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In a recent paper [P. H. Yoon and G. Choe, Phys. Plasmas 28, 082306 (2021)], the weak turbulence theory for incompressible magnetohydrodynamics is formulated by employing the method customarily applied in the context of kinetic weak plasma turbulence theory. Such an approach simplified certain mathematical procedures including achieving the closure relationship. The formulation in the above-cited paper starts from the equations of incompressible magnetohydrodynamic (MHD) theory expressed via Elsasser variables. The derivation of nonlinear wave kinetic equation therein is obtained via a truncated solution at the second-order of iteration following the standard practice. In the present paper, the weak MHD turbulence theory is alternatively formulated by employing the pristine form of incompressible MHD equation rather than that expressed in terms of Elsasser fields. The perturbative expansion of the nonlinear momentum equation is carried out up to the third-order iteration rather than imposing the truncation at the second order. It is found that while the resulting wave kinetic equation is identical to that obtained in the previous paper cited above, the third-order nonlinear correction plays an essential role for properly calculating derived quantities such as the total and residual energies. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel diffuse interface model of two-phase magnetohydrodynamics (MHD) based on a magnetic vector potential formulation in the three-dimensional case. This model ensures an exact divergence-free approximation of the magnetic field by introducing a magnetic vector potential A and defining the magnetic field by B = curl A. The resulting framework constitutes a highly coupled, nonlinear saddle point system consisting of the Cahn–Hilliard system and MHD potential system. To solve the model efficiently, we present two fully decoupled, first-order, linear, and unconditionally energy-stable schemes and strictly prove their well-posedness and energy stability. Finally, we present several numerical examples that demonstrate the stability and effectiveness of our schemes. [ABSTRACT FROM AUTHOR]

This paper is devoted to the characterization of magnetohydrodynamics (MHD) tearing modes causing plasma–wall interaction (PWI) in the Reversed-Field eXperiment (RFX-mod) reversed-field pinch (RFP) device. We study an example of a magnetic reconnection event in a high plasma current discharge. The PWI is measured via a fast camera looking at the graphite-covered inner wall, showing two separated footprints of neutral carbon radiation. A first, simple analysis shows that the phase-locking of m = 1 tearing modes is the principal cause of enhanced PWI, as it is well documented in literature. Many modes contribute to the phase-locking, actually more than those measured with the magnetic sensors. A more refined analysis is based on calculation of the Connection Length to the wall and of the loss time of Maxwellian ions via the Hamiltonian guiding center code Orbit. This analysis confirms the importance of the m = 1 phase-locking as a loss channel of high-energy particles, which is the mechanism that dominates the PWI pattern, but an additional role of the m = 0 , n = 7 mode is highlighted, which is a new result for the RFP. The PWI mediated by the m = 0 islands is milder, which is a good outlook for the RFX-mod2 upgraded device, currently in the assembly phase. [ABSTRACT FROM AUTHOR]

Energy flux analysis of power-law fluid is a novel contribution to recent developments in computational fluid dynamics. The study of the unsteady two-dimensional flow with double diffusive effect inside a complex enclosure exhibits great potential in optimizing the heat transfer rate due to the wavy nature of the side walls. The enclosure is confined with the flow circulation due to the thermal and solutal gradients acting along the left and right wavy walls. The computational time and accuracy in results are estimated and compared by implementing the finite volume method and element-free Galerkin technique. The results are obtained in terms of streamlines, isotherms, isoconcentrations, average Nusselt number, Sherwood number, and total entropy generation due to the effect of conventional parameters, namely, power-law index, Rayleigh number, buoyancy ratio parameter, thermophoresis parameter, Brownian motion parameter, and Lewis number with a fixed Prandtl number throughout the computation. The optimized double-diffusive natural convection analysis is based on entropy generation and a calculated Bejan number. The novelty of this paper lies in the implementation of a mesh-free approach, which may be useful for the further analysis of elliptical/semi-elliptical structures. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamics of unidirectionally propagating surface Alfvén waves, employing magnetohydrodynamic numerical simulations and statistical methodologies. The primary goal of this work is to enhance our understanding of the nonlinear self-cascade of surface Alfvén waves, which we term as uniturbulence, by unraveling the complex relationships between various length scales and their interplay with turbulent energy transfer mechanisms. To achieve this, we extensively analyze the phenomenon of uniturbulence using methods such as power spectrum analysis, radially averaged Fourier transform, and kurtosis. We employ these techniques to investigate the spatiotemporal distributions of kinetic and magnetic energy in uniturbulent flows. We also reveal the crucial role of the density contrast's variations and the role of Yaglom's law in characterizing energy transfer mechanisms. Our findings reveal that the inertial range of the perpendicular kinetic energy and magnetic energy along the z-axis depicts a progressive change in slope values, ultimately approaching the often-observed values of −5/3 and −3/2, respectively. Furthermore, our kurtosis analysis highlights the non-Gaussian behavior of the flow field at different length scales and over time, offering a perspective on uniturbulence dynamics. The correlations observed among diverse statistical approaches emphasize the complex interplay between different length scales in the context of uniturbulence. Our findings contribute to understanding this phenomenon, establishing a basis for future investigations to clarify the connections regulating these turbulent dynamics. [ABSTRACT FROM AUTHOR]

