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| Frisch U. — Turbulence. The legacy of A.N. Kolmogorov |
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| Предметный указатель |
Loitsyansky's “invariant” 114
Loop expansion 215
Lyapunov exponent 205
Mach number 110 134 135 146 155
Magnetic field 221
Magnetic field, dynamo effect 21 191 232
Magnetic field, passive 204 217
Magnetic field, solar 191
Magnetic field, spurious fractals 205
Magnetic flux tube 184
Magnetohydrodynamics (MHD) 221 232 238
Mapping function 193
Material invariant 203
Maximum entropy principle 245
Mean-free-path 110 150 222 225
Metric transitivity 37
Mirror-invariance 234
Mixing length 222 224
Molecules 224 252
Molecules, fluid 224
Moments 41
Moments, divergent 167
Multifractal model 133 144 143—146 146; spurious
Multifractal model, based on the dissipation 159 159—165
Multifractal model, effect of viscosity 149—155
Multifractal model, intermediate dissipation range 149—155
Multifractal model, Legendre transformation 145
Multifractal model, motivated by experimental data 133
Multifractal model, probabilistic formulation 146—149
Multifractal model, skewness and flatness 155—159
Multifractal universality 152 181
Multifractal universality, experimental test of 153
Multiscale methods 225—234
Navier — Stokes equation 1 14
Navier — Stokes equation as a dynamical system 37
Navier — Stokes equation in two dimensions 240
Navier — Stokes equation, incompressibility violated 135
Navier — Stokes equation, linearized 232
Navier — Stokes equation, poor man's 31
Navier — Stokes equation, symmetries 17 72 74 115
Negative temperature 244
Nonintrusive measurements 60
Nonlinear Schrodinger equation 248
Nonuniversality 97 111
Novikov — Stewart model 167; see also  -model
Novikov's inequality 172
NULL-SPACE 227—229
Numerical simulation, memory required 107
Numerical simulation, operation count 107
Observable 213
Oceanic currents 241
Ornstein — Uhlenbeck process 55
Ozone hole 241
Pade approximant 117
Palinstrophy 21
Parity-invariance 17 49 232 233
Partition function 247
Passive scalar 217; see also transport
Periodic boundary conditions 14 17
Permanence of large eddies 113
Phase transition 141
Phenomenology see turbulence
Physical space 16
Poisson equation 15
Polar vortex 241
Polymer 189
Power spectrum see spectrum
Pressure 14
Pressure as Lagrange multiplier 202
Pressure elimination 15
Pressure lows 184
Pressure, strain-vorticity relation 21
Probability density function (p.d.f.) 41
Probability theory 40—56 168—171
Punctuated conservative dynamics 249—250
Quasi-algebraic behavior 152
Quasi-inviscid equilibrium theory 248 249 251
Quasi-Lagrangian coordinates 215
Quasi-normal approximation 220 222
Random coupling model 218
Random function 45
Random function, Gaussian 46
Random function, homogeneous 49 206
Random function, stationary 46 46^18 206
Random function, with stationary increments 48
Random variable 40
Random variable, centered 41
Random variable, Gaussian 41
Random variable, infinitely divisible 190
Random variable, moment relation 44
Rate function see Cramer function
Recirculation pockets 232
Reconnection 116 252
Refined similarity hypothesis 164 163—165
Relief 60 155
Renormalization (quantum electrodynamics) 235
Renormalization group (RG) 97 235—240 240;
Renormalization group (RG) as iterated multiscale method 237
Renormalization group (RG), Forster — Nelson — Stephen theory 235—238
Resonant wave interactions 222
Response function see Green's function
Reynolds number 2 2 9
Reynolds number, bare 237
Reynolds number, expansion in powers of 218
Reynolds number, extreme, supersonic velocities 135 172 179
Reynolds Number, high 11 92; inertial level turbulence universality
Reynolds number, high restored symmetries 11
Reynolds number, high, validity of hydrodynamic approximation 110 196
Reynolds number, integral-scale based 106
Reynolds number, local fluctuating 164
Reynolds number, of vortex tube 185
Reynolds number, renormalized 237
Reynolds number, small 4 233 237
Reynolds number, Taylor-scale based 107
Reynolds stresses 222 232
Richardson's four-thirds law 102
SCALE 22
Scale, small 74
Scale-invariance 9 49 74 75 84 97 104
Scale-invariance, local see multifractal model
Scaling exponent 18
Self-avoiding random walk 189
Self-similarity 75 121 125 see
Self-similarity, infrared 113
Sensitivity 34
Separation of scales 225 233 238
Shear see velocity gradient
Shear layer 105 185
Shell models 174—178
Shell models, Desnyansky — Novikov 174
Shell models, Gledzer — Ohkitani — Yamada (GOY) 175
Shell models, K41 solutions 174 178
Shell models, pulse solutions 177
Shocks see Burgers' equation
Signed measure 191
Similarity principle 2 18 68
Singularity 99 110 119 199—202
Singularity, complex-space 92 126
Singularity, complex-space, tracing of 117
Singularity, finite-time see blow-up
Singularity, not needed to explain unpredictability 204
Singularity, ruled out in 2-D 116
Sinh-Poisson equation 245
skewness 41
Skewness in K41 155
| Skewness of velocity derivative 111; see also multifractal model
Slow variables 227
Solvability condition 228
Spectral method 70; see also numerical simulation
Spectrum 53 52—56 113 139 152 180 189 197 206 219—221
Spectrum,  98
