Magnetohydrodynamics and Fluid Dynamics:

Action Principles and Conservation Laws

• Introduction
• The Model**
  • The MHD Equations
  • Energy Conservation
  • Faraday’s Equation and Flux Conservation
  • Field Line or Vortex Line Preservation
  • Incompressible Fluid and MHD Limit
  • Reduced MHD
  • Solar and Heliospheric Physics Applications
• Helicity in Fluids and MHD**
  • Helicity in Fluid Dynamics
  • Helicity in MHD
    • Magnetic Field Line Flow
    • Magnetic Helicity Conservation Law
    • Cross Helicity
  • Nonlocal Conservation Laws
• Noether’s Theorems and the DirectMethod.
• Advected Invariants
• Topological Invariants.
• Euler-Poincaré Equation Approach
• Hamiltonian Approach
• Multi-Symplectic Clebsch Approach
• The Lagrangian Map.
• Symmetries and Noether’s Theorem in MHD.
• MHD Stability
• Appendix A Lie Derivatives .
• Appendix B Weber Transformations
• Appendix C Cauchy Invariant b = B/Rho
• Appendix D Magnetosonic N-Waves
• Appendix E Aharonov Bohm Effects in MHD
• Appendix F Equivalence Transformations
• Appendix G Covariant, Non-relativistic MHD**