Ãëàâíàÿ    Ex Libris    Êíèãè    Æóðíàëû    Ñòàòüè    Ñåðèè    Êàòàëîã    Wanted    Çàãðóçêà    ÕóäËèò    Ñïðàâêà    Ïîèñê ïî èíäåêñàì    Ïîèñê    Ôîðóì   
blank
Àâòîðèçàöèÿ

       
blank
Ïîèñê ïî óêàçàòåëÿì

blank
blank
blank
Êðàñîòà
blank
Chorin A.J. — Vorticity and turbulence
Chorin A.J. — Vorticity and turbulence



Îáñóäèòå êíèãó íà íàó÷íîì ôîðóìå



Íàøëè îïå÷àòêó?
Âûäåëèòå åå ìûøêîé è íàæìèòå Ctrl+Enter


Íàçâàíèå: Vorticity and turbulence

Àâòîð: Chorin A.J.

Àííîòàöèÿ:

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.


ßçûê: en

Ðóáðèêà: Ôèçèêà/Êëàññè÷åñêàÿ ôèçèêà/Ìåõàíèêà æèäêîñòè è ãàçà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1998

Êîëè÷åñòâî ñòðàíèö: 173

Äîáàâëåíà â êàòàëîã: 13.10.2005

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
blank
Ïðåäìåòíûé óêàçàòåëü
$\lambda$-transition      134
$\lambda$-transition, in superfluids      149—152
$\sigma$-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, $\lambda$-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
1 2
blank
Ðåêëàìà
blank
blank
HR
@Mail.ru
       © Ýëåêòðîííàÿ áèáëèîòåêà ïîïå÷èòåëüñêîãî ñîâåòà ìåõìàòà ÌÃÓ, 2004-2024
Ýëåêòðîííàÿ áèáëèîòåêà ìåõìàòà ÌÃÓ | Valid HTML 4.01! | Valid CSS! Î ïðîåêòå