• Preface (6)
• Acknowledgements (8)
• Contents (10)
• 1 Introduction (13)
• 2 Vortex Filaments and Where to Find Them (21)
  • 2.1 Hydrodynamics (21)
    • 2.1.1 Planetary Atmospheres (22)
    • 2.1.2 Aerodynamic Problems (25)
    • 2.1.3 Bathtub Vortex (27)
    • 2.1.4 Deep Ocean Convection (27)
  • 2.2 Quantized Vortices (28)
    • 2.2.1 Bose–Einstein Condensates (29)
    • 2.2.2 Superconductors (30)
  • 2.3 Plasmas (32)
    • 2.3.1 Magnetohydrodynamics (33)
    • 2.3.2 Atmospheric Plasma (35)
    • 2.3.3 Solar Dynamics (35)
    • 2.3.4 Astrophysical Plasmas (35)
  • 2.4 Concluding Remarks (36)
• 3 Statistical Mechanics (37)
  • 3.1 History (38)
  • 3.2 Ensembles (39)
  • 3.3 Assumptions (43)
  • 3.4 Methods (44)
    • 3.4.1 The Variational Approach (44)
    • 3.4.2 The Integral Approach (49)
      • 3.4.2.1 Canonical Ensemble (49)
      • 3.4.2.2 Microcanonical Ensemble (50)
  • 3.5 Statistical and Fluid Mechanics (52)
• 4 Parallel Filaments (54)
  • 4.1 The Point Vortex Gas (55)
  • 4.2 Negative Temperature States (58)
  • 4.3 The Guiding Center Model (62)
  • 4.4 Continuous Vorticity (65)
• 5 Curved Filaments (68)
  • 5.1 Motion of a Vortex Filament (68)
    • 5.1.1 The Curvilinear Formulation (70)
    • 5.1.2 A Small Example of Matched Expansion (73)
    • 5.1.3 Matched Equations (74)
  • 5.2 Nearly Parallel Vortex Filaments (76)
  • 5.3 Filament Crossing and Reconnection (78)
  • 5.4 Concluding Remarks (80)
• 6 Quantum Fluids (81)
  • 6.1 Bose–Einstein Condensates (81)
    • 6.1.1 Modeling Quantized Vortex Lines in BECs (82)
  • 6.2 Superconductors (85)
• 7 Plasmas (91)
  • 7.1 Magnetohydrodynamics (91)
  • 7.2 Confined 2D Plasmas (93)
  • 7.3 Quasi-2D Electron Columns (93)
    • 7.3.1 A Mean-Field Approach (96)
    • 7.3.2 A Variational Approach (100)
  • 7.4 Interpretation of Negative Specific Heat (106)
• 8 Computational Methods (108)
  • 8.1 Numerical PDEs (108)
  • 8.2 Canonical Ensemble (110)
    • 8.2.1 Monte Carlo (110)
    • 8.2.2 Metropolis (111)
    • 8.2.3 Path Integral Methods (112)
  • 8.3 Microcanonical Ensemble (114)
    • 8.3.1 Demon Algorithm (115)
    • 8.3.2 Hamiltonian Flow (117)
  • 8.4 Numerical Simulations in Vorticity (118)
  • 8.5 Concluding Remarks (118)
• 9 Quasi-2D Monte Carlo in Deep Ocean Convection (119)
  • 9.1 The Nearly Parallel Vortex Filament Model's Entropy-DrivenShift (121)
    • 9.1.1 Background (121)
    • 9.1.2 Hypothesis (122)
    • 9.1.3 Mathematical Model (122)
  • 9.2 A Mean-Field Approach (123)
  • 9.3 Solving for the Square Radius (125)
    • 9.3.1 Harmonic Oscillator Approach (125)
    • 9.3.2 Spherical Method Approach (128)
  • 9.4 Monte Carlo Comparison (131)
  • 9.5 Related Work (134)
  • 9.6 Conclusion (134)
• 10 Conclusion (136)
• References (138)
• Index (144)