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| Àâòîðèçàöèÿ |
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| Ïîèñê ïî óêàçàòåëÿì |
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| Chorin A.J. — Vorticity and turbulence |
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| Ïðåäìåòíûé óêàçàòåëü |
 -transition 134
-transition, in superfluids 149—152
 -algebra 25
Algebras of sets 40
Bibliography 157—168
Biot — Savart kernel 146
Biot — Savart law 10
Boltzmann’s constant 69
Bond percolation 123
Borel sets 26
Bounded domains 7
Brownian motion 44—45 88—89
Brownian path 44 45
Brownian walk 48
Brownian walk, in space 47
Brownian walk, in time 46
Buttke loops 20
canonical ensemble 83
Cantor set 59
Capacity, fractalization and 99—101
Capacity, zero 99
Centered moments 28
Central limit theorem 29—30
Chemical potential of vortex segment 99
Circulation 9
Circulation theorem 9—10
Circulation, of vortex filaments 139
Closed vortex loops 147
Closed vortex tubes 16
Cluster hull 123
Combinatorial method approach to equilibrium and negative temperatures 74—76
Connectivity constraints 16
Consolidation/filamentation event 84 86—87
Continuity, equation of 5—6
continuum limit 80—83
coordinates 5
Correlated percolation 132—133
Correlation function, defined 31
correlation length 114
Critical point 114
Curdling, progressive 88
Deformation matrix 9
Detailed balance condition 116
Differentiation vector 6
Dirac delta function 14
Dissipation range 52
Dissipation spectrum 38—39
Domains, bounded 7
Domains, infinite 7—8
Domains, periodic 7
Eddies 49
Elementary random measure 40
Elementary vortex loops 132—134
Energy cascade 55—58
Energy dissipation 62
Energy integral 16
Energy range 52
Energy shell 22—23 69
Energy spectrum 23
Enstrophy 62—65
Enstrophy, cascading 89
Enstrophy, equilibrium and 108—109 111
Enstrophy, infinite 108
entropy 69 70—72
Entropy, per vortex leg 137
Entropy, scaled 81
Equilibrium 70
Equilibrium ensemble 68—69
Equilibrium measure 68
Equilibrium, combinatorial approach to 74—76
Equilibrium, enstrophy and 108—109 111
Equilibrium, mechanical 68
Equilibrium, physical system in 76
Equilibrium, relaxation to 84—89
Equilibrium, statistical see “Statistical equilibrium”
Equilibrium, universal 51
Equilibrium, “absolute” 73
Equipartition ensemble 73
Ergodicity 116
Euler equations 7 57 79
Euler equations, gauge-invariant form of 17—18
Events 25
Events, independent 27
Expected value 26
experiments 25
Fields, random 30—36
Finite additivity 40
Flory exponent 117 140
Flow field 32
Flow field, homogeneous, random Fourier transform of 39—44
Flow field, random 32
Flow map 6
Flow, inhomogeneous 98
Flow, inviscid 7 9
Flow, Lal — Madras — Sokal 119
Flow, periodic, Fourier representation for 21—24
Flow, random 31
Fluid particle, trajectory of 6
Fluid turbulence see “Turbulence”
Folding, fractalization by 101
Fourier representation for periodic flow 21—24
Fourier transform, random see “Random Fourier transform”
Fractal sets 58—61
Fractalization, by folding 101
Fractalization, capacity and 99—101
Gaussian variables 29
Gibbs probability 116
Gibbs probability density 71
Hamiltonian formulations 17
Hausdorff dimension 59
Hausdorff measure 58—59
Helicity 11
Helicity, invariance of 96
Hexagonal lattice, smart walk on 125
Homogeneity assumption 51
Impulse 11—12
Impulse density 20
Independent events 27
Inertial range 52
Infinite domains 7—8
Infinite enstrophy 108
Inhomogeneous flow 98
interaction energy 99 102
Intermittency 61—64
Intermittency correction 64
Intermittency, vortex filaments and 101—106
Inverse cascade 107
Inviscid flow 7 9
Inviscid vorticity equation 46
Ising model 113—114
Ising model, magnetization in 114
Ising model, one-dimensional 126
Joyce — Montgomery equation 79—80
Joyce — Montgomery equation, collapse of 81
Joyce — Montgomery equation, two-sign 85
Jump discontinuities 73
kinetic energy 8
Kinetic energy, defined 11
Knotted vortex filaments 96
Kolmogorov exponent 142
Kolmogorov law 52—53
Kolmogorov law, 2/3 law 54
Kolmogorov law, 5/3 law 56
Kolmogorov scale 53
Kolmogorov spectrum 55 60
Kolmogorov theory 3
Kolmogorov theory, dimensional considerations 51—55
Kosterlitz — Thouless transition 128—132
Kraichnan/Kolmogorov picture 105
Lal — Madras — Sokal flow 119
| Laplace operator 6
Lattice sites 113
Lattice spacing 120
Lattice vortex 103
Lebesgue measure 27