The study of kinetic sorptive effects on the transport phenomena of reactive solute has numerous real-world applications, including in the industrial and environmental sectors. These kinds of investigations become more realistic when an oscillatory pressure gradient with both the reversible and irreversible reactions at the channel walls is considered in a magnetohydrodynamics flow. In the past, Ng and Yip [J. Fluid Mech. 446, 321–345 (2001)] studied the effect of sorptive phase exchange at boundaries on the solute transport phenomena in an open-channel flow using Mei's multiple-scale homogenization technique. They considered fluid flows without magnetic field and boundary absorption. This work uses the above-mentioned method to investigate the phase exchange kinetics of Taylor dispersion phenomena in a two-dimensional magnetohydrodynamics fluid flowing through a parallel channel. The paper discusses how various parameters and dimensionless numbers, such as the Hartmann, oscillatory Reynolds, and Damkohler, affect the flow velocity, transport coefficient, multi-dimensional concentration distributions, and transverse variation rate. Due to the strong magnetic field, the flow velocity and Taylor dispersivity are adversely affected and conspicuously reduced. Additionally, for large Damkohler numbers, the total dispersion coefficient and the Taylor dispersion coefficient both decrease. However, the longitudinal concentration distribution rises with the Hartmann number and partition coefficient. It is worth noting that in the presence of unequal boundary absorption, there is no occurrence of transverse symmetry in solute concentration at any given time. Controlling various processes of tracer dispersion in environmental systems, especially water purification and the chemical industry, may benefit from these intriguing findings. [ABSTRACT FROM AUTHOR]

Large eddy simulations of high-magnetic Reynolds number (Rem) inhomogeneous magnetohydrodynamic (MHD) flows are performed. Dynamic Smagorinsky sub-grid scale model is used for closure. A hybrid formulation of spectral and finite difference methods is developed to carry out the simulations. The current code is validated by comparing it to the previously published benchmark channel flow results. The simulations are carried out at a bulk Reynolds number of 2200 and a unity magnetic Prandtl number for increasing values of interaction parameters. This paper aims to explore the effect of velocity shear on initially band or striae-type structure of magnetic field, using MHD simulations at Rem of 2200 for low (0.0088) and high (0.5) interaction parameters (N). The flow is analyzed by plotting mean quantity variations with time and in the inhomogeneous direction, spectra of (a) kinetic and magnetic energy; (b) transfer of energy from large to small scales; and (c) transfer of energy between kinetic and magnetic field. It is observed that for higher interaction parameter, the transition from laminar to turbulent is inhibited, while for the lower value, a turbulent state is observed. The final state for N = 0.0088 is characterized by a homogeneous distribution of large and small scales formed due to the breakdown of initial striae or laminar structures as seen from the distribution of x-direction magnetic field, iso-surface plots of current density, and the second invariant of velocity gradient tensor. [ABSTRACT FROM AUTHOR]

