磁動(dòng)力學(xué)導(dǎo)論

內(nèi)容概要

　　magnetic fields influence many natural and man-made flows.
they are routinely used in industry to heat, pump, stir and
levitate liquid metals.there is the terrestrial magnetic field
which is maintained by fluid motion in the earth's core, the solar
magnetic field which generates sunspots and solar flares, and the
galactic field which influences the formation of stars.this is an
introductory text on magnetohydrodynamics (mhd) - the study of the
interaction of magnetic fields and conducting fluids.
　　this book is intended to serve as an introductory text for
advanced undergraduate and postgraduate students in physics,
applied mathematics and engineering. the material in the text is
heavily weighted towards incompressible flows and to terrestrial
(as distinct from astrophysical) applications. the final sections
of the text also contain an outline of the latest advances in the
metallurgical applications of mhd and so are relevant to
professional researchers in applied mathematics, engineering and
metallurgy.

作者簡(jiǎn)介

作者：(英國(guó))戴維森(P.A.Davidson)

書籍目錄

preface
part a: the fundamentals of mhd
　introduction: the aims of part a
　1 a qualitative overview of mhd
　　1.1 what is mhd?
　　1.2 a brief history of mhd
　　1.3 from electrodynamics to mhd: a simple experiment
　　　1.3.1 some important parameters in electrodynamics and mhd
　　　1.3.2 a brief reminder of the laws of electrodynamics
　　　1.3.3 a familiar high-school experiment
　　　1.3.4 a summary of the key results for mhd
　　1.4 some simple applications of mhd
　2 the governing equations of eiectrodynamics
　　2.1 the electric field and the lorentz force
　　2.2 ohm's law and the volumetric lorentz force
　　2.3 ampere's law
　　2.4 faraday's law in differential form
　　2.5 the reduced form of maxwell's equations for mhd
　　2.6 a transport equation for b
　　2.7 on the remarkable nature of faraday and of faraday's
law
　　　2.7.1 an historical footnote
　　　2.7.2 an important kinematic equation
　　　2.7.3 the full significance of faraday's law
　　　2.7.4 faraday's law in ideal conductors: alfvtn's theorem
　3 the governing equations of fluid mechanics
　　part 1: fluid flow in the absence of lorentz forces
　　　3.1 elementary concepts
　　　　3.1.1 different categories of fluid flow
　　　　3.1.2 the navier-stokes equation
　　　3.2 vorticity, angular momentum and the biot-savart law
　　　3.3 advection and diffusion of vorticity
　　　　3.3.1 the vorticity equation
　　　　3.3.2 advection and diffusion of vorticity: temperature as a
prototype
　　　　3.3.3 vortex line stretching
　　　3.4 kelvin's theorem, helmholtz's laws and helieity
　　　　3.4.1 kelvin's theorem and helmholtz's laws
　　　　3.4.2 helicity
　　　3.5 the prandti-batchelor theorem
　　　3.6 boundary layers, reynolds stresses and turbulence
models
　　　　3.6.1 boundary layers
　　　　3.6.2 reynolds stresses and turbulence models
　　　3.7 ekman pumping in rotating flows
　　part 2: incorporating the lorentz force
　　　3.8 the full equations of mhd and key dimensionless groups
　　　3.9 maxwell stresses
　4 kinematics of mhd: advection and diffusion of a magnetic
field
　5 dynamics at low magnetic reynolds numbers
　6 dynamics at moderate to high magnetic reynolds' number
　7 mhd turbulence at low and high magnetic reynolds number
Part b: applications in engineering and metallrugy
　8 introduction: an overview of metallurgical applications
　9 magnetic damping using static fields
　10 axisymmetric flows driven by the injection of current
　11 mhd instabilities in reduction cells
　12 high-frequency fields: magnetic levitation and induction
heating
appendices
bibliography
subject index

章節(jié)摘錄

版權(quán)頁(yè)：插圖：are usually fairly straightforward. It pays, therefore, when confrontedwith a welter of mathematical detail, to follow the advice of Kelvinand keep asking the question: 'What is really going on？ In line with this principle, we start, in 1.3, not with fully fledged MHD, but rather with a simple laboratory experiment. This consists ofa static magnetic field at right angles to a conducting rod which in turnslides along two conducting rails. Such an apparatus is commonly used inhigh schools to illustrate Faraday's law of induction. However, when thedynamics of the sliding rod are investigated we discover a lot more thanjust Faraday's law. In fact, this simple experiment illustrates many of thekey physical phenomena to be found in MHD. That is to say, a magneticfield, B, and a moving, conducting medium interact in such a way as torestrain the relative motion of the field and medium.  We start our formal analysis in Chapters 2 and 3, where we set out thegoverning equations of MHD. These consist of the Navier-Stokes equation and a simplified version of Maxwelrs equations from which Gauss'slaw is omitted and displacement currents are neglected.In Chapter 4 we consider one half of the coupling between B and themedium. Specifically, we look at the influence of a prescribed fluid velocity, u, on the magnetic field without worrying about the origin of thevelocity field or the backreaction of the Lorentz force on the fluid. Ineffect, we take u to be prescribed, dispense with the Navier-Stokes equation, and focus on the r61e of u when using Maxwell's equations.We finally introduce dynamics in Chapters 5 and 6. We start, in Chapter 5, by considering weakly conducting or slowly moving fluidsin which the magnetic field greatly influences the motion of the conductorbut there is little back-reaction on the imposed magnetic field. This typifies much of liquid-metal MHD. Next, in Chapter 6, we consider highlyconducting, or rapidly moving, fluids in which the two-way coupling of Band u is strong. Here interest focuses on stability theory, which is important in plasma containment, and on dynamo theory, a phenomenon which is of considerable importance in geophysics. We end, in Chapter 7, with a discussion of MHD turbulence.

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