Contents -- Preface -- Foreword by Joeseph B . Keller -- 1 . Circular Discrepancy and a Monte Carlo Algorithm for Generating a Low Circular Discrepancy Sequence -- Abstract -- 1.1 Introduction -- 1.2 Circular discrepancy -- 1.3 Measuring -- 1.4 The vortex points -- 1.5 Other sequences -- 1.5.1 Mapping the square to a disc -- 1.5.2 Hammersley sequence -- 1.5.3 Antonov-Saleev variant of the Sobol sequence -- 1.5.3.1 Example -- 1.6 Numerical results 1 -- 1.7 Numerical results 2 -- 1.8 Conclusion -- Acknowledgement -- Bibliography -- 2 . Periodic and Quasiperiodic Motion of Point Vortices -- Abstract -- 2.1 Introduction -- 2.2 Symplectic preliminaries -- 2.3 Fixed point theorems -- 2.4 Hamiltonian formulation of point vortex dynamics -- 2.5 Decomposition of the Hamiltonian -- 2.6 Estimates of the non-integrable perturbations -- 2.7 Application of KAM and fixed point theorems -- 2.8 Concluding remarks -- Acknowledgment -- Bibliography -- 3 . Experiments on Heave/Pitch Limit-Cycle Oscillations of a Supercritical Airfoil Close to the Transonic Dip -- Abstract -- 3.1 Introduction -- 3.2 Test set-up -- 3.3 Equations of motion -- 3.3.1 Structural-dynamic parameters -- 3.3.2 Method of flutter calculations -- 3.4 Results and discussion -- 3.4.1 Transonic dip -- 3.4.2 Limit-cycle oscillations -- 3.4.3 Energy exchange in limit-cycle oscillations -- 3.5 Concluding remarks -- Acknowledgment -- Bibliography -- 4 . Vortices in Superconductors -- Abstract -- 4.1 Introduction -- 4.2 The Ginzburg-Landau model -- 4.2.1 The time-dependent Ginzburg-Landau equations -- 4.2.2 A simplified GL model valid for high values of K. -- 4.3 The vortex state in non-ideal superconductors -- 4.3.1 Pinning of vortices -- 4.3.2 Josephson junctions -- 4.3.3 Surface superconductivity in high fields -- 4.3.4 Thermal fluctuations -- Acknowledgment -- Bibliography.

5 . Accurate Numerical Simulation of Three-dimensional Lid-driven Cavity Flows with Different Span Lengths -- Abstract -- 5.1 Introduction -- 5.2 Formulation and numerical method -- 5.2.1 Governing equations -- 5.2.2 Numerical method -- 5.3 Results -- 5.4 Concluding remarks -- Acknowledgment -- Bibliography -- 6 . Geometric, Stochastic and Algebraic Vortices -- Abstract -- 6.1 Introduction -- 6.2 Geometric vortices -- 6.2.1 Conservation laws -- 6.2.2 Slender vortices -- 6.2.3 Diffusive vortices -- 6.3 Stochastic vortices -- 6.3.1 Proper orthogonal decomposition -- 6.3.2 A de-noising definition of coherent vortices -- 6.3.3 A probabilistic version of the vorticity equation -- 6.4 Algebraic vortices -- 6.4.1 Numerical vortex methods -- 6.4.2 Adaptive wavelet method for the vorticity equation -- 6.5 Conclusions -- Acknowledgment -- Bibliography -- 7 . Experimental Investigation & Numerical Simulation of Oblique Shock/Vortex Interaction -- 7.1 Dedication to Professor Lu Ting -- 7.2 Introduction -- 7.3 Experimental investigation -- 7.3.1 Experimental setup -- 7.3.2 Measurement techniques -- 7.3.3 Experimental program -- 7.4 Numerical investigation -- 7.4.1 Computational setup and boundary conditions -- 7.5 Results -- 7.5.1 Experimental results -- 7.5.1.1 Weak/moderate interaction -- 7.5.2 Numerical results -- 7.6 Conclusions -- Bibliography -- 8 . Breakdown of Slender Vortices: The State of the Art -- Abstract -- 8.1 Introduction -- 8.2 Inviscid incompressible flow -- 8.3 Viscous incompressible flow -- 8.4 Concluding remarks -- Bibliography -- 9 . A Numerical Analysis of Vortex Dislocation in Wake-type Flow with Different Spanwise Nonuniformity -- Abstract -- 9.1 Introduction -- 9.2 Numerical simulation and method -- 9.3 Numerical results -- 9.3.1 Local spanwise nonuniformity -- 9.3.2 Stepped spanwise nonuniformity -- 9.4 Concluding remarks.

Acknowledgment -- Bibliography -- 10 . Vortex Dipole Coordinates on the Sphere -- Abstract -- 10.1 Introduction -- 10.2 The dipole coordinate system -- 10.3 One and two dipoles -- 10.4 The fundamental interactions -- Exchange scattering mode -- Loop-scattering mode -- 10.5 Concluding remarks -- Bibliography -- 11 . Magneto-Fluid-Dynamic Flow Control -- 11.1 Dedication -- 11.2 Abstract -- 11.3 Introduction -- 11.4 Governing equations -- 11.5 Plasma models -- 11.6 Electro-fluid-dynamic interaction -- 11.7 Magneto-fluid-dynamic interaction -- 11.8 Concluding remarks -- Acknowledgment -- Bibliography -- 12 . Interaction between Longitudinal Vortices and Normal and Oblique Shocks -- Abstract -- 12.1 Introduction -- 12.2 Governing equations -- 12.3 Computational setup and boundary conditions -- 12.4 Numerical method and vortex identification -- 12.5 Results -- 12.6 Conclusions -- Bibliography -- 13 . Analysis of Rotor Vortex Wake Structure Using 3-C PIV Measurements -- Abstract -- 13.1 Introduction -- 13.2 Test set-up and 3-C PIV measurements -- 13.3 PIV data process -- 13.4 Rotation of PIV measuring plane -- 13.5 Concluding remarks -- Acknowledgments -- Bibliography -- 14 . Typical Vortex Phenomena in Flow Fields Past Space Vehicles -- Abstract -- 14.1 Introduction -- 14.2 Numerical simulation tool -- 14.3 Vortical flow effects on space vehicles -- 14.3.1 General -- 14.3.2 Influence on lift -- 14.3.3 Influence on drag -- 14.3.4 Influence on heat flux -- 14.3.5 Hot wall effects -- 14.4 Conclusions -- Bibliography.