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Ting L., Klein R. — Viscous Vortical Flows (Lecture Notes in Physics)
Ting  L., Klein R. — Viscous Vortical Flows (Lecture Notes in Physics)

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Название: Viscous Vortical Flows (Lecture Notes in Physics)

Авторы: Ting L., Klein R.

Аннотация:

From the reviews:

"...an indispensable learning and reference source for anyone wishing to study the motion of viscous vortices...permeating the book is the obvious insight and intuition of Lu Ting into vortex dynamics and his record for translating this insight and intuition into practical methods and solutions" Max D. Gunzberger, Virginia Tech

"An up-to-date description of the theory of viscous incompressible vortical flows including important remarks on their numerical treatment. … The book is very well-written … and will most certainly quickly develop into the standard reference for many years to come. … will be the source of innumerable insights even for inclined beginners who are willing to work hard. It is certainly indispensable for the research worker and well-suited to be used in a graduate course. … is simply a ‘must’." (Thomas Sonar, Zeitschrift für Angewandte Mathematik und Physik, Vol. 59, 2008)

"This monograph familiarizes the reader with theoretical foundations of vortex-dominated flows, provides in-depth analyses via matched and multiscale asymptotics, and demonstrates how insight gained through these analyses can be exploited in the construction of robust, efficient, and accurate numerical techniques. … this book serves both for graduate students and researchers working in the areas of applied mathematics and of theoretical and/or computational fluid dynamics." (Felix Kaplanski, Zentralblatt MATH, Vol. 1130 (8), 2008)