Magnetized liner inertial fusion (MagLIF) is a magneto-inertial-fusion concept that is studied on the 20-MA, 100-ns rise time Z Pulsed Power Facility at Sandia National Laboratories. Given the relative success of the platform, there is a wide interest in studying the scaled performance of this concept at a next-generation pulsed-power facility that may produce peak currents upward of 60 MA. An important aspect that requires more research is the instability dynamics of the imploding MagLIF liner, specifically how instabilities are initially seeded. It has been shown in magnetized 1-MA thin-foil liner Z-pinch implosion simulations that a Hall interchange instability (HII) effect [J. M. Woolstrum et al., Phys. Plasmas 29, 122701 (2022)] can provide an independent seeding mechanism for helical magneto-Rayleigh–Taylor instabilities. In this paper, we explore this instability at higher peak currents for MagLIF using 2D discontinuous Galerkin PERSEUS simulations, an extended magneto-hydrodynamics code [C. E. Seyler and M. R. Martin, Phys. Plasmas 18, 012703 (2011)], which includes Hall physics. Our simulations of scaled MagLIF loads show that the growth rate of the HII is invariant to the peak current, suggesting that studies at 20-MA are directly relevant to 60-MA class machines. [ABSTRACT FROM AUTHOR]

The linear stability of a fully developed liquid–metal magnetohydrodynamic pipe flow subject to a transverse magnetic field is studied numerically. Because of the lack of axial symmetry in the mean velocity profile, we need to perform a BiGlobal stability analysis. For that purpose, we develop a two-dimensional complex eigenvalue solver relying on a Chebyshev–Fourier collocation method in physical space. By performing an extensive parametric study, we show that in contrast to the Hagen–Poiseuille flow known to be linearly stable for all Reynolds numbers, the magnetohydrodynamic pipe flow with transverse magnetic field is unstable to three-dimensional disturbances at sufficiently high values of the Hartmann number and wall conductance ratio. The instability observed in this regime is attributed to the presence of velocity overspeed in the so-called Roberts layers and the corresponding inflection points in the mean velocity profile. The nature and characteristics of the most unstable modes are investigated, and we show that they vary significantly depending on the wall conductance ratio. A major result of this paper is that the global critical Reynolds number for the magnetohydrodynamic pipe flow with transverse magnetic field is Re = 45 230, and it occurs for a perfectly conducting pipe wall and the Hartmann number Ha = 19.7. [ABSTRACT FROM AUTHOR]

This paper is concerned with the validity of Prandtl boundary layer expansions for 2D steady viscous incompressible magnetohydrodynamic (MHD) flows over a rotating disk {(θ, r) ∈ [0, θ0] × [R0, ∞)} with a moving curved boundary {r = R0}. We establish the validity of boundary layer expansions and convergence rates in the Sobolev sense. Then, we extend the results by Iyer [Arch. Ration. Mech. Anal. 224(2), 421–469 (2017)] for Navier–Stokes equations to the MHD flows. [ABSTRACT FROM AUTHOR]

This paper investigates the role of magnetohydrodynamics (MHD) on the aerothermodynamics (ATD) of a representative entry vehicle while flying into the Martian atmosphere. By strategically placing a flight-ready superconducting magnet at varied positions in the Schiaparelli reentry capsule of the ExoMars mission, we discern its impact on essential flow properties. The primary consequence of MHD during atmospheric entry is the generation of the Lorentz force, which increases the shock standoff distance resulting in a reduction of the heat flux on the spacecraft by pushing high-energy plasma particles away. Through different magnet configurations, three distinct cases are formed to comprehensively understand the effects and implications of each setup. The study is performed using the COOLFluiD MHD for EnTries, an in-house ATD solver. For case 1, the magnet's placement behind the ExoMars forebody at the stagnation point reduces the heat flux. In case 2, the magnet's relocation to the shoulder region explores its potential to mitigate communication blackouts by influencing the wake region's flow. However, this positioning also induces shock bending, leading to variations in post-shock species mass fractions and heat flux spikes in the post-shock region. Case 3, involving an additional magnet where the shock bends in case 1, showcases a consistent increase in shock standoff distance across the forebody, providing a longer relaxation zone for species equilibration. Our findings highlight that while the strength of the applied magnetic field is crucial, the magnet's size is equally pivotal in determining ATD behavior. Case 3 emerges as the most promising configuration, consistently reducing heat flux across the forebody and maintaining it in the afterbody. This study underscores the potential of multi-magnet configurations as next-generation MHD heat shields for Martian atmospheric entry, emphasizing the criticality of magnet placement and configuration in enabling future MHD-enhanced deep space exploration missions. [ABSTRACT FROM AUTHOR]