Spectrum,  61—66 91 182 187 206 219 238 239
Spectrum, , log-corrected 239
Spectrum, -model 139
Spectrum, angle averaged 117
Spectrum, compensated 64
Spectrum, cumulative 53 80
Spectrum, DIA's  law 219; see also direct interaction approximation
Spectrum, dissipation-range 92 126 196 199
Spectrum, dissipation-range, far 152
Spectrum, dissipation-range, intermediate 152
Spectrum, equipartition 209
Spectrum, Euler flow 117
Spectrum, for Burgers' model 216
Spectrum, forcing 83 97 142 236—239
Spectrum, initial 114
Spectrum, injection see forcing
Spectrum, Kolmogorov's universal 92
Spectrum, lack of positivity 220
Spectrum, multifractal see 
Spectrum, of temperature 181
Spectrum, positivity 53
Spectrum, power-law 54
Spectrum, two-dimensional 243
Spectrum, two-dimensional,  242 243
Spectrum, two-dimensional, 251
Spectrum, two-dimensional, small wavenumbers 242
Spiral models 138 187
Spurious multifractality, for seismic data 162
Spurious multifractality, for turbulence 162 190
Statistical mechanics 169; see also two-dimensional turbulence absolute
Statistical mechanics, three-dimensional vortex filaments 191
Stellar dynamics 245
Stochastic model 217
Stochastic process see random function
Stream function 240
Stretched exponential 192
Structure function 139 141 151 152; intermittency K41 multifractal
Structure function, experimental data 127—133
Structure function, exponent 127
Structure function, for multifractal model 144 145 147 148 150
Structure function, for passive scalar 217
Structure function, for shell models 175 177
Structure function, negative orders 164
Structure function, nondecreasing exponents 135
Structure function, of order p 89
Structure function, positive and negative increments 148
Structure function, second order 54 56 61 74—76 91 127 129 172 189
Structure function, second order, -model 139
Structure function, second order, longitudinal 57
Structure function, second order, transverse 60
Structure function, sixth order 129 130
Structure function, third order 76 83 88 105 128 129 145
Structure function, with absolute value 90
Superensemble 94
Supersonic see Reynolds number (extreme)
Sweeping (of small by large eddies) 105 107 215 219
Symmetry 2—11 17 17—18 27 72—75 115 181 204 229
Symmetry, broken xi 4 6 6 73 121 245
Symmetry, restored 2 11 73 74 204
Symmetry, statistical 46^19
Taylor hypothesis 58 59 129 161
Taylor hypothesis, corrections to 59
Taylor hypothesis, not safe for jets 66
Taylor scale see Reynolds number (Taylor-scale based)
Taylor — Green vortex 70
Taylor — Green vortex, no evidence for blow-up 117
Taylor's eddy diffusivity formula 231
Test field model 240
Time averaging see ergodicity
Transport (turbulent), scalars 230—232
Transport (turbulent), vectors 232—234
Tropical cyclones 241
Turbulence, anisotropic 77 79
Turbulence, decaying 77
Turbulence, fully developed 2 11 57 59 61 76 84 93 100 108 109 182 193 199 203 204 235 242
Turbulence, homogeneous 58 69 73 74 77—80 87 88 195—198 210 225
Turbulence, incompressible 110 135 146
Turbulence, inhomogeneous 198 204 206 222
Turbulence, intensity 58
Turbulence, isotropic 9 58 61 75 76 79 81 83 86 87 105 111 155 220
Turbulence, mathematical aspects 199—203
Turbulence, phenomenology 100—119
Turbulence, shear flow 198
Turbulence, superfluid 183
Turbulence, wall-bounded 204
Turbulence, with homogeneous increments 74 88 113
Two-dimensional turbulence 240 240—254
Two-dimensional turbulence, anomalous scaling for passive scalars 217
Two-dimensional turbulence, bounds on dimension of attractors 109
Two-dimensional turbulence, conformal theory 207 251
Two-dimensional turbulence, enstrophy conservation 21
Two-dimensional turbulence, liquid 250
Two-dimensional turbulence, statistical mechanics of 243—249
Two-dimensional turbulence, vortices 241—243
Two-thirds law 57 57—66 97 98 189
Ultraviolet 54 105
Ultraviolet catastrophe 196
Uniform analyticity 93
Unifractal 167
Uniqueness 21 38 109 200
Universality 72 164; multifractal
Universality, lack of 93
Unpredictability 27 38;
Variational approach 193
Velocity gradient 105
Velocity gradient, distribution 111 112 192 194
Velocity gradient, rate-of-strain 21
Velocity gradient, shear 222
Velocity increments see also refined similarity hypothesis structure
Velocity increments, correspondence between spatial and temporal see Taylor hypothesis
Velocity increments, distribution 147 192—194
Velocity increments, longitudinal 57
Velocity increments, positive and negative 146
Velocity increments, transverse 61
Vertex, bare 214
Vertex, corrections 218 238
Vertex, renormalization 234
Virtual mass 235
viscosity 2 14 222 223 223; multifractal Reynolds
Viscosity, dynamical 14
Viscosity, microscopic expression of 110
Vortex, breakdown 185
Vortex, filaments 105 183—192
Vortex, patch 202
Vortex, sheet 199
Vortex, stretching 71 156 221 241
Vortex, tangle 189
Vortices see punctuated conservative dynamics two-dimensional
Vortices, Karman 6
Vorticity 16 240
Vorticity, coarse-grained 246
Vorticity, conservation (2-D) 241
Vorticity, hair 249
Wavelets 23 129 149 164
Weak solution 200
White noise 209 236 238
Wiener — Khinchin formula 54
Wind tunnel 58
Young measure 246
Zeeman effect 191
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