Search Results (88)

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 and utility of renormalizing equations of motion in turbulence where velocity and magnetic fields become Hölder singular; (ii) the breakdown of Laplacian determinism of classical physics (spontaneous stochasticity or super chaos) in turbulence; and (iii) the possibility of eliminating the notion of magnetic field lines in magnetized plasmas, using instead magnetic path lines as trajectories of Alfvénic wave packets. These methodologies are then exemplified with their application to the problem of magnetic reconnection—rapid change in magnetic field pattern that accelerates plasma—a ubiquitous phenomenon in astrophysics and laboratory plasmas. Renormalizing rough velocity and magnetic fields on any finite scale l in turbulence inertial range, to remove singularities, implies that magnetohydrodynamic equations should be regarded as effective field theories with running parameters depending upon the scale l. A high wave-number cut-off should also be introduced in fluctuating equations of motion, e.g., Navier–Stokes, which makes them effective, low-wave-number field theories rather than stochastic differential equations. Full article

A pioneering detailed comparative study of the dynamics of plasma flows generated by high-power nanosecond and high-intensity femtosecond laser pulses with similar fluences of up to $3\times {10}^4$ J/cm² is presented. The experiments were conducted on the petawatt laser facility PEARL using two types of high-power laser radiation: femtosecond pulses with energy exceeding 10 J and a duration less than 60 fs, and nanosecond pulses with energy exceeding 10 J and a duration on the order of 1 ns. In the experiments, high-velocity (>100 km/s) flows of «femtosecond» (created by femtosecond laser pulses) and «nanosecond» plasmas propagated in a vacuum across a uniform magnetic field with a strength over 14 T. A significant difference in the dynamics of «femtosecond» and «nanosecond» plasma flows was observed: (i) The «femtosecond» plasma initially propagated in a vacuum (no B-field) as a collimated flow, while the «nanosecond» flow diverged. (ii) The «nanosecond» plasma interacting with external magnetic field formed a quasi-spherical cavity with Rayleigh–Taylor instability flutes. In the case of «femtosecond» plasma, such flutes were not observed, and the flow was immediately redirected into a narrow plasma sheet (or «tongue») propagating across the magnetic field at an approximately constant velocity. (iii) Elongated «nanosecond» and «femtosecond» plasma slabs interacting with a transverse magnetic field broke up into Rayleigh–Taylor «tongues». (iv) The ends of these «tongues» in the femtosecond case twisted into vortex structures aligned with the ion motion in the external magnetic field, whereas the «tongues» in the nanosecond case were randomly oriented. It was suggested that the twisting of femtosecond «tongues» is related to Hall effects. The experimental results are complemented by and consistent with numerical 3D magnetohydrodynamic simulations. The potential applications of these findings for astrophysical objects, such as short bursts in active galactic nuclei, are discussed. Full article

An analytical study is conducted on unsteady, one-directional magnetohydrodynamic (MHD) flows of electrically conducting, incompressible, and viscous fluids, where the viscosity varies with pressure following a power-law relationship. The flow takes place within a planar channel and is driven by the lower plate, which moves along its own plane with an arbitrary, time-dependent speed. The effects of gravitational acceleration are also considered. General exact formulas are derived for both the dimensionless velocity of the fluid and the resulting non-zero shear stress. Moreover, these are the only general solutions for the MHD motions of the fluids considered, and they can produce precise solutions for any motion of this type for respective fluids. The proposed analytical method leads to simple forms of analytical solutions and can be useful in the study of other cases of fluids with viscosity depending on pressure. As an example, solutions related to the modified Stokes’ second problem are presented and confirmed through graphical validation. These solutions also help highlight the impact of the magnetic field on fluid dynamics and determine the time needed for the system to achieve a steady state. Graphical representations indicate that a steady state is reached more quickly and the fluid moves more slowly when a magnetic field is applied. Full article

In this study, during the efficient preparation of nanofibers using a spherical section free surface electrospinning (SSFSE) device with different sphere radii, the formation mechanism and motion characteristics of multiple jets were thoroughly investigated through the numerical simulation method. The mechanical model of multiple jets was established, and the key role of electric field intensity in the formation and motion of jets was defined; in addition, the relationship between the jet initial velocity and the electric field intensity distribution on the solution surface was established. On this basis, a magnetohydrodynamic model was introduced, and a turbulence model as well as a volume of fluid model were combined to numerically simulate the jet motion during the SSFSE process. The results showed that as the sphere radius increased, the maximum velocity of the jets gradually decreased. However, the area of multiple jets generated increased, and the interaction force between the jets increased, resulting in a more obvious outward expansion of the jet trajectory. Therefore, the optimal SSFSE device with a sphere radius of 75 mm was determined. Finally, the results of numerical simulation were verified by experiments using a polymeric solution with low conductivity. This study can play a guiding role in effectively increasing the number of jets per unit area of solution surface in actual production, thus achieving continuous, uniform, and efficient preparation of micro-/nanofibers. Full article

