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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**