Vortex Dominated Flows

A Volume Celebrating Lu Ting's 80th Birthday

By: Chee Tung (Editor), Egon Krause (Editor), Denis Blackmore (Editor)

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Hardcover | 12 August 2005

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300 Pages

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23.5 x 16.2 x 2.1

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Honoring the contributions of one of the field's leading experts, Lu Ting, this indispensable volume contains important new results at the cutting edge of research. A wide variety of significant new analytical and numerical results in critical areas are presented, including point vortex dynamics, superconductor vortices, cavity flows, vortex breakdown, shock/vortex interaction, wake flows, magneto-hydrodynamics, rotary wake flows, and hypersonic vortex phenomena.The book will be invaluable for those interested in the state of the art of vortex dominated flows, both from a theoretical and applied perspective.Professor Lu Ting and Joe Keller have worked together for over 40 years. In their first joint work entitled "Periodic vibrations of systems governed by nonlinear partial differential equations", perturbation analysis and bifurcation theory were used to determine the frequencies and modes of vibration of various physical systems. The novelty was the application to partial differential equations of methods which, previously, had been used almost exclusively on ordinary differential equations. Professsor Lu Ting is an expert in both fluid dynamics and the use of matched asymptotic expansions. His physical insight into fluid flows has led the way to finding the appropriate mathematical simplications used in the solutions to many difficult flow problems.

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Non-Fiction Science Physics Classical Mathematics Fluid Mechanics Engineering & Technology Mechanical Engineering & Materials Materials Science Mechanics of Fluids Flow Applied Physics Astrophysics

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Preface	p. xiii
Foreword	p. xxix
Circular Discrepancy and a Monte Carlo Algorithm for Generating a Low Circular Discrepancy Sequence	p. 1
Introduction	p. 1
Circular discrepancy	p. 3
Measuring [Delta] [P]	p. 3
The vortex points	p. 7
Other sequences	p. 9
Mapping the square to a disc	p. 10
Hammersley sequence	p. 11
Antonov-Saleev variant of the Sobol sequence	p. 11
Example	p. 12
Numerical results 1	p. 13
Numerical results 2	p. 14
Conclusion	p. 15
Periodic and Quasiperiodic Motion of Point Vortices	p. 21
Introduction	p. 22
Symplectic preliminaries	p. 24
Fixed point theorems	p. 26
Hamiltonian formulation of point vortex dynamics	p. 27
Decomposition of the Hamiltonian	p. 33
Estimates of the non-integrable perturbations	p. 35
Application of KAM and fixed point theorems	p. 36
Concluding remarks	p. 39
Experiments on Heave/Pitch Limit-Cycle Oscillations of a Supercritical Airfoil Close to the Transonic Dip	p. 43
Introduction	p. 44
Test set-up	p. 47
Equations of motion	p. 48
Structural-dynamic parameters	p. 50
Method of flutter calculations	p. 50
Results and discussion	p. 52
Transonic dip	p. 52
Limit-cycle oscillations	p. 56
Energy exchange in limit-cycle oscillations	p. 59
Concluding remarks	p. 63
Vortices in Superconductors	p. 67
Introduction	p. 68
The Ginzburg-Landau model	p. 69
The time-dependent Ginzburg-Landau equations	p. 72
A simplified GL model valid for high values of [kappa]	p. 74
The vortex state in non-ideal superconductors	p. 75
Pinning of vortices	p. 76
Josephson junctions	p. 78
Surface superconductivity in high fields	p. 80
Thermal fluctuations	p. 82
Accurate Numerical Simulation of Three-dimensional Lid-driven Cavity Flows with Different Span Lengths	p. 87
Introduction	p. 88
Formulation and numerical method	p. 88
Governing equations	p. 88
Numerical method	p. 89
Results	p. 93
Concluding remarks	p. 96
Geometric, Stochastic and Algebraic Vortices	p. 99
Introduction	p. 99
Geometric vortices	p. 103
Conservation laws	p. 103
Slender vortices	p. 104
Diffusive vortices	p. 105
Stochastic vortices	p. 106
Proper orthogonal decomposition	p. 106
A de-noising definition of coherent vortices	p. 107
A probabilistic version of the vorticity equation	p. 109
Algebraic vortices	p. 110
Numerical vortex methods	p. 110
Adaptive wavelet method for the vorticity equation	p. 113
Conclusions	p. 115
Experimental Investigation & Numerical Simulation of Oblique Shock/Vortex Interaction	p. 119
Dedication to Professor Lu Ting	p. 119
Introduction	p. 119
Experimental investigation	p. 121
Experimental setup	p. 122
Measurement techniques	p. 123
Experimental program	p. 124
Numerical investigation	p. 126
Computational setup and boundary conditions	p. 126
Results	p. 127
Experimental results	p. 127
Weak/moderate interaction	p. 127
Numerical results	p. 129
Conclusions	p. 130
Breakdown of Slender Vortices: The State of the Art	p. 135
Introduction	p. 136
Inviscid incompressible flow	p. 138
Viscous incompressible flow	p. 145
Concluding remarks	p. 153
A Numerical Analysis of Vortex Dislocation in Wake-type Flow with Different Spanwise Nonuniformity	p. 157
Introduction	p. 158
Numerical simulation and method	p. 159
Numerical results	p. 162
Local spanwise nonuniformity	p. 162
Stepped spanwise nonuniformity	p. 165
Concluding remarks	p. 166
Vortex Dipole Coordinates on the Sphere	p. 169
Introduction	p. 169
The dipole coordinate system	p. 172
One and two dipoles	p. 174
The fundamental interactions	p. 177
Concluding remarks	p. 180
Magneto-Fluid-Dynamic Flow Control	p. 183
Dedication	p. 183
Abstract	p. 183
Introduction	p. 184
Governing equations	p. 185
Plasma models	p. 187
Electro-fluid-dynamic interaction	p. 188
Magneto-fluid-dynamic interaction	p. 190
Concluding remarks	p. 192
Interaction between Longitudinal Vortices and Normal and Oblique Shocks	p. 199
Introduction	p. 199
Governing equations	p. 201
Computational setup and boundary conditions	p. 203
Numerical method and vortex identification	p. 211
Results	p. 213
Conclusions	p. 221
Analysis of Rotor Vortex Wake Structure Using 3-C PIV Measurements	p. 229
Introduction	p. 229
Test set-up and 3-C PIV measurements	p. 231
PIV data process	p. 231
Rotation of PIV measuring plane	p. 233
Concluding remarks	p. 235
Typical Vortex Phenomena in Flow Fields Past Space Vehicles	p. 251
Introduction	p. 252
Numerical simulation tool	p. 253
Vortical flow effects on space vehicles	p. 256
General	p. 256
Influence on lift	p. 256
Influence on drag	p. 257
Influence on heat flux	p. 258
Hot wall effects	p. 259
Conclusions	p. 260
Table of Contents provided by Ingram. All Rights Reserved.

Vortex Dominated Flows

A Volume Celebrating Lu Ting's 80th Birthday

At a Glance

Hardcover

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