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Frisch U. — Turbulence. The legacy of A.N. Kolmogorov
Frisch U. — Turbulence. The legacy of A.N. Kolmogorov

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Название: Turbulence. The legacy of A.N. Kolmogorov

Автор: Frisch U.

Аннотация:

This textbook presents a modern account of turbulence, one of the greatest challenges in physics. The state-of-the-art is put into historical perspective five centuries after the first studies of Leonardo and half a century after the first attempt by A. N. Kolmogorov to predict the properties of flow at very high Reynolds numbers. Such "fully developed turbulence" is ubiquitous in both cosmical and natural environments, in engineering applications and in everyday life.


Язык: en

Рубрика: Физика/Классическая физика/Механика жидкости и газа/

Серия: Посвящена 110-летию со дня рождения Колмогорова Андрея Николаевича

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 296

Добавлена в каталог: 19.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\beta$-model      135—140
$\beta$-model, exact for Burgers' equation      143
$\beta$-model, history      180 181
$\beta$-model, Novikov — Stewart formulation      167
$\beta$-model, random      167
$\mu$      see lognormal model
Absolute equilibrium      209 242
Active scalar      202
Alpha effect      232
Analyticity      126
Analyticity, strip      117
Anisotropic kinetic alpha (AKA) effect      232
Anomalous scaling for scalars      216—217
Anticommuting ghost fields      214
Arnold — Beltrami — Childress (ABC) flow      204
axial anomaly      77
Bifractal model      140—143
Bifractal model, Burgers' equation      142
Bifurcation, Andronov — Hopf      4 72
Bifurcation, symmetry-increasing      11
Blow-up      202 221
Blow-up for Euler (ideal) flow      115—119
Blow-up for viscous flow      119
Blow-up of supremum of vorticity      200 201
Blow-up, not implied by fractal / multifractal models      199
Blow-up, spurious, predicted by closure      221
Boltzmann equation      225
boundary conditions      1 2 6
Breakdown of hydrodynamics      110
Brownian motion      48 121 205
Burgers' equation      142 142; refined
Burgers' equation, blow-up at zero viscosity      199
Burgers' equation, failure of all-order perturbation theory      216
Burgers' vortex      187 252
Cahn — Hilliard equation      234
Cancellation index      191
Cantor set      122 130 137
Cascade      21; see also energy
Cascade in two dimensions      243
Cascade of enstrophy      242 251
Cascade of helicity      21
Cascade, deterministic model of      171
Cascade, inverse      251
Cascade, nonconservative      166
Cascade, random model of      165—168 170 171 173 179 180
Cascade, Richardson      100 103—106 135 179 235
Cascade, terminated almost surely      137; see also fractal dimension (negative)
Cascade, two-dimensional      241
Catastrophes, battle of      141
Central limit theorem      51
Chaos      xi 8 31 38 72 116 204;
Chaotic advection      204
Characteristic function      41
Characteristic functional      46
Chiral nonlinearity      234
Circulation      18 191 191
Circulation time      71
Closure      98 197 206 211
Closure is renormalization group conceptually superior?      240
Closure, its shortcomings      219—221
Closure, law of decay of energy      115
Closure, Obukhov's derivation of $k^{-5/3}$ law      98
Closure, realizable      220
Codimension      130 136
Coherent structures      108 182 199 243 252
Composite operators      216
Compressible turbulence      197
Conservation laws      18—21
Cramer function      148 161 169 169 171—173
Cramer renormalization      182
Critical phenomena      235
Critical phenomena, dynamical      236
Cumulants      44 210
Cumulants, hierarchy      210 211 220
Cylinder      2
D(h)      144 148;
Debye screening      192
Decay      see energy (law of decay of)
Decimation      238
Degrees of freedom      106—110 150 192 204 243
Degrees of freedom, microscopic / macroscopic      110
Degrees of freedom, predicted by K41      107 150
Depletion of nonlinearity      119 201 243 251 252
Depletion of nonlinearity, not captured by closure      221
Deterministic chaos      27—36 171
