Related papers: Technical Considerations in Magnetic Analogue Mode…
In this article we revisit the significance of the often debated structural similarity between the equations of electromagnetism and fluid dynamics. Although the matching of the two sets of equations has successfully been done for…
The similarity between electromagnetics and hydrodynamics has been noticed for a long time. Maxwell developed an analogy, where the magnetic field and the vector potential in electromagnetics are compared to the vorticity and velocity in…
We present an ansatz for the relationship between magnetic flux density and fluid vorticity evolution equations. We also suggest that the magnetic flux density evolution equations be compared to the evolution equation for an effective…
Magnetic and vorticity fields evolution equations are known to obey the same equation when effects of dissipation and sources terms are negligible. We investigate the analogy between the two fields for non-vanishing dissipation and sources.…
A physically consistent approach is considered for defining an external magnetic field as needed in computational fluid dynamics problems involving magnetohydrodynamics (MHD). The approach results in simple analytical formulae that can be…
Context. Magnetic helicity is an important quantity in studies of magnetized plasmas as it provides a measure of the geometrical complexity of the magnetic field in a given volume. A more detailed description of the spatial distribution of…
In this note, we propose an exegesis of the Maxwell equations for electromagnetism. We begin with an analogy between the homogeneous Maxwell equations and the equations needed to describe the vorticity field of an incompressible inviscid…
We briefly review the recent developments in magnetohydrodynamics, which in particular deal with the evolution of magnetic fields in turbulent plasmas. We especially emphasize (i) the necessity of renormalizing equations of motion in…
Investigations of the inverse cascade of magnetic helicity are conducted with pseudospectral, three-dimensional direct numerical simulations of forced and decaying incompressible magnetohydrodynamic turbulence. The high-resolution…
In this note, we analyze the relationships that should govern the use of thermodynamics in fluid mechanics in a way that we believe is understandable to mathematicians. We also aim to better define the reasons why mechanics and…
Hydrodynamical simulations played an important role in understanding the dynamics and shaping of planetary nebulae in the past century. However, hydrodynamical simulations were just a first order approach. The new millennium arrived with…
We review our current understanding of galactic dynamo theory, paying particular attention to numerical simulations both of the mean-field equations and the original three-dimensional equations relevant to describing the magnetic field…
Analogue gravity offers an approach for testing the universality and robustness of quantum field theories in curved spacetimes and validating them using down-to-earth, laboratory-based experiments. Fluid interfaces are a promising framework…
Persistent currents and magnetization are considered for a two-dimensional electron (or gas of electrons) coupled to various magnetic fields. Thermodynamic formulae for the magnetization and the persistent current are established and the…
Magnetic winding is a fundamental topological quantity that underpins magnetic helicity and measures the entanglement of magnetic field lines. Like magnetic helicity, magnetic winding is also an invariant of ideal magnetohydrodynamics. In…
Magnetic helicity is a quantity that underpins many theories of magnetic relaxation in electrically conducting fluids, both laminar and turbulent. Although much theoretical effort has been expended on magnetic fields that are everywhere…
Continuum mechanics (e.g., hydrodynamics, elasticity theory) is based on the assumption that a small set of fields provides a closed description on large space and time scales. Conditions governing the choice for these fields are discussed…
Analogue gravity is a research programme that explores analogues of general relativistic gravitational fields within other physical systems, particularly but not exclusively in condensed matter systems, with the aim of gaining new insights…
Analogies are elaborated in the qualitative description of two systems: the magnetohydrodynamic (MHD) flow moving through a region where an external local magnetic field (magnetic obstacle) is applied, and the ordinary hydrodynamic flow…
In the framework of relativistic ideal hydrodynamics, we study the production mechanism for vorticity and magnetic field in relativistic ideal fluids. It is demonstrated that in the uncharged fluids the thermal vorticity will always satisfy…