Weakly ionized plasmas, formed in high enthalpy hypersonic flows, can be actively manipulated via imposed magnetic fields—a concept termed magnetohydrodynamic (MHD) flow control. Imposed MHD effects, within flows that exhibit multiple shock interactions, are consequential for emerging aerospace technologies, including the possibility of replacing mechanical control surfaces with magnetic actuation. However, numerical modeling of this flow type remains challenging due to the sensitivity of feature formation and the real gas modeling of weakly ionized, electrically conductive, air plasma. In this work, numerical simulation capabilities have been developed for the study of MHD affected, hypersonic flows, around two-dimensional axisymmetric non-simple geometries. The validated numerical methodology, combined with an advanced 19 species equation of state for air plasma, permits the realistic and efficient simulation of air plasmas in the equilibrium regime. Quantitative agreement is achieved between simulation and experiment for a Mach 5.6 double cone geometry with applied magnetic field. In the context of the magnetic actuation concept, numerical studies are conducted for varied conical surface angle and magnetic field configuration. For simple geometries with an elemental shock type, the MHD enhancement effect produces a self-similar shock structure. This paper demonstrates how, for hypersonic flows with complex shock interactions, the MHD affected flow is not only augmented in terms of shock position but may exhibit topological adaptations in the fundamental flow structure. A classification system is introduced for the emergent flow topologies identified in this work. Fluid-magnetic interactions are explored and explained in terms of the coupled mechanisms leading to (1) differences in magnitude of MHD enhancement effect and (2) structural adaptations of the flow topology. The applied numerical studies examine why increased conical surface angle does not amplify the MHD enhancement effect as expected from the base flow conditions, and the mechanisms by which the magnetic field configuration influences the MHD augmented shock structure. Most critically, classes of conditions are identified that produce topological equivalence between the magnetic interaction effects and a generalized mechanical control surface. [ABSTRACT FROM AUTHOR]

Nonlinear wave interactions in magnetohydrodynamics (MHD), such as shock refraction at an inclined density interface, lead to a plethora of wave patterns with numerous wave types. Identification of different types of MHD waves is an important and challenging task in such complex wave patterns. Moreover, owing to the multiplicity of solutions and their admissibility for different systems, especially for intermediate-type MHD shock waves, the identification of MHD wave types is complicated if one relies on the Rankine–Hugoniot jump conditions. MHD wave detection is further exacerbated by nonphysical smearing of discontinuous shock waves in numerical simulations. This paper proposes two MHD wave detection methods based on convolutional neural network to enable wave classification and identify their locations. The first method separates the output into regression (location prediction) and classification problems, assuming the number of waves for each training data is fixed. In contrast, the second method does not specify the number of waves a priori, and the algorithm predicts wave locations and classifies types using only regression. We use one-dimensional input data (density, velocity, and magnetic fields) to train the two models that successfully reproduce a complex two-dimensional MHD shock refraction structure. The first fixed output model efficiently provides high precision and recall, achieving total neural network accuracy up to 99%, and the classification accuracy of some waves approaches unity. The second detection model has relatively low performance, with more sensitivity to the setting of parameters, such as the number of grid cells Ngrid and the thresholds of confidence score and class probability, etc. The detection model achieves better than 90% accuracy with F1 score >0.95. The proposed two methods demonstrate very strong potential for MHD wave detection in complex wave structures and interactions. [ABSTRACT FROM AUTHOR]