The ‘dynamo problem’ requires that the origin of the primarily dipole geomagnetic field be found. The source of the geomagnetic field lies within the outer core of the Earth, which contains a turbulent magnetofluid whose motion is described by the equations of magnetohydrodynamics (MHD). A mathematical model can be based on the approximate but essential features of the problem, i.e., a rotating spherical shell containing an incompressible turbulent magnetofluid that is either ideal or real but maintained in an equilibrium state. Galerkin methods use orthogonal function expansions to represent dynamical fields, with each orthogonal function individually satisfying imposed boundary conditions. These Galerkin methods transform the problem from a few partial differential equations in physical space into a huge number of coupled, non-linear ordinary differential equations in the phase space of expansion coefficients, creating a dynamical system. In the ideal case, using Dirichlet boundary conditions, equilibrium statistical mechanics has provided a solution to the problem. As has been presented elsewhere, the solution also has relevance to the non-ideal case. Here, we examine and compare Galerkin methods imposing Neumann or mixed boundary conditions, in addition to Dirichlet conditions. Any of these Galerkin methods produce a dynamical system representing MHD turbulence and the application of equilibrium statistical mechanics in the ideal case gives solutions of the dynamo problem that differ only slightly in their individual sets of wavenumbers. One set of boundary conditions, Neumann on the outer and Dirichlet on the inner surface, might seem appropriate for modeling the outer core as it allows for a non-zero radial component of the internal, turbulent magnetic field to emerge and form the geomagnetic field. However, this does not provide the necessary transition of a turbulent MHD energy spectrum to match that of the surface geomagnetic field. Instead, we conclude that the model with Dirichlet conditions on both the outer and the inner surfaces is the most appropriate because it provides for a correct transition of the magnetic field, through an electrically conducting mantle, from the Earth’s outer core to its surface, solving the dynamo problem. In addition, we consider how a Galerkin model velocity field can satisfy no-slip conditions on solid boundaries and conclude that some slight, kinetically driven compressibility must exist, and we show how this can be accomplished. Full article

Magnetohydrodynamic (MHD) generators are direct energy conversion devices that transform the motion of an electrically conducting fluid into electricity through interaction with a magnetic field. Developed as an alternative to conventional turbine-generator systems, MHD generators evolved through the 20th century from large units, which are intended to transform thermal energy into electricity using plasma as a working fluid, to smaller units that can harness heat from a variety of sources. In the last few decades, an effort has been made to develop energy conversion systems that incorporate MHD generators to harvest renewable sources such as solar and ocean energy, strengthening the sustainability of this technology. This review briefly synthesizes the main steps in the evolution of MHD technology for electricity generation, starting by outlining its physical principles and the proposals to convert thermal energy into electricity, either using a high-temperature plasma as a working fluid or a liquid metal in a one- or two-phase flow at lower temperatures. The use of wave energy in the form of acoustic waves, which were obtained from the conversion of thermal energy through thermoacoustic devices coupled to liquid metal and plasma MHD generators, as well as alternatives for the transformation of environmental energy resources employing MHD transducers, is also assessed. Finally, proposals for the conversion of ocean energy, mainly in the form of waves and tides, into electric energy, through MHD generators using either seawater or liquid metal as working fluids, are presented along with some of the challenges of MHD conversion technology. Full article

Two classes of magnetohydrodynamic (MHD) motions of the incompressible Oldroyd-B fluids through an infinite cylinder are analytically investigated. General expressions are firstly established for shear stress and velocity fields corresponding to the motion induced by longitudinal shear stress on the boundary. For validation, the expression of the shear stress is determined by two different methods. Using an important remark regarding the governing equations for shear stress and fluid velocity corresponding to the two different motions, this expression is then used to provide the dimensionless velocity field of the MHD motion of the same fluids generated by a cylinder that rotates around its symmetry axis. Obtained results can generate exact solutions for any motion of this kind of Oldroyd-B fluids. Consequently, both types of motions are completely solved. For illustration, some case studies are considered, and adequate velocity fields are provided. The steady-state components of these velocities are presented in different forms whose equivalence is graphically proved. The influence of the magnetic field on the fluid behavior is graphically investigated. It was found that the fluid flows slower, and a steady state is earlier reached in the presence of a magnetic field. The fluid behavior when shear stress is given on the boundary is also investigated. Full article