Devil's staircase      122
Diagrammatic methods      44 115 214—217
Diffusion, anomalous      231
Diffusion, equation      228 230
Diffusion, subdiffusive      231
Diffusion, superdiffusive      231
Diffusivity, effective      226
Dimension of attractor      108 204; two-dimensional
Direct interaction approximation (DIA)      105 197 206 217—219
Dissipation fluctuations      see multifractal model refined
Dissipation range      92; see also intermittency K41 multifractal spectrum
Dissipation range, far      152
Dissipation rate      see energy (dissipation rate)
Dissipation, correlation function      216
Dissipation, scale (Kolmogorov)      91
Dissipation, wavenumber      91
Dissipativity      200 243
Dominant balance      229
Drag coefficient      67
Drag crisis      69
Dynamical systems      36 37 73 108 126 180 181 203—205 205; fractals
Eddy damped quasi-normal Markovian approximation (EDQNM)      206 220
Eddy diffusivity      222 226—228 230 231
Eddy diffusivity, Taylor's expression      231
Eddy noise      238 239
Eddy turnover time      101
Eddy turnover time, large      106
Eddy viscosity      xii 105 233
Eddy viscosity, caveats      233
Eddy viscosity, complex      233
Eddy viscosity, for the Kolmogorov flow      234
Eddy viscosity, history      222—226
Eddy viscosity, negative      233 242
Eddy viscosity, renormalization group      237 240
Eddy viscosity, scale-dependent      237
Ekman friction      242
Electrolyte      250
Energy      see also spectrum
Energy, balance equation      20 21
Energy, breakdown of conservation of      20
Energy, budget, scale-by-scale      21—26
Energy, cascade      98 104 115 239
Energy, conservation      20 174 246 249
Energy, cumulative      25
Energy, dissipation      26 67—71 75 76 88 180 188
Energy, dissipation rate      90 92 98 102 129
Energy, divergence of total      212 239
Energy, equipartition      209
Energy, finite dissipation of      57 103 129 244
Energy, flux      25 80 79—83 101 105 138 140 220
Energy, in terms of velocity increments      81
Energy, injection      26
Energy, inverse cascade of      84 114 196 233 242 242
Energy, law of decay of      112—115
Energy, local      159 159—165 178
Energy, mean      20 86
Energy, mean dissipation of      20
Energy, mean kinetic      53
Energy, of interaction of vortices      244
Energy, physical-space      78
Energy, redistributed among scales      22
Energy, transfer      83 83 115 211 220
Energy-containing eddies      105 219
Enstrophy      20; see also cascade
Equality in law      47
Ergodicity      35 37 49 58 248
Euler equation      18 116 200 247; Hamiltonian
Euler equation as geodesic flow      202
Euler equation, symplectic structure      203
Euler equation, well-posedness      116
Eulerian correlation time      215
Extended self-similarity (ESS)      131 158
external noise      204
F(X)      160 161 162;
Fast variables      227
Feynman graphs      see diagrammatic methods
Feynman integrals      see functional integrals
Filaments (2-D)      249
Filtering, band-pass      101 126
Filtering, high-pass      22 122
Filtering, low-pass      22 52 80
Five-thirds law      see spectrum ($k^{-5/3}$)
Flatland      251
Flatness      41 122 124—126
Flatness of velocity derivative      111 190;
Flatness, hyper-      129
Forster — Nelson — Stephen (FNS) theory      see renormalization group
Four-fifths law      76 76—89 128 197 198
Four-fifths law, deviations from      129
Four-fifths law, implies $h= 1/3$      89
Four-fifths law, implies $\zeta_3=1$      133
Four-fifths law, Kolmogorov's derivation      97
Fourier space      16
Fourth-cumulant-discard approximation      see quasi-normal approximation
Fractal attractor      38
Fractal dimension      136 138 161
Fractal dimension, capacitary      137
Fractal dimension, capacity      137
Fractal dimension, correlation      161
Fractal dimension, covering      137
Fractal dimension, Hausdorff      137 138 180 200
Fractal dimension, information      161
Fractal dimension, negative      137
Fractal dimension, Renyi      160 181
Fractals      205
Fractals, convoluted coastlines      180
Fractals, due to level crossing      205
Fractals, lacunarity      130
Functional and diagrammatic methods      212 217