Forward modeling is used to interpret inversion patterns of the pedestal–Scrape of Layer (SOL) Electron Cyclotron Emission (ECE) in DIII-D H-mode experiments. The modeling not only significantly improves the ECE data interpretation quality but also leads to the potential measurements of (1) the magnetic field strength |B| at the separatrix, (2) the pedestal |B| evolution during an inter-Edge Localized Mode (ELM) period, and (3) the pedestal Magnetohydrodynamics (MHD) radial structure. The ECE shine-through effect leads to three types of pedestal–SOL radiation inversions that are discussed in this paper. The first type of inversion is the non-monotonic Te,rad profile with respect to the major radius. Using the ECE frequency at the minimum Te,rad, the inversion can be applied to measure the magnetic field |B| at the separatrix and calibrate the mapping of the ECE channels with respect to the separatrix. The second type of inversion refers to the opposite phase between the radiation fluctuations δTe,rad at the pedestal and SOL. This δTe,rad phase inversion is sensitive to density and temperature fluctuations at the pedestal foot and, thus, can be used to qualitatively measure the MHD radial structure. The third type of inversion appears when the pedestal and SOL Te,rad evolve in an opposite trend, which can be used to infer the pedestal |B| field change during an inter-ELM period. The bandwidth effect on measuring δTe,rad due to pedestal MHD is also investigated in the radiation modeling. [ABSTRACT FROM AUTHOR]

In hydrodynamics, Taylor's frozen-in hypothesis connects the wavenumber spectrum to the frequency spectrum of a time series measured in real space. In this paper, we generalize Taylor's frozen-in hypothesis to magnetohydrodynamic turbulence. We analytically derive one-point two-time correlation functions for Elsässer variables whose Fourier transform yields the corresponding frequency spectra, E ± (f). We show that for isotropic turbulence, E ± (f) ∝ | U 0 ∓ B 0 | 2 / 3 in the Kolmogorov-like model and E ± (f) ∝ (B 0 | U 0 ∓ B 0 |) 1 / 2 in the Iroshnikov–Kraichnan model, where U 0 and B 0 are the mean velocity and mean magnetic fields, respectively, and f ± = k | U 0 ∓ B 0 | / (2 π) are the respective frequencies for a wavenumber k. However, for anisotropic magnetohydrodynamic turbulence, E ± (f) ∝ B 0 2 / 3 when U 0 ≪ B 0 . These results are important for the analysis of solar wind, in particular, those measured by Parker Solar Probe. [ABSTRACT FROM AUTHOR]

In this paper, a stable novel meshless coupled method is proposed to simulate the non-isothermal magnetohydrodynamics (MHD) flow problems (multi-physics quantities) inside a lid-driven cavity around complex obstacle. The proposed method is mainly motivated by a Lagrangian–Eulerian (L–E) weighted-least squares (WLS) scheme combined with a stream function-vorticity (SFV) and other stable techniques, and it is further to investigate the non-isothermal MHD flow around an airfoil obstacle at large Hartmann (Ha) or Reynolds (Re) number, for the first time. In the present meshless coupled approach (named L–E WLS–SFV), the traditional MHD equations are derived as another form with an SFV method under divergence-free constraint, which can avoid the tedious treatment of pressure on complex irregular obstacle. Then, a stable L–E WLS coupled algorithm is proposed to approximate the space derivatives of multi-physical quantities (velocity, magnetic, temperature, etc.), in which a corrected particle shifting technique is employed to improve the tensile instability among Lagrangian particles moving inside the domain and a second-order upwind scheme is adopted to stabilize large Re number problem in Eulerian fixed nodes near the boundary. Several benchmarks are simulated to show the numerical accuracy and convergence rates of the proposed WLS scheme for MHD flow at different parameters. Subsequently, the case of the non-isothermal MHD flow around a square obstacle under large parameters is simulated by the proposed L–E WLS–SFV method and compared with other numerical results to demonstrate the validity and capacity of the proposed method for multi-physical flow and the necessity of imposing the above two stable techniques. Finally, the case of non-isothermal MHD flow around the circular or airfoil obstacle is numerically investigated, and the important effects of the Hartmann, Rayleigh, and Reynolds numbers on the multi-physical quantities (stream function, vorticity, temperature, and magnetic field) are discussed. The advantages of the proposed method for the muti-physical flow around irregular obstacles are also exemplified. All the numerical results show that the proposed L–E WLS–SVF method is robust and accurate to simulate the multi-physical fluid flow around complex obstacles. [ABSTRACT FROM AUTHOR]