In this article, we analytically investigate the isothermal magnetohydrodynamic axial symmetric flows of ordinary and fractional incompressible Oldroyd-B fluids through a porous medium in an annular channel. The fluid’s motion is generated by an outer cylinder, which moves along its symmetry axis with an arbitrary time-dependent velocity $Vh(t)$. Closed-form expressions are established for the dimensionless velocity fields of both kinds of fluids, generating exact solutions for any motion of this type. To illustrate the concept, two particular cases are considered, and the velocity fields corresponding to the flow induced by the outer cylinder are presented in simple forms, with the results validated graphically. The motion of fractional and ordinary fluids becomes steady over time, and their corresponding velocities are presented as the sum of their steady and transient components. Moreover, the steady components of these velocities are identical. The influence of magnetic fields and porous media on the flow of fractional fluids is graphically depicted and discussed. It was found that a steady state is reached earlier in the presence of a magnetic field and later in the presence of a porous medium. Moreover, this state is obtained earlier in fractional fluids compared with ordinary fluids. Full article

The motion of viscous incompressible magnetohydrodynamics (MHD) is considered in a domain that is bounded by a free surface. The motion interacts through the free surface with an electromagnetic field located in a domain exterior to the free surface and bounded by a given fixed surface. Some electromagnetic fields are prescribed on this fixed boundary. On the free surface, jumps in the magnetic and electric fields are assumed. The global existence of solutions to this problem assuming appropriate smallness conditions on the initial and boundary data is proved. Full article

We analytically investigated the magnetohydrodynamic motions of electrically conductive, incompressible Oldroyd-B fluids through an infinite circular cylinder filled with a porous medium. A general expression was established for the dimensionless velocity of fluid as a cylinder moves along its symmetry axis with an arbitrary velocity; the expression can generate exact solutions for any motion of this fluid type, solving the discussed problem. Special cases were considered and validated through graphical investigation to illustrate important characteristics of fluid behavior. In application, this is the first presentation of an exact general expression for non-trivial shear stress related to the magnetohydrodynamic motions of Oldroyd-B fluids when a longitudinal time-dependent shear stress is applied to the fluid by a cylinder. Solutions for the motions of rate-type fluids are lacking. The graphical representations show that in the presence of a magnetic field or porous medium, fluids flow more slowly and the steady state is reached earlier. Full article

This study explores the synergistic impact of zero flux and convective boundary conditions on the magnetohydrodynamic (MHD) boundary-layer slip flow of nanofluid over a moving surface, utilizing Buongiorno’s model. In a landscape of expanding nanofluid applications, understanding boundary condition interactions is crucial. Employing a systematic approach, we varied key parameters, including surface velocity, thermophoresis, Brownian motion, Eckert number, Prandtl number, and Lewis number, systematically investigating their effects on flow and heat transfer. Numerical simulations focused on critical metrics such as skin friction coefficients; Nusselt and Sherwood numbers; and temperature, concentration, and velocity profiles. Noteworthy findings include the amplifying effect of a magnetic field and viscous dissipation on temperature profiles and the dual impact of heightened velocity slip on temperature and velocity profiles, which result in a thicker concentration boundary layer. Beyond academia, we envision our research having practical applications in optimizing high-temperature processes, bio-sensors, paints, pharmaceuticals, coatings, cosmetics, and space technology. Full article

The contributions of magnetohydrodynamic (MHD) vortexes to chiral electrodeposition in a vertical magnetic field were theoretically examined based on the three-generation model of the 2D nucleus, 3D nucleus, and screw dislocation; for the vortexes to rotate in the second and third-generation, the kinematic viscosity must be at least 10⁻¹⁸ and 10⁻³⁰ times lower than the ordinary value in the first generation, i.e., almost equal to zero. This implies that the ionic vacancy created on the electrode surface works as an atomic-scale lubricant. At the same time, the vortexes played three roles: promotion and suppression of nucleation, and transport of the chirality from the upper generation to the lower generation through precessional motion. Then, the rule of the chirality transfer was established, and finally, the relationship between the chiral activity and magnetic field was clarified in the presence and absence of chloride ions. Full article

