Existence of Electromagnetic-Hydrodynamic Waves

Turbulent diffusion of lines and circulations

“…It has recently been argued that the Kelvin theorem in fact breaks down in turbulent flows, in the sense that the circulation is not strictly conserved for every loop [18,19]. Similar breakdown of Alfvén's theorem on magnetic-flux conservation [20] is expected in plasma turbulence at high magnetic Reynolds numbers [21].…”

“…where C(t) is the material line advected by u(t) which started as line C at the initial time (14) represents gauge-invariant magnetic flux and the conservation law corresponds to Alfvén's theorem [20].…”

Ultra‐High‐Resolution Observations of MHD Waves in Photospheric Magnetic Structures

“…Aside from the numerous theoretical studies related to Alfvén wave generation and dissipation, and as documented by Mathioudakis et al [2013], observationally identifying pure torsional Alfvén waves in the solar atmosphere has been a monumental struggle ever since they were postulated by Alfvén [1942]. In their most simplistic form (i.e., the torsional Alfvén wave with azimuthal wave number m = 0), their incompressible nature provides the inability to detect them through typical intensity (i.e., density) measurements, and the azimuthal nature of the oscillation provides no transversal deflection of the magnetic structure about its central axis.…”

The Near-Saturn Magnetic Field Environment

“…The latter corresponds to the converse when the magnetic field lines can decouple from the plasma structure and diffuse down field gradients. In ideal MHD, the diffusive term vanishes in the limit of an infinite conductivity (where η = 1/σμ 0 is the magnetic diffusivity) and the induction equation is reduced to only the convective term [Alfvén, 1942;Bondi and Gold, 1950].…”

“…Equation 1.18 shows the dispersion relation followed by another characteristic wave, the Alfvén wave, with a speed v A [Alfvén, 1942].…”