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 227

Добавлена в каталог: 14.11.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Accuracy      $\rightarrow$ "Numerical"
Acoustic, monopole      3 27 34 102
Acoustic, potential      34
Acoustic, quadrupole      3 27 34 42 102
Approximate, boundary data      8 124 126
Approximate, N.-S.-solution      8 118 133 150 153 155
Asymmetric/symmetric parts of solutions      65ff
Atmosphere      189 also
Axial mass flux in a vortex core      109
Axial, core dynamics      181
Axisymmetric (coaxial) vortex rings      162
Axisymmetric problems      2 6 9 16 103
Background, rotational flow      $\rightarrow$ "Rotational"
Background, velocity potential      11 38/39
Bessel vortex      175 189 190
Biot-Savart integral      5 38/39 52 79 177
Biot-Savart integral, finite part of      55 82 90
Body forces      175 also
Boundary data for farfield acoustics      33
Boundary data, proximate      8 117 121 126
Boundary layer      29 176 187
Cancellation of vorticity      112 133 157 168 169 172
Center of vorticity      18 19 136 143
Center of vorticity, of positive sign (2-D)      137
Circulation (vortex strength)      4 42 78 86
Circulation (vortex strength) for axisymmetric flow      17 162
Classical inviscid theory      5 8 42 70
Classification of mergings      $\rightarrow$ "Merging"
Coaxial moment      13 22
Coaxial vortex rings      $\rightarrow$ "Vortex rings"
Compatibility conditions for 2-D vortices      63
Compatibility conditions for filaments      6 84 85
Complex potential      44 51
Composite numerical schemes      129 131 132
Composite solutions      100
Compressibility effects      3 26
Consistency conditions      2 9 13 20 22
Convection of background vorticity      186
coordinates      $\rightarrow$ "Curvilinear"
Core size      $\rightarrow$ "Vortex-"
Core structure      5 6
Core structure for 2-D vortices      55 66 76
Core structure for filaments      86 94ff 181
Core structure for vortex rings      103
Cross flow behind wings      142
Curvilinear coordinates      52 79
Cutting of a filament      $\rightarrow$ "Filament"
Decay length      4 118
Decay, farfield of vorticity      2 12 19 20 134 150
Decay, time of polar moment      19
Delta wing      181
Density, fluctuation      $\rightarrow$ "Fluctuation"
Dilatation      3 30 31
Dissipation function      29 16
Dissipation, rate of energy      3 9 16 28 36 102
Doublet as long time limit      138
Doublet farfield in 2-D flows      44 76
Doublet in farfield acoustics      34
Doublet in general farfield expansions      3 9 16 18 25
Doublet optimum      136
Doublet, long time motion      159
Doublet, vector      16
Effective height      $\rightarrow$ "Atmosphere"
Efficient numerical scheme      7
Efficient numerical scheme, meaning of      123 126
Energy dissipation      $\rightarrow$ "Dissipation"
Errors, sources of numerical      121 125
Euler background solution      187
Euler equations      5
Expansion parameter for 2-D vortices      45 57
Expansion parameter for farfield acoustics      26
Expansion parameter for slender filaments      3
Expansion scheme for 2-D flows      49 59 61/62
Expansion scheme for filaments      81
Extended asymptotic solution      133 139 149 168
Extended asymptotic solution, comparison with approx. solution      153 38ff
Farfield condition      2 9 11 85 89
Farfield expansion      2 9 11 15 117 122 164
Farfield, potential      20
Filament Function      177
Filament(s)      78ff
Filament(s) in rotational background      175 185ff
Filament(s) velocity      88—90
Filament(s), cut by a surface      194ff
Filament(s), head-on collision of      126
Filament(s), interacting      129ff
Filament(s), intersecting      118 129
Filament(s), long      175 also
Filament(s), multiple axial scales on      176ff 181ff
Filament(s), near surfaces/boundaries      16 176 185ff 193ff
Filament(s), perturbed      175 176ff
Filament(s), reconnection of      132
Finite part      also $\rightarrow$ "Biot-Savart"
Finite part of filament vector potential      53 55
Fluctuation      27 36
Fourier decomposition      69 71 88
Geostrophic      175 189
Geostrophic, inner solution for vortex      191
Global merging      $\rightarrow$ "Merging"
Half span      $\rightarrow$ "Semi span"
Hasimoto transform      177
Induced velocity      5 53 153
Induced, vector potentials      52 131
Integral invariants      $\rightarrow$ "Invariants"
Interaction of 2-D vortices      133ff
Interaction of filaments      103 108
Interaction of vortices and boundaries      193
Interaction terms for merging filaments      130
Interaction, Biot-Savart      $\rightarrow$ "Biot-Savart"
Interaction, Poisson      $\rightarrow$ "Poisson"
Interface (of a 2-D vortex)      47
Intersection of filaments      $\rightarrow$ "filaments"
Invariants      128
Invariants for filaments      93
Invariants in two dimensions      19 133ff
Inviscid      86 94 also
Inviscid theory for vortex lines in 3-D      52ff
Inviscid theory for vortices in 2-D      42ff 139
Joukowski (theorem/force)      43 76
kinetic energy      16 32 40
Laguerre polynomials      67
Lamb vortex      2 5 src='/math_tex/e5d134f35dc4949fab12ec64d186248a82.gif'
