor for more than 40 years. His published research has extended from MHD instability to various topics in fluid mechanics such as shallow flow over curved beds and waves, and he is particularly well known for mathematical modelling of moving loads on ice sheets and floating ladder rail tracks.  He co-authored the research monograph "Moving Loads on Ice Plates" and co-edited "Aspects of Mathematical Modelling" (both available from Springer), and earlier co-authored a textbook for beginning undergraduate students entitled "First Steps in Numerical Analysis".  Professor Hosking is a Fellow of the Australian Mathematical Society, a Fellow of the Institute of Mathematics and its Applications, and a Managing Editor of the East Asian Journal on Applied Mathematics.

Professor Dewar has more than 40 years experience as a researcher in the general area of theoretical plasma physics, which provides a rich array of problems in classicalfield theory, fluid dynamics, nonlinear dynamics and chaos, and kinetic theory. He has well over 100 publications in refereed journals, and in the field of MHD in particular he is well known as a pioneer in the use of semiclassical (WKB) methods for understanding wave propagation and the spectrum of instabilities in complex geometries, with applications ranging from astrophysics to fusion power research. He has co-edited five books containing the proceedings of summer schools, workshops and conferences. Professor Dewar is a Member of the Australian Mathematical Society and is an Associate Editor of the Australian and New Zealand Industrial and Applied Mathematics Journal. He is a Fellow of the Australian Institute of Physics, the American Physical Society, and the Australian Academy of Science.
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