Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSymmetries of Reduced Magnetohydrodynamics
105
0
0.0
(
0
)
Added by
Panagiotis Koutsomitopoulos
Publication date
2019
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Lie-symmetry methods are used to determine the symmetry group of reduced magnetohydrodynamics. This group allows for arbitrary, continuous transformations of the fields themselves, along with space-time transformations. The derivation reveals, in addition to the predictable translation and rotation groups, some unexpected symmetries. It also uncovers novel, exact nonlinear solutions to the reduced system. A similar analysis of a related but simpler system, describing nonlinear plasma turbulence in terms of a single field, is also presented.
rate research
Read More
Metriplectic dynamics is applied to compute equilibria of fluid dynamical systems. The result is a relaxation method in which Hamiltonian dynamics (symplectic structure) is combined with dissipative mechanisms (metric structure) that relaxes the system to the desired equilibrium point. The specific metric operator, which is considered in this work, is formally analogous to the Landau collision operator. These ideas are illustrated by means of case studies. The considered physical models are the Euler equations in vorticity form, the Grad-Shafranov equation, and force-free MHD equilibria.
Magnetic induction in magnetohydrodynamic fluids at magnetic Reynolds number (Rm) less than~1 has long been known to cause magnetic drag. Here, we show that when $mathrm{Rm} gg 1$ and the fluid is in a hydrodynamic-dominated regime in which the magnetic energy is much smaller than the kinetic energy, induction due to a mean shear flow leads to a magnetic eddy viscosity. The magnetic viscosity is derived from simple physical arguments, where a coherent response due to shear flow builds up in the magnetic field until decorrelated by turbulent motion. The dynamic viscosity coefficient is approximately $(B_p^2/2mu_0) tau_{rm corr}$, the poloidal magnetic energy density multiplied by the correlation time. We confirm the magnetic eddy viscosity through numerical simulations of two-dimensional incompressible magnetohydrodynamics. We also consider the three-dimensional case, and in cylindrical or spherical geometry, theoretical considerations similarly point to a nonzero viscosity whenever there is differential rotation. Hence, these results serve as a dynamical generalization of Ferraros law of isorotation. The magnetic eddy viscosity leads to transport of angular momentum and may be of importance to zonal flows in astrophysical domains such as the interior of some gas giants.
The magnetohydrodynamic (MHD) description of plasmas with relativistic particles necessarily includes an additional new field, the chiral chemical potential associated with the axial charge (i.e., the number difference between right- and left-handed relativistic fermions). This chiral chemical potential gives rise to a contribution to the electric current density of the plasma (emph{chiral magnetic effect}). We present a self-consistent treatment of the emph{chiral MHD equations}, which include the back-reaction of the magnetic field on a chiral chemical potential and its interaction with the plasma velocity field. A number of novel phenomena are exhibited. First, we show that the chiral magnetic effect decreases the frequency of the Alfv{e}n wave for incompressible flows, increases the frequencies of the Alfv{e}n wave and of the fast magnetosonic wave for compressible flows, and decreases the frequency of the slow magnetosonic wave. Second, we show that, in addition to the well-known laminar chiral dynamo effect, which is not related to fluid motions, there is a dynamo caused by the joint action of velocity shear and chiral magnetic effect. In the presence of turbulence with vanishing mean kinetic helicity, the derived mean-field chiral MHD equations describe turbulent large-scale dynamos caused by the chiral alpha effect, which is dominant for large fluid and magnetic Reynolds numbers. The chiral alpha effect is due to an interaction of the chiral magnetic effect and fluctuations of the small-scale current produced by tangling magnetic fluctuations (which are generated by tangling of the large-scale magnetic field by sheared velocity fluctuations). These dynamo effects may have interesting consequences in the dynamics of the early universe, neutron stars, and the quark--gluon plasma.
We demonstrate that, for the case of quasi-equipartition between the velocity and the magnetic field, the Lagrangian-averaged magnetohydrodynamics alpha-model (LAMHD) reproduces well both the large-scale and small-scale properties of turbulent flows; in particular, it displays no increased (super-filter) bottleneck effect with its ensuing enhanced energy spectrum at the onset of the sub-filter-scales. This is in contrast to the case of the neutral fluid in which the Lagrangian-averaged Navier-Stokes alpha-model is somewhat limited in its applications because of the formation of spatial regions with no internal degrees of freedom and subsequent contamination of super-filter-scale spectral properties. No such regions are found in LAMHD, making this method capable of large reductions in required numerical degrees of freedom; specifically, we find a reduction factor of 200 when compared to a direct numerical simulation on a large grid of 1536^3 points at the same Reynolds number.
The excitations of nonlinear magnetosonic waves in presence of charged space debris in the low Earth orbital plasma region is investigated taking into account effects of electron inertia in the framework of classical magnetohydrodynamics, which is also referred to as inertial magnetohydrodynamics. Magnetosonic waves are found to be governed by a forced Kadomtsev-Petviashvili equation with the forcing term representing effects of space debris particles. The dynamical behaviors of both slow and fast magnetosonic solitary waves is explored in detail. Exact accelerated magnetosonic lump solutions are shown to be stable for the entire region in parameter space of slow waves and a large region in parameter space of fast waves. In a similar way, magnetosonic curved solitary waves become stable for a small region in parameter space of fast waves. These exact solutions with special properties are derived for specific choices of debris functions. These novel results can have potential applications in scientific and technological aspects of space debris detection and mitigation.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