Since the middle of the 20th century, an understanding of the diversity of the natural magnetohydrodynamic phenomena surrounding us has begun to emerge. Magnetohydrodynamic nature manifests itself in such seemingly heterogeneous processes as the flow of water in the world’s oceans, the movements of Earth’s liquid core, the dynamics of the solar magnetosphere and galactic electromagnetic fields. Their close relationship and multifaceted influence on human life are becoming more and more clearly revealed. The study of these phenomena requires the development of theory both fundamental and analytical, unifying a wide range of phenomena, and specialized areas that describe specific processes. The theory of translational fluid motion is well developed, but for most natural phenomena, this condition leads to a rather limited model. The fluid motion in the cavity of a rotating body such that the Coriolis forces are significant has been studied much less. A distinctive feature of the problems under consideration is their significant nonlinearity, (i.e., the absence of a linear approximation that allows one to obtain nontrivial useful results). From this point of view, the studies presented here were selected. This review presents studies on the movements of ideal and viscous fluids without taking into account electromagnetic phenomena (non-conducting, non-magnetic fluid) and while taking them into account (conducting fluid). Much attention is payed to the macroscopic movements of sea water (conducting liquid) located in Earth’s magnetic field, which spawns electric currents and, as a result, an induced magnetic field. Exploring the processes of generating magnetic fields in the moving turbulent flows of conducting fluid in the frame of dynamic systems with distributed parameters allows better understanding of the origin of cosmic magnetic fields (those of planets, stars, and galaxies). Various approaches are presented for rotational and librational movements. In particular, an analytical solution of three-dimensional unsteady magnetohydrodynamic equations for problems in a plane-parallel configuration is presented. Full article

We review and extend the theory of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence. The theory contains a solution to the ‘dynamo problem’, i.e., the problem of determining how a planetary or stellar body produces a global dipole magnetic field. We extend the theory to the case of ideal MHD turbulence with a mean magnetic field that is aligned with a rotation axis. The existing theory is also extended by developing the thermodynamics of ideal MHD turbulence based on entropy. A mathematical model is created by Fourier transforming the MHD equations and dynamical variables, resulting in a dynamical system consisting of the independent Fourier coefficients of the velocity and magnetic fields. This dynamical system has a large but finite-dimensional phase space in which the phase flow is divergenceless in the ideal case. There may be several constants of the motion, in addition to energy, which depend on the presence, or lack thereof, of a mean magnetic field or system rotation or both imposed on the magnetofluid; this leads to five different cases of MHD turbulence that must be considered. The constants of the motion (ideal invariants)—the most important being energy and magnetic helicity—are used to construct canonical probability densities and partition functions that enable ensemble predictions to be made. These predictions are compared with time averages from numerical simulations to test whether or not the system is ergodic. In the cases most pertinent to planets and stars, nonergodicity is observed at the largest length-scales and occurs when the components of the dipole field become quasi-stationary and dipole energy is directly proportional to magnetic helicity. This nonergodicity is evident in the thermodynamics, while dipole alignment with a rotation axis may be seen as the result of dynamical symmetry breaking, i.e., ‘broken ergodicity’. The relevance of ideal theoretical results to real (forced, dissipative) MHD turbulence is shown through numerical simulation. Again, an important result is a statistical solution of the ‘dynamo problem’. Full article

The numerical study of relativistic magnetohydrodynamics (MHD) plays a crucial role in high-energy astrophysics but unfortunately is computationally demanding, given the complex physics involved (high Lorentz factor flows, extreme magnetization, and curved spacetimes near compact objects) and the large variety of spatial scales needed to resolve turbulent motions. A great benefit comes from the porting of existing codes running on standard processors to GPU-based platforms. However, this usually requires a drastic rewriting of the original code, the use of specific languages like CUDA, and a complex analysis of data management and optimization of parallel processes. Here, we describe the porting of the ECHO code for special and general relativistic MHD to accelerated devices, simply based on native Fortran language built-in constructs, especially do concurrent loops, few OpenACC directives, and straightforward data management provided by the Unified Memory option of NVIDIA compilers. Thanks to these very minor modifications to the original code, the new version of ECHO runs at least 16 times faster on GPU platforms as compared to CPU-based ones. The chosen benchmark is the 3D propagation of a relativistic MHD Alfvén wave, for which strong and weak scaling tests performed on the LEONARDO pre-exascale supercomputer at CINECA are provided (using up to 256 nodes corresponding to 1024 GPUs, and over 14 billion cells). Finally, an example of high-resolution relativistic MHD Alfvénic turbulence simulation is shown, demonstrating the potential for astrophysical plasmas of the new GPU-based version of ECHO. Full article