Physical experiments and numerical simulations have observed a remarkable phenomenon that a background magnetic field can smooth and stabilize the electrically conducting turbulent fluids. To understand the mechanism of this phenomenon, we will focus on a special 2D magnetohydrodynamic (MHD) system with no viscosity and partial magnetic resistive and examine the stability near a background magnetic field. Due to the lack of dissipation for velocity field, this stability problem is not trivial. Without the presence of a magnetic field, the fluid velocity is governed by the 2D incompressible Euler equation. And it is well known that solutions to the 2D incompressible Euler equation can grow rather rapidly. Our result in this paper then shows the stabilization effect of magnetic filed for conductive fluids. By coupling a suitable magnetic filed, we can obtain the uniform upper bound of solutions. Moreover, we will derive the exponentially decay of solutions on one direction. The approach is based on delicate energy estimate together with some observations such as Poincáre's inequality in one direction and cancellation structure. [ABSTRACT FROM AUTHOR]

In this paper, we consider the initial-boundary-value problem for planar magnetohydrodynamics equations. In particular, the influence of radiation on the dynamics at high-temperature regimes is taken into account. For the viscosity depending on the specific volume of the gas and the heat-conductivity proportional to a positive power of the temperature, we establish the global existence and uniqueness of strong solutions with large initial data to the initial-boundary-value problem, which means no shock wave, vacuum, or mass or heat concentration will be developed in finite time, although the interaction between the magnetodynamic effects and hydrodynamic is complex and the motion of the flow has large oscillations. [ABSTRACT FROM AUTHOR]

One method and two results have contributed to the complete understanding of magnetohydrodynamic laminar flow in an annular channel with a transverse magnetic field in this paper. In terms of the method, a computationally cheap semi-analytic algorithm is developed based on the spectral method and perturbation expansion. By virtue of the fast computation, dense cases with almost continuous varying Hartmann number M, Reynolds number Re, and cross section ratio η are calculated to explore the flow patterns that are missed in previous research. In terms of the results of the inertialess regime, we establish the average velocity map and electric-flow coupling delimitation in η-M space. Seven phenomenological flow patterns and their analytical approaches are identified. In terms of the results of the inertial regime, we examine the law of decreasing order-of-magnitude of inertial perturbation on primary flow with increasing Hartmann number. The proposed semi-analytic solution coincides with the R e 2 / M 4 suppression theory of J. A. Baylis and J. C. R. Hunt ["MHD flow in an annular channel; theory and experiment," J. Fluid Mech. 43, 423–428 (1971)] in the case of M < 40. When M > 40, the pair of trapezoid vortices of secondary flow begins to crack, and there is, therefore, a faster drop in inertial perturbation as R e 2 / M 5 , which is a new suppression theory. When M > 80, the anomalous reverse vortices are fully developed near Shercliff layers resulting in the weaker suppression mode of R e 2 / M 2.5 , which confirms the theoretical prediction of P. Tabeling and J. P. Chabrerie ["Magnetohydrodynamic secondary flows at high Hartmann numbers," J. Fluid Mech. 103(1), 225–239 (1981)]. [ABSTRACT FROM AUTHOR]

This study numerically investigates the fully developed two-dimensional, steady, viscous, incompressible magnetohydrodynamic fluid flow that passes through a rotating curved duct with an aspect ratio of 3. The curvature of the duct has been taken over a wide range of 0.01 ≤ δ ≤ 0.5. The governing equations are derived from the Navier–Stokes equations, and these equations are transformed into their non-dimensional form by applying usual transformations. The velocity of the flow is influenced by a pressure gradient force (namely, Dean forces) along the axial direction of the curved duct. The flow is also accelerated due to the combined action of the centrifugal and Coriolis forces. The effects of the Dean number, rotation, magnetic, Hall, and ion-slip parameters are examined on that flow. The spectral method is used as the primary tool to calculate the numerical solution, while the Chebyshev polynomial, collocation, and Newton–Raphson methods are used as supporting tools. The arc length method has also been used to calculate the results at any point of the critical zone of the solution curve. The main focal point of this paper is to investigate the effect of the magnetic parameter, Hall parameter, and ion-slip parameter on the flow characteristics in the rotational curve duct with a comparatively large aspect ratio. There are symmetric 2-, 4-, up to 12-vortex solutions that have been found for the streamlines of the secondary flow. In contrast, 1-, 2-, up to uncountable contour plots have been found for the axial flow. Specifically, asymmetric flow structures have been found for a small curvature and large Dean number. [ABSTRACT FROM AUTHOR]