Lamb vortex as approximate core structure      67 118
Lamb vortex as initial data      139
Lamb vortex in merging problems      147
Lamb vortex, 3-D generalization of      99
Lamb vortex, age of a      147
Lamb vortices, superposition of      133 149 153
Legendre polynomials      12
Length scales for merging problems, $\ell$, $\ell_{m}$, $\ell_{d}$      117ff
Length scales, characteristic for filaments      38 175 176 182/183
Load/lift distribution      142
Local induction approximation      177
Long filaments      $\rightarrow$ "Filaments"
Mach number      3 9 27
Matching conditions      $\rightarrow$ "Farfield"
Maxwell's representation      21
Merging of type 1(a)      124 135 162 170
Merging of type 1(b)      124 126 135 145 164 171
Merging of type II      124 129 131
Merging of vortex filaments      170
Merging of vortices      117 133 138 156
Merging, (three) stages of      141 150 170
Merging, classification of problems      117
Merging, global      8 117 132 133 145 162
Merging, local      8 117 129 133
Merging, rules of      8 133 147 148
Milne — Thomson      39 43 44
Minimum principle      8 118 133
Moments of vorticity      9 12 28 36 125 127
Momentum equation      $\rightarrow$ "Navier — Stokes"
monopole      $\rightarrow$ "Acoustic"
Multiple scales      $\rightarrow$ "Length scales" $\rightarrow$ "One-time" $\rightarrow$ "Two-time"
Navier — Stokes (N-S) Equations      6 10 29 56 80
Nonlocal self induction      180
Nonuniform outer (shear) flow      77 188
Normal length      38 46 76
Normal plane      79
Normal time      6 40 46 69 76
Numerical accuracy      121 139
One-domain method      123 124
One-time solution      6 8 40 79 80
One-time solution vs. averaged two-time solution      64ff 74
Optimum, doublet      136 138
Optimum, filament core structure      106
Optimum, Lamb vortex      6 133 141
Optimum, similarity solution      6 8 66 98 99 also
Optimum, time shift      67ff
Orthogonal coordinates      $\rightarrow$ "Curvilinear"
Oscillation of a disc/2-D vortex      39 43 47 71ff 76
Oscillation of a vortex interface      51
Overlap (of vortex rings)      113
Poincare relations      118 134 147
Point vortex      42 136
Poisson integral      12 126 139 163 164
Poisson solver      123 126
Polar moment      6 15 118 134 148
Potential, acoustic      3 34
Potential, scalar      2 9 10 20 25
Potential, vector      2 9 23 100 also
Practical region of validity      7 42 103 139
Prandtl      81
Pressure fluctuation      $\rightarrow$ "Fluctuation"
Quadrupoles      2 9 also
Quadrupoles for rolling up shear layers      136
Quadrupoles in 2-D flows      45 76
Quadrupoles in general farfield expansions      25 27 31
Rankine vortex      6 39 45 47
Rate of (energy) dissipation      $\rightarrow$ "Dissipation"
Reconnection      $\rightarrow$ "Filaments"
Retarded      9 27 102
Reynolds' number      5 118/119
Reynolds' number for 2-D flow      57
Reynolds' number for vortex filaments      40 109
Roll-up of a vortex layer      $\rightarrow$ "Vortex layers"
Rotational background flow      8 175 185
Rules of merging      $\rightarrow$ "Merging"
Scalar potential      $\rightarrow$ "Potential"
Schrodinger equation (cubic)      177
Semispan      144
Serret — Frenet formulae      52 80 178
Similarity solution for 2-D vortices      66 74 148 also
Similarity solution for vortex filaments      98 99
Slender vortex approximation      185
Slenderness      3 175
Sound generation      3 26 36 41 102
Sphere & vortex ring      104
Spherical harmonics      21
Spinning disc      5 43
Stream function for 2-D flow      19 42 46 134 135 139
Stream function for axisymmetric flow      18 162 165
Stream function for filaments      85 88
Stretching      $\rightarrow$ "Vortex stretching"
subdomains      127 135
Superposition      $\rightarrow$ "Lamb vortices"
Swirling flow      38 79
Symbols & terminology      1
Symmetric/asymmetric      $\rightarrow$ "Asymmetric"
Tangent plane approximation      189 175
Terminology      $\rightarrow$ "Symbols"
Time invariants      2 9 12
Torsion      80 177
Trailing vortex layer      138 141
Trajectory of a 2-D vortex      51 69 74
Trajectory of a spinning disc      44
Turbulence      28 36
Turbulence in geostrophic vortex      191
Two-dimensional problems      2 5 9 18 56ff
Two-domain method      124 164
Two-time analysis/solution      5 6 40 46 60 71 also
Validity      $\rightarrow$ "Practical region ...."
Vector potential      also $\rightarrow$ "Potential"
Vector potential, composite solution      100
Vector potential, curl free      23 24
Vortex/vortices line      52ff
Vortex/vortices merging      $\rightarrow$ "Merging"
Vortex/vortices rings      17 162 164
Vortex/vortices, (axial) core dynamics      181
Vortex/vortices, (self-) stretching      168 178 180
Vortex/vortices, breakdown      181
Vortex/vortices, center (velocity)      58 70
Vortex/vortices, core size      5 78 139
Vortex/vortices, geostrophic      $\rightarrow$ "geostrophic"
Vortex/vortices, layers/sheets      133 135 138 142 51
Vorticity, antisymmetric distribution (2-D)      137
Vorticity, evolution equation      10 14 162
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