磁动力学导论(英文版)

.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
4.1 the analogy to vorticity
4.2 diffusion of a magnetic field
4.3 advection in ideal conductors: alfven's theorem
4.3.1 alfvtn's theorem
4.3.2 an aside: sunspots
4.4 magnetic helicity
4.5 advection plus diffusion
4.5.1 field sweeping
4.5.2 flux expulsion
4.5.3 azimuthal field generation by differential rotation
4.5.4 magnetic reconnection
5 dynamics at low magnetic reynolds numbers
5.1 the low-rm approximation in mhd
part 1: suppression of motion
5.2 magnetic damping
5.2.1 the destruction of mechanical energy via joule dissipation
5.2.2 the damping of a two-dimensional jet
5.2.3 damping of a vortex
5.3 a glimpse at mhd turbulence
5.4 natural convection in the presence of a magnetic field
5.4.1 rayleigh-btnard convection
5.4.2 the governing equations
5.4.3 an energy analysis of the rayleigh-btnard instability
5.4.4 natural convection in other configurations
part 2: generation of motion
5.5 rotating fields and swirling motions
5.5.1 stirring of a long column of metal
5.5.2 swirling flow induced between two parallel plates
5.6 motion driven by current injection
5.6.1 a model problem
5.6.2 a useful energy equation
5.6.3 estimates of the induced velocity
5.6.4 a paradox
part 3: boundary layers
5.7 hartmann boundary layers
5.7.1 the hartmann layer
5.7.2 hartmann flow between two planes
5.8 examples of hartmann and related flows
5.8.1 flow-meters and mhd generators
5.8.2 pumps, propulsion and projectiles
5.9 conclusion
6 dynamics at moderate to high magnetic reynolds' number
6.1 alfven waves and magnetostrophic waves
6.1.1 alfven waves
6.1.2 magnetostrophic waves
6.2 elements of geo-dynamo theory
6.2.1 why do we need a dynamo theory for the earth?
6.2.2 a large magnetic reynolds number is needed
6.2.3 an axisymmetric dynamo is not possible
6.2.4 the influence of small-scale turbulence: the 0t-effect
6.2.5 some elementary dynamical considerations
6.2.6 competing kinematic theories for the geo-dynamo
6.3 a qualitative discussion of solar mhd
6.3.1 the structure of the sun
6.3.2 is there a solar dynamo?
6.3.3 sunspots and the solar cycle
6.3.4 the location of the solar dynamo
6.3.5 solar flares
6.4 energy-based stability theorems for ideal mhd
6.4.1 the need for stability theorems in ideal mhd: plasma containment
6.4.2 the energy method for magnetostatic equilibria
6.4.3 an alternative method for magnetostatic equilibrium
6.4.4 proof that the energy method provides both necessary and sufficient conditions for stability
6.4.5 the stability of non-static equilibria
6.5 conclusion
7 mhd turbulence at low and high magnetic reynolds number
7.1 a survey of conventional turbulence
7.1.1 a historical interlude
7.1.2 a note on tensor notation
7.1.3 the structure of turbulent flows: the kolmogorov picture of turbulence
7.1.4 velocity correlation functions and the karmanhowarth equation
7.1.5 decaying turbulence: kolmogorov's law, loitsyansky's integral, landau's angular momentum and batchelor's pressure forces
7.1.6 on the difficulties of direct numerical simulations
7.2 mhd turbulence
7.2.1 the growth of anisotropy at low and high r,,
7.2.2 decay laws at low rm
7.2.3 the spontaneous growth of a magnetic field at high rm
7.3 two-dimensional turbulence
7.3.1 batchelor's self-similar spectrum and the inverse energy cascade
7.3.2 coherent vortices
7.3.3 the governing equations of two-dimensional turbulence
7.3.4 variational principles for predicting the final state in confined domains
part b: applications in engineering and metallurgy
8 introduction: an overview of metallurgical applications
8 magnetic stirring using rotating fields
8.1 casting, stirring and metallurgy
8.2 early models of stirring
8.3 the dominance of ekman pumping in the stirring of confined liquids
8.4 the stirring of steel
9 magnetic damping using static fields
9.1 metallurgical applications
9.2 conservation of momentum, destruction of energy and the growth of anisotropy
9.3 magnetic damping of submerged jets
9.4 magnetic damping of vortices
9.4.1 general considerations
9.4.2 damping of transverse vortices
9.4.3 damping of parallel vortices
9.4.4 implications for low-rm turbulence
9.5 damping of natural convection
9.5.1 natural convection in an aluminium ingot
9.5.2 magnetic damping in an aluminium ingot
10 axisymmetric flows driven by the injection of current
10.1 the var process and a model problem
10.1.1 the var process
10.1.2 integral constraints on the flow
10.2 the work done by the lorentz force
10.3 structure and scaling of the flow
10.3.1 differences between confined and unconfined flows
10.3.2 shercliff's self-similar solution for unconfined flows
10.3.3 confined flows
10.4 the influence of buoyancy
10.5 stability of the flow and the apparent growth of swirl
10.5.1 an extraordinary experiment
10.5.2 there is no spontaneous growth of swirl!
10.6 flaws in the traditional explanation for the emergence of swirl
10.7 the r61e of ekman pumping in establishing the dominance of swirl
10.7.1 a glimpse at the mechanisms
10.7.2 a formal analysis
10.7.3 some numerical experiments
11 mhd instabilities in reduction cells
11.1 interfacial waves in aluminium reduction cells
11.1.1 early attempts to produce aluminium by electrolysis
11.1.2 the instability of modern reduction cells
11.2 a simple mechanical analogue for the instability
11.3 simplifying assumptions
11.4 a shallow-water wave equation and key dimensionless groups
11.4.1 a shallow-water wave equation
11.4.2 key dimensionless groups
11.5 travelling wave and standing wave instabilities
11.5.1 travelling waves
11.5.2 standing waves in circular domains
11.5.3 standing waves in rectangular domains
11.6 implications for reduction cell design
12 high-frequency fields: magnetic levitation and induction heating
12.1 the skin effect
12.2 magnetic pressure, induction heating and highfrequency stirring
12.3 applications in the casting of steel, aluminium and super-alloys
12.3.1 the induction furnace
12.3.2 the cold crucible
12.3.3 levitation melting
12.3.4 processes which rely on magnetic repulsion em valves and em casters
appendices
1 vector identities and theorems
2 stability criteria for ideal mhd based on the hamiltonian
3 physical properties of liquid metals
4 mhd turbulence at low rm
bibliography
suggested books on fluid mechanics
suggested books on electromagnetism
suggested books on mhd
journal references for part b and appendix 2
subject index