Related papers: Magnetic helicity in multiply connected domains
Magnetostatics defines a class of boundary value problems in which the topology of the domain plays a subtle role. For example, representability of a divergence-free field as the curl of a vector potential comes about because of homological…
Relative magnetic helicity is a gauge invariant quantity suitable for the study of the magnetic helicity content of heliospheric plasmas. Relative magnetic helicity can be decomposed uniquely into two gauge invariant quantities, the…
Observations of magnetic helicity transportation through the solar photosphere reflect the interaction of turbulent plasma movements and magnetic fields in the solar dynamo process. In this chapter, we have reviewed the research process of…
Obtaining observational constraints on the role of turbulent effects for the solar dynamo is a difficult, yet crucial, task. Without such knowledge, the full picture of the operation mechanism of the solar dynamo cannot be formed. The…
Besides total energy, three-dimensional incompressible Hall magnetohydrodynamics (MHD) possesses two inviscid invariants which are the magnetic helicity and the generalized helicity. New exact relations are derived for homogeneous…
We briefly review helicity dynamics, inverse and bi-directional cascades in fluid and magnetohydrodynamic (MHD) turbulence, with an emphasis on the latter. The energy of a turbulent system, an invariant in the non-dissipative case, is…
A two-dimensional mean field dynamo model is solved where magnetic helicity conservation is fully included. The model has a negative radial velocity gradient giving rise to equatorward migration of magnetic activity patterns. In addition…
We recently proposed a method to calculate the relative magnetic helicity in a finite volume for a given magnetic field which however required the flux to be balanced separately on all the sides of the considered volume. In order to allow…
We construct a magnetic helicity conserving dynamo theory which incorporates a calculated magnetic helicity current. In this model the fluid helicity plays a small role in large scale magnetic field generation. Instead, the dynamo process…
We revisit the issue of conservation of magnetic helicity and the Woltjer-Taylor relaxation theory in magnetohydrodynamics in the context of weak solutions. We introduce a relaxed system for the ideal MHD system, which decouples the effects…
We introduce an alternative approach to the third order helicity of a volume preserving vector field $B$, which leads us to a lower bound for the $L^2$-energy of $B$. The proposed approach exploits correspondence between the Milnor…
The origin and evolution of the magnetic helicity in the solar corona are not well understood. For instance, the magnetic helicity of an active region is often about $10^{42}$ Mx$^2$ ($10^{26}$ Wb$^{2}$), but the observed processes whereby…
Astrophysical objects with negligible resistivity are often threaded by large scale magnetic fields. The generation of these fields is somewhat mysterious, since a magnetic field in a perfectly conducting fluid cannot change the flux…
The goal of this paper is to describe and clarify as much as possible the 3-dimensional topology underlying the Helmholtz cuts method, which occurs in a wide theoretic and applied literature about Electromagnetism, Fluid dynamics and…
A non-linear, time-dependent, magnetically driven dynamo theory which shows how magnetically dominated configurations can relax to become helical on the largest scale available is presented. Coupled time-dependent differential equations for…
Kinetic helicity (hereafter helicity) is defined by the correlation between the velocity and the flow-aligned vorticity. Helicity, as well as energy, is an inviscid invariant of the hydrodynamic equations. In contrast to energy, a measure…
The average helicity of a given electromagnetic field measures the difference between the number of left- and right-handed photons contained in the field. In here, the average helicity is derived using the conformally-invariant…
The Godbillon-Vey invariant occurs in homology theory, and algebraic topology, when conditions for a co-dimension 1, foliation of a 3D manifold are satisfied. The magnetic Godbillon-Vey helicity invariant in magnetohydrodynamics (MHD) is a…
Strong incompressible three-dimensional magnetohydrodynamic turbulence is investigated by means of high resolution direct numerical simulations. The simulations show that the configuration space is characterized by regions of positive and…
It is well known that the three-dimensional ideal magnetohydrodynamics (MHD) equations possess three magnetic invariants: (M) magnetic helicity, (C) cross helicity, and (P) the mean-square magnetic potential, in addition to the fundamental…