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Chorin A.J. Ч Vorticity and turbulence
Chorin A.J. Ч Vorticity and turbulence

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Ќазвание: Vorticity and turbulence

јвтор: Chorin A.J.


This book provides an introduction to turbulence in vortex systems, and to turbulence theory for incompressible flow described in terms of the vorticity field. It is the author's hope that by the end of the book the reader will believe that these subjects are identical, and constitute a special case of fairly standard statistical mechanics, with both equilibrium and non-equilibrium aspects. The author's main goal is to relate turbulence to statistical mechanics. The book is organized as follows: the first three chapters constitute a fairly standard introduction to homogeneous turbulence in incompressible flow; a quick review of fluid mechanics; a summary of the appropriate Fourier theory; a summary of Kolmogorov's theory of the inertial range. The next four chapters present the statistical theory of vortex notion, and the vortex dynamics of turbulence. The book ends with the major conclusion that turbulence can no longer be viewed as incomprehensible. This book wi! ll be appropriate for professionals in the fields of applied mathematics, mechanical engineering, or physics, as well as graduate students in these noted areas.

язык: en

–убрика: ‘изика/ лассическа€ физика/ћеханика жидкости и газа/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1998

 оличество страниц: 173

ƒобавлена в каталог: 13.10.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
ѕредметный указатель
$\lambda$-transition      134
$\lambda$-transition, in superfluids      149Ч152
$\sigma$-algebra      25
Algebras of sets      40
Bibliography      157Ч168
Biot Ч Savart kernel      146
Biot Ч Savart law      10
BoltzmannТs constant      69
Bond percolation      123
Borel sets      26
Bounded domains      7
Brownian motion      44Ч45 88Ч89
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      99Ч101
Capacity, zero      99
Centered moments      28
Central limit theorem      29Ч30
Chemical potential of vortex segment      99
Circulation      9
Circulation theorem      9Ч10
Circulation, of vortex filaments      139
Closed vortex loops      147
Closed vortex tubes      16
Cluster hull      123
Combinatorial method approach to equilibrium and negative temperatures      74Ч76
Connectivity constraints      16
Consolidation/filamentation event      84 86Ч87
Continuity, equation of      5Ч6
continuum limit      80Ч83
coordinates      5
Correlated percolation      132Ч133
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      38Ч39
Domains, bounded      7
Domains, infinite      7Ч8
Domains, periodic      7
Eddies      49
Elementary random measure      40
Elementary vortex loops      132Ч134
Energy cascade      55Ч58
Energy dissipation      62
Energy integral      16
Energy range      52
Energy shell      22Ч23 69
Energy spectrum      23
Enstrophy      62Ч65
Enstrophy, cascading      89
Enstrophy, equilibrium and      108Ч109 111
Enstrophy, infinite      108
entropy      69 70Ч72
Entropy, per vortex leg      137
Entropy, scaled      81
Equilibrium      70
Equilibrium ensemble      68Ч69
Equilibrium measure      68
Equilibrium, combinatorial approach to      74Ч76
Equilibrium, enstrophy and      108Ч109 111
Equilibrium, mechanical      68
Equilibrium, physical system in      76
Equilibrium, relaxation to      84Ч89
Equilibrium, statistical      see УStatistical equilibriumФ
Equilibrium, universal      51
Equilibrium, УabsoluteФ      73
Equipartition ensemble      73
Ergodicity      116
Euler equations      7 57 79
Euler equations, gauge-invariant form of      17Ч18
Events      25
Events, independent      27
Expected value      26
experiments      25
Fields, random      30Ч36
Finite additivity      40
Flory exponent      117 140
Flow field      32
Flow field, homogeneous, random Fourier transform of      39Ч44
Flow field, random      32
Flow map      6
Flow, inhomogeneous      98
Flow, inviscid      7 9
Flow, Lal Ч Madras Ч Sokal      119
Flow, periodic, Fourier representation for      21Ч24
Flow, random      31
Fluid particle, trajectory of      6
Fluid turbulence      see УTurbulenceФ
Folding, fractalization by      101
Fourier representation for periodic flow      21Ч24
Fourier transform, random      see УRandom Fourier transformФ
Fractal sets      58Ч61
Fractalization, by folding      101
Fractalization, capacity and      99Ч101
Gaussian variables      29
Gibbs probability      116
Gibbs probability density      71
Hamiltonian formulations      17
Hausdorff dimension      59
Hausdorff measure      58Ч59
Helicity      11
Helicity, invariance of      96
Hexagonal lattice, smart walk on      125
Homogeneity assumption      51
Impulse      11Ч12
Impulse density      20
Independent events      27
Inertial range      52
Infinite domains      7Ч8
Infinite enstrophy      108
Inhomogeneous flow      98
interaction energy      99 102
Intermittency      61Ч64
Intermittency correction      64
Intermittency, vortex filaments and      101Ч106
Inverse cascade      107
Inviscid flow      7 9
Inviscid vorticity equation      46
Ising model      113Ч114
Ising model, magnetization in      114
Ising model, one-dimensional      126
