Topological Invariants

  • Gary Webb
Part of the Lecture Notes in Physics book series (LNP, volume 946)


In this chapter we discuss topological invariants of MHD and gas dynamics. Topological invariants and integrals of differential forms over a volume V that are non-zero are sometimes referred to as topological charges. A more complete discussion is given by Tur and Yanovsky (J. Fluid Mech. 248:67–106, 1993). Topological fluid dynamics and invariants are discussed in more detail in Arnold (Sel. Math. Sov. 5(4):326–345, 1986), Arnold and Khesin (Topological Methods in Hydrodynamics, 1998), Berger and Field (J. Fluid. Mech. 147:133–148, 1984), and in many other works. Tur and Yanovsky (Coherent Vortex Structures in Fluids and Plasmas, 2017) present examples of vortices in two fluid plasmas with nontrivial topology in which the streamlines and magnetic field lines are linked. They also discuss MHD topological solitons.


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© Springer International Publishing AG 2018

Authors and Affiliations

  • Gary Webb
    • 1
  1. 1.CSPARThe University of Alabama in HuntsvilleHuntsvilleUSA

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