Vortex DynamicsCambridge University Press, 24 feb 1995 - 311 pagina's The discovery of coherent structures in turbulence has fostered the hope that the study of vortices will lead to models and an understanding of turbulent flow, thereby solving or at least making less mysterious one of the great unresolved problems of classical physics. Vortex dynamics is a natural paradigm for the field of chaotic motion and modern dynamical system theory. The emphasis in this monograph is on the classical theory of inviscid incompressible fluids containing finite regions of vorticity. The effects of viscosity, compressiblity, inhomogeneity, and stratification are enormously important in many fields of application, from hypersonic flight to global environmental fluid mechanics. However, this volume focuses on those aspects of fluid motion that are primarily controlled by the vorticity and are such that the effects of the other fluid properties are secondary. This book will be of interest to students of fluid mechanics, turbulence, and vortex methods as well as to applied mathematicians and engineers. |
Inhoudsopgave
Fundamental properties of vorticity | 1 |
12 Vorticity and rotation | 6 |
13 Circulation | 8 |
1 5 The laws of vortex motion | 10 |
16 Kelvins circulation theorem | 14 |
17 Cauchys equations | 16 |
18 Irrotational flow | 17 |
19 Bernoullis equation | 18 |
Dynamics of line vortices in twodimensional flow | 116 |
72 Vortices near walls | 119 |
73 KirchhoffRouth path function | 123 |
74 Conformal mapping and the KirchhoffRouth path function | 126 |
75 Stability of infinite periodic arrays | 130 |
76 The Karman vortex street | 133 |
77 Statistical mechanics of assemblies of line vortices | 138 |
Vortex sheets in two dimensions | 141 |
Singular distributions of vorticity | 20 |
22 Vortex sheets | 25 |
23 Line vortices | 33 |
24 Image vorticity | 39 |
Vortex momentum | 46 |
32 Hydrodynamic impulse | 48 |
33 Impulsive generation from rest | 51 |
34 Effect of compressibility | 53 |
35 Angular impulse | 55 |
36 Effect of viscosity | 56 |
38 Impulse of a line vortex | 60 |
39 Vortex centroid | 61 |
310 Impulse in two dimensions | 62 |
311 Kinetic energy of vortices | 67 |
312 Helicity | 69 |
313 Axisymmetric motion with swirl | 71 |
Motion with surfaces | 74 |
42 Virtual momentum and impulse | 76 |
43 Virtual angular momentum | 78 |
44 Twodimensional motion with circulation | 79 |
Some applications | 81 |
52 Attraction of vortices or bodies to walls | 84 |
53 Force on a body in a nonuniform stream | 87 |
55 Rotating bodies | 89 |
56 Torque on a body in a nonuniform stream | 91 |
57 Selfpropulsion of a deformable body | 92 |
58 Buoyant vortex rings | 93 |
Creation of Vorticity | 95 |
62 Leading edge suction on the sheet | 97 |
63 Approximate development of the sheet into a vortex pair | 99 |
64 Formation of a vortex ring | 103 |
65 Creation of circulation about a body | 105 |
66 Generation of vorticity by flow separation | 107 |
67 Accelerated flow past a wing | 109 |
82 KelvinHelmholtz instability | 142 |
83 The illposedness of vortex sheets | 145 |
The Kaden spiral | 147 |
85 General similarity solutions single and multibranched spirals | 152 |
Dynamics of twodimensional vortex patches | 160 |
92 Contour dynamics and Schwarz functions | 163 |
93 The Kirchhoff vortex and elliptical patches in uniform strain | 167 |
94 Equilibrium configurations for single patches | 171 |
95 Filamentation | 175 |
96 Vortex pairs | 179 |
97 Arrays of vortex patches | 183 |
Axisymmetric vortex rings | 192 |
102 Thin cored rings | 195 |
103 Lambs transformation and general core structure | 201 |
104 Canonical coordinates for thin rings | 206 |
Dynamics of vortex filaments | 209 |
112 The cutoff method | 212 |
113 Kelvin waves on a filament | 215 |
114 Justification of the cutoff and higherorder approximations | 218 |
Threedimensional vortex instability | 230 |
122 Longwave cooperative instabilities | 235 |
123 Shortwave cooperative instability | 241 |
124 Ultra shortwave cooperative instability | 250 |
Effects of viscosity | 253 |
132 Decay of trailing vortices | 257 |
133 Burgers vortices | 264 |
Miscellaneous topics | 271 |
142 Kelvins variational principle | 273 |
143 Hamiltonian dynamics of vortex patch moments | 278 |
144 Vortex breakdown | 285 |
Epilogue | 295 |
| 296 | |
| 309 | |
Overige edities - Alles bekijken
Veelvoorkomende woorden en zinsdelen
angular impulse approximation asymptotic axial axis axisymmetric Bernoulli's equation body bound vorticity boundary conditions calculation centre centroid circular circulation co-ordinates complex potential components conservation constant core curve defined denotes disturbances dynamics elliptical Euler equations external force finite flow given Hamiltonian Hence hydrodynamic impulse incompressible induced infinite infinitesimal infinity inside instability integral inviscid irrotational Kelvin Kelvin's circulation theorem kinetic energy Kutta condition line vortex Moore and Saffman motion obtain perturbation plane pressure R₁ radius right-hand side ring roll-up rotation satisfied singular solution spiral stability steady stream function streamlines strength surface symmetry term theorem two-dimensional u₁ uniform vanishes vector velocity field velocity potential viscosity vortex filament vortex force vortex lines vortex pair vortex patches vortex sheet vortex tube vorticity vorticity field wavenumber wing zero ік
Populaire passages
Pagina 302 - Moore, DW 1976. The stability of an evolving two-dimensional vortex sheet. Mathematika 23, 35-44. Moore, DW 1978. The equation of motion of a vortex layer of small thickness. Stud.
Pagina 302 - Moore, DW 1974 A numerical study of the roll-up of a finite vortex sheet.
Pagina 302 - Styczek, AS 1986 A moment model for vortex interactions of the two-dimensional Euler equations. Part 1. Computational validation of a Hamiltonian elliptical representation, J. Fluid Mech. 167, 95 — 115 Melander, MV; Zabusky, NJ; McWilliams, JC 1988 Symmetric vortex merger in two dimensions: causes and conditions, J.
Pagina 302 - The linear two-dimensional stability of inviscid vortex streets of finite-cored vortices. J. Fluid Mech. 147, 187-212.
Pagina 302 - Meiron, DI, Baker, GR & Orszag, SA 1982 Analytic Structure of Vortex Sheet Dynamics. Part I. Kelvin-Helmholtz Instability. J. Fluid Mech 114, 283.
Pagina 305 - PG (1984) .Three-Dimensional Stability of an Elliptical Vortex in a Straining Field'.