Joyce Ч Montgomery equation      79Ч80
Joyce Ч Montgomery equation, collapse of      81
Joyce Ч Montgomery equation, two-sign      85
Jump discontinuities      73
kinetic energy      8
Kinetic energy, defined      11
Knotted vortex filaments      96
Kolmogorov exponent      142
Kolmogorov law      52Ч53
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      51Ч55
Kosterlitz Ч Thouless transition      128Ч132
Kraichnan/Kolmogorov picture      105
Lal Ч Madras Ч Sokal flow      119
Laplace operator      6
Lattice sites      113
Lattice spacing      120
Lattice vortex      103
Lebesgue measure      27
LiouvilleТs theorem      68
Lognormal variables      106
magnetization      114
Magnetization variables      17Ч21
Magnetization, in Ising model      114
Magnetostatic variables      20
Mean energy      35Ч36
Mean energy, spatial      33
Mechanical equilibrium      68
Metropolis flow      115
Momenta      67
Moments      28
Moments, centered      28
Monomers      118
Motion, equations of      5Ч24
Moving average representation of random field      44
Multifractal vorticity distribution      64
Navier Ч Stokes equations      7
Navier Ч Stokes equations, diffusion part of      47
Navier Ч Stokes equations, Fourier form of      21Ч22
Navier Ч Stokes equations, in component form      38
Navier Ч Stokes equations, inviscid limit of      63
Navier Ч Stokes equations, magnetization form of      21
Navier Ч Stokes equations, projection form of      7
Navier Ч Stokes equations, random solutions of      36Ч39
NewtonТs law      6
Notation      3
Onsager theory      77
Order parameter      114 115
Parameter flow      127
Partition function      71
Percolation      121Ч124
Percolation clusters      122
Percolation loci      151
Percolation threshold      122
Percolation, bond      123
Percolation, correlated      132Ч133
Percolation, polymers and      124Ч125
Periodic domains      7
Periodic flow, Fourier representation for      21Ч24
Phase space      67
Plaquettes      122Ч124
Polymers      117
Polymers, percolation and      124Ч125
Polymers, vector-vector correlation exponent for      119Ч121
Positions      67
probability density      26 27
Probability measure      26 68
Probability space      26
Probability theory      25Ч30
Progressive curdling      88
Projection form of Navier Ч Stokes equations      7
Quantum vortices      151Ч152
Random fields      30Ч36 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      39Ч44
Random measure, elementary      40
Random variables      26Ч27
Random walk      59Ч60
Renormalization      126Ч127
Renormalization group equations      127
Renormalization, of vortex dynamics in turbulent regime      152Ч155
Rotation vector      9
Sample space      25
SAW (self-avoiding walk)      116Ч119
Scales of motion      49Ч50
Scales of motion, small      50
Self-avoiding vortex      103
Self-avoiding vortex filaments      137Ч140
Self-avoiding walk (SAW)      116Ч119
Self-energy      15 102
Self-energy, folding of vortex filaments and      96Ч99
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      23Ч24
Spectral density      34
Spectral distribution function      34
Spectral representation      83
Spin      113
Statistical equilibrium      67Ч72
Statistical equilibrium, УabsoluteФ, in wave number space      72Ч74
Statistical mechanics, turbulence and      2
Stream function      15
Stretching term      10
Structure function      40
Superfluids, $\lambda$-transition in      149Ч152
Temperature, defined      69
Temperature, effect of      8
Temperature, negative, combinatorial approach to      74Ч76
Trajectory of fluid particle      6
Turbulence theory      v
Turbulence theory, goals of      49Ч51
Turbulence, kinds of      3
Turbulence, properties of      1
Turbulence, statistical mechanics and      2
Turbulent regime, renormalization of, vortex dynamics in      152Ч155
Unit sphere      92
Universal equilibrium      51
Variables      25
Variables, Gaussian      29
Variables, lognormal      106
Variables, random      26Ч27
Vector norm      35
Vector-vector correlation exponent      138
Vector-vector correlation exponent, for polymers      119Ч121
Vectors      5
Velocity field      5 9 68
viscosity      146
Viscosity coefficient      6
Vortex centerline      107
Vortex cross-sections      106Ч108
Vortex cylinder      94
Vortex dynamics, renormalization of, in turbulent regime      152Ч155
Vortex equilibria, in three-dimensional space      135Ч155
Vortex filament model      135Ч136
Vortex filaments      16 94Ч96
Vortex filaments, balled-up      141
Vortex filaments, circulation of      139
Vortex filaments, dynamics of      144Ч149
Vortex filaments, folding of, self-energy and      96Ч99
Vortex filaments, geometry of      108
Vortex filaments, intermittency and      101Ч106
Vortex filaments, knotted      96
Vortex filaments, self-avoiding      137Ч140
Vortex filaments, shedding of vortex loops by      146
Vortex filaments, smooth      144
Vortex filaments, sparse suspension of      95Ч96
Vortex filaments, thin closed      20
Vortex folding      93
Vortex gas      130
Vortex legs      60Ч61 103
Vortex legs, entropy per      137
Vortex lines      9
Vortex lines, stretching      91Ч94
Vortex loops, closed      147
Vortex loops, elementary      132Ч134
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