Liouville’s theorem 68
Lognormal variables 106
magnetization 114
Magnetization variables 17—21
Magnetization, in Ising model 114
Magnetostatic variables 20
Mean energy 35—36
Mean energy, spatial 33
Mechanical equilibrium 68
Metropolis flow 115
Momenta 67
Moments 28
Moments, centered 28
Monomers 118
Motion, equations of 5—24
Moving average representation of random field 44
Multifractal vorticity distribution 64
Navier — Stokes equations 7
Navier — Stokes equations, diffusion part of 47
Navier — Stokes equations, Fourier form of 21—22
Navier — Stokes equations, in component form 38
Navier — Stokes equations, inviscid limit of 63
Navier — Stokes equations, magnetization form of 21
Navier — Stokes equations, projection form of 7
Navier — Stokes equations, random solutions of 36—39
Newton’s law 6
Notation 3
Onsager theory 77
Order parameter 114 115
Parameter flow 127
Partition function 71
Percolation 121—124
Percolation clusters 122
Percolation loci 151
Percolation threshold 122
Percolation, bond 123
Percolation, correlated 132—133
Percolation, polymers and 124—125
Periodic domains 7
Periodic flow, Fourier representation for 21—24
Phase space 67
Plaquettes 122—124
Polymers 117
Polymers, percolation and 124—125
Polymers, vector-vector correlation exponent for 119—121
Positions 67
probability density 26 27
Probability measure 26 68
Probability space 26
Probability theory 25—30
Progressive curdling 88
Projection form of Navier — Stokes equations 7
Quantum vortices 151—152
Random fields 30—36 42
Random fields, defined 44
Random fields, moving average representation of 44
Random flow 31
Random flow field 32
Random Fourier transform 39 43
Random Fourier transform, of homogeneous flow field 39—44
Random measure, elementary 40
Random variables 26—27
Random walk 59—60
Renormalization 126—127
Renormalization group equations 127
Renormalization, of vortex dynamics in turbulent regime 152—155
Rotation vector 9
Sample space 25
SAW (self-avoiding walk) 116—119
Scales of motion 49—50
Scales of motion, small 50
Self-avoiding vortex 103
Self-avoiding vortex filaments 137—140
Self-avoiding walk (SAW) 116—119
Self-energy 15 102
Self-energy, folding of vortex filaments and 96—99
Self-energy, growth of 104
Shedding of vortex loops by vortex filaments 146
Sheetification 107
Simple functions 41
skewness 62
Smooth vortex filaments 144
Spatial mean energy 33
Spectral calculations 23—24
Spectral density 34
Spectral distribution function 34
Spectral representation 83
Spin 113
Statistical equilibrium 67—72
Statistical equilibrium, “absolute”, in wave number space 72—74
Statistical mechanics, turbulence and 2
Stream function 15
Stretching term 10
Structure function 40
Superfluids, -transition in 149—152
Temperature, defined 69
Temperature, effect of 8
Temperature, negative, combinatorial approach to 74—76
Trajectory of fluid particle 6
Turbulence theory v
Turbulence theory, goals of 49—51
Turbulence, kinds of 3
Turbulence, properties of 1
Turbulence, statistical mechanics and 2
Turbulent regime, renormalization of, vortex dynamics in 152—155
Unit sphere 92
Universal equilibrium 51
Variables 25
Variables, Gaussian 29
Variables, lognormal 106
Variables, random 26—27
Vector norm 35
Vector-vector correlation exponent 138
Vector-vector correlation exponent, for polymers 119—121
Vectors 5
Velocity field 5 9 68
viscosity 146
Viscosity coefficient 6
Vortex centerline 107
Vortex cross-sections 106—108
Vortex cylinder 94
Vortex dynamics, renormalization of, in turbulent regime 152—155
Vortex equilibria, in three-dimensional space 135—155
Vortex filament model 135—136
Vortex filaments 16 94—96
Vortex filaments, balled-up 141
Vortex filaments, circulation of 139
Vortex filaments, dynamics of 144—149
Vortex filaments, folding of, self-energy and 96—99
Vortex filaments, geometry of 108
Vortex filaments, intermittency and 101—106
Vortex filaments, knotted 96
Vortex filaments, self-avoiding 137—140
Vortex filaments, shedding of vortex loops by 146
Vortex filaments, smooth 144
Vortex filaments, sparse suspension of 95—96
Vortex filaments, thin closed 20
Vortex folding 93
Vortex gas 130
Vortex legs 60—61 103
Vortex legs, entropy per 137
Vortex lines 9
Vortex lines, stretching 91—94
Vortex loops, closed 147
Vortex loops, elementary 132—134
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