Related papers: A geometric look at MHD and the Braginsky dynamo
Many interesting terrestrial and astrophysical scenarios involving magnetic fields can be approached in axial geometry. Even though the Lagrangian smoothed particle hydrodynamics (SPH) technique has been successfully extended to handle…
Magnetohydrodynamics in divergence form describes a hyperbolic system of covariant and constraint-free equations. It comprises a linear combination of an algebraic constraint and Faraday's equations. Here, we study the problem of…
Using relativistic, steady, axisymmetric, ideal magnetohydrodynamics (MHD) we analyze the super-Alfvenic regime of a pulsar wind by means of solving the momentum equation along the flow as well as in the transfield direction. Employing a…
The exact law for fully developed homogeneous compressible magnetohydrodynamics (CMHD) turbulence is derived. For an isothermal plasma, without the assumption of isotropy, the exact law is expressed as a function of the plasma velocity…
Invariant finite-difference schemes for the one-dimensional shallow water equations in the presence of a magnetic field for various bottom topographies are constructed. Based on the results of the group classification recently carried out…
This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The Legendre transform of the Lagrangian formulation of these SPDEs yields their Lie-Poisson Hamiltonian…
This study shows the connection between three previously observed but seemingly unrelated phenomena in hydrodynamic (HD) and magnetohydrodynamic (MHD) turbulent flows, involving the emergence of fluctuations occurring on very long time…
This article reproduces the Karl Schwarzschild lecture 2013. Some of the basic ideas of electrodynamics and magnetohydrodynamics of mean fields in turbulently moving conducting fluids are explained. It is stressed that the connection of the…
Magnetohydrodynamics is a theory of long-lived, gapless excitations in plasmas. It was argued from the point of view of fluid with higher-form symmetry that magnetohydrodynamics remains a consistent, non-dissipative theory even in the limit…
The paper presents a detailed review of the smooth particle hydrodynamics (SPH) method with particular focus on its astrophysical applications. We start by introducing the basic ideas and concepts and thereby outline all ingredients that…
The global regularity for the incompressible magnetohydrodynamic equations (MHD) in three dimensions is a long standing open problem of fluid dynamics and PDE theory. The Navier-Stokes equations can be viewed as a special case of MHD with a…
We derive a new shell model of magnetohydrodynamic (MHD) turbulence in which the energy transfers are not necessary local. Like the original MHD equations, the model conserves the total energy, magnetic helicity, cross-helicity and volume…
In ideal MHD, the magnetic flux is advected by the plasma motion, freezing flux-surfaces into the flow. An MHD equilibrium is reached when the flow relaxes and force balance is achieved. We ask what classes of MHD equilibria can be accessed…
In this paper we show how a Lagrangian variational principle can be used to derive the SPMHD (smoothed particle magnetohydrodynamics) equations for ideal MHD. We also consider the effect of a variable smoothing length in the SPH kernels…
We construct and analyze a model of the relativistic steady-state magnetohydrodynamic (MHD) rarefaction that is induced when a planar symmetric flow (with one ignorable Cartesian coordinate) propagates under a steep drop of the external…
Steady plasma flows have been studied almost exclusively in systems with continuous symmetry or in open domains. In the absence of continuous symmetry, the lack of a conserved quantity makes the study of flows intrinsically challenging. In…
We explore a new action formulation of hyperfluids, fluids with intrinsic hypermomentum. Brown's Lagrangian for a relativistic perfect fluid is generalised by incorporating the degrees of freedom encoded in the hypermomentum tensor, namely…
Ideal magnetohydrodynamic (MHD) equilibria on a Riemannian 3-manifold satisfy the stationary Euler equations for ideal fluids. A stationary solution $X$ admits a large set of ``adapted" metrics in $M$ for which $X$ solves the corresponding…
Relativistic hydrodynamics of classic plasmas is derived from the microscopic model in the limit of ideal plasmas. The chain of equations is constructed step by step starting from the concentration evolution. It happens that the energy…
A systematic theory of the asymptotic expansion of the magnetohydrodynamic (MHD) equilibrium in the distance from the magnetic axis is developed to include arbitrary smooth currents near the magnetic axis. Compared to the vacuum and the…