Functional integrals      212
Galerkin truncation      242
Galilean invariance      17
Galilean invariance, broken by forcing      87 232
Galilean invariance, random      17 87 212 215
Gaussian      see random variable random
Gaussian integration by parts      43
Geometry      202
Global regularity      200
GOY      see shell models
Great Red Spot      249
Green's function      213
Grid turbulence      8 73 95 111 134
Guiding-center approximation      241
Hamiltonian formulation, Euler equation      203
Hamiltonian formulation, point vortices      244 245 249
Hamiltonian formulation, tracer dynamics      204
Heat equation      226
Heat flux      226 229
Helicity      19 21 189 232;
Helium facility      65 130 158
Henon map      38
histogram      29
Hoelder continuity      99 200
Homogenization      see multiscale methods
Hopf's equation      207—212
Hyperviscosity      see dissipativity
Inertial range      62 86
Inertial range, practical determination of      129
Inertial range, span of      107
Infrared      54 105
Infrared cutoff      55
Infrared divergence      212
Integral scale      50
Intermediate dissipation range      see multifractal model
Intermittency      120—194 194; singularities
Intermittency and vortex filaments      183 192
Intermittency factor      139
Intermittency in shell models      175—178
Intermittency in the dissipation range      125—126
Intermittency of local dissipation      162
Intermittency vs self-similarity      121 125
Intermittency, exact results      133—135
Intermittency, experimental data      127—133
Intermittency, external      96
Intermittency, not captured by closure      220
Intermittency, not disrupted by power-law forcing      239
Intermittency, revealed by high-pass filtering      125
Intermittency, small-scale      122
Intermittency, spurious      216
Invariant measure      34 35 38
Irrelevant term      238
Jeans — Vlasov — Poisson equation      245
K41      74 75 72—99 104 139 140 145 211 239
K41 and fractal level crossing      205
K41 and the correlation of the dissipation      216
K41 and the Richardson cascade      106
K41, consistent with anomalous correlation of the dissipation      216
K41, consistent with Burgers' equation      216
K41, consistent with cumulant hierarchy      211
K41, consistent with dissipation-range intermittency      126
K41, consistent with Richardson's diffusion law      102
K41, corrections to      104 106 127 133 172 180
K41, effect of viscosity      91—93
K41, historical remarks      98—99
K41, Landau's remark on      94—98 178 219
K41, renormalization group approach      238—240
K41, requires a chaotic cascade      116
K41, requires self-similarity      121
K41, structure functions      127
K41, universality      75 92 152—154
K41, viscous correction at inertial-range scales      216
Karman street      see vortices (Karman)
Karman — Howarth — Monin relation      78
Knudsen number      225
Kolmogorov 1941 theory      see K41
Kolmogorov flow      234 250
Kolmogorov — Arnold — Moser (KAM) tori      232
kurtosis      see flatness
Lagrange multiplier      202 247
Lagrangian      214
Lagrangian history direct interaction approximation (LHDI)      219
Lagrangian turbulence      see chaotic advection
Lagrangian, autocorrelation time      231
Lagrangian, coordinates      215
Lagrangian, derivative      116 201
Landau      see K41
Large deviations      51 148 168—171 181
Large-scale, dynamics      230
Large-scale, equation      229
Large-scale, instability      233 234
Law of Large Numbers      49
Legendre transformation      see multifractal model
Level crossing      205
Local dissipation      21
Localness of interactions      87 104 105 212 220
Localness of interactions, is it related to Galilean invariance?      219
Localness of interactions, not true in two dimensions      242
Log-Hopf equation      210
Log-periodic corrections to scaling      130 131
Log-Poisson model      190
Logarithmic law (von Karman)      225
Logistic map      31
Lognormal model      132 171 171—173
Lognormal model, exponent $\mu$      165
Lognormal model, incorrectly derived by central limit theorem      173
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