In this paper, we will give the first result concerning the non-uniform dependence on initial data for the 2D magnetohydrodynamics (MHD)-Boussinesq equations as a hyperbolic-parabolic system. More precisely, we prove that the data-to-solution map of the Cauchy problem to the 2D MHD-Boussinesq equations is not uniformly continuous in Hs with s > 2. [ABSTRACT FROM AUTHOR]

An arc extinguishing lightning protection device with a multi-arc extinguishing chamber structure has been gradually applied to the overhead line lightning protection, but the process and key factors of the arc building of the internal multi-phase flow suppression arc still need to be studied. In this paper, based on the theory of arc magnetohydrodynamics and Euler's high velocity flow field model, a simplified model of arc coupled polyphase longitudinal air flow in a multi-pipe structure is established, the approximate solution of the model is made, and the development process of polyphase air flow and the extinction mechanism of the arc are obtained. At the same time, the arc quenching process of polyphase longitudinal air flow is also studied experimentally. The experimental results show that the continuous arc of power frequency can be stopped quickly and will not be reignited under the condition of polyphase air flow. [ABSTRACT FROM AUTHOR]

A recent paper by Davies et al. [Phys. Plasmas 28, 012305 (2021)] presents rational interpolants for the resistive (α) and thermoelectric (β) transport coefficients as functions of the Hall parameter χ and the ion charge state Z. Here, this discussion is augmented by showing that, at least in the Lorentz limit Z → ∞ , the proposed rational interpolants for α ⊥ and β ⊥ can be made even more accurate over a larger range of χ by making slight modifications to ensure the exact asymptotic limits are preserved. Although the authors do not discuss the conductivity (κ) coefficients, this exercise can also be repeated for the rational interpolants of κ ⊥ and κ ∧ published in a similar work [Phys. Rev. Lett. 126, 075001 (2021)]. [ABSTRACT FROM AUTHOR]

In a previous paper by V. D. Pustovitov [Phys. Plasmas 24, 112513 (2017)], it is claimed that the proofs of the "Resistive-Wall-Mode theorem" by Pfirsch and Tasso [Nucl. Fusion 11, 259 (1971)] and extensions of that theorem for time dependent wall resistivity and equilibrium plasma flow are not detailed and that there are limitations restricting their applicability. In response, we provide here pertinent detailed derivations, showing that the proofs of the above-mentioned theorems are rigorous and complete, unlike the considerations of V. D. Pustovitov [Phys. Plasmas 24, 112513 (2017)], which ignore the self-adjointness of the operator ∇ × ∇ × and the fact that the force operator in the linearized ideal MHD momentum equation remains self-adjoint in the presence of equilibrium flows. [ABSTRACT FROM AUTHOR]

Helical magneto-Rayleigh–Taylor instability (MRTI) structures have been observed in z-pinch-driven liner implosion experiments with a pre-imposed axial magnetic field. We show that the formation of these helical structures can be described by a Hall magnetohydrodynamical (HMHD) model. We used the 3D extended magnetohydrodynamics simulation code PERSEUS (which includes Hall physics) [Seyler and Martin, Phys. Plasmas 18, 012703 (2011)] to study these helical instabilities and show that a Hall interchange instability in low-density coronal plasma immediately surrounding the dense liner is responsible for producing helically oriented effects in the magnetic field and current density within the coronal layer. This seeds the helical pitch angle of the MRTI even when other proposed helical seeding mechanisms are either not present in the experiments or not accounted for in the simulations. For example, this mechanism does not require low-density power-feed plasmas to be swept in from large radius or the development of electrothermal instabilities. The Hall Instability is, thus, a new, independent explanation for the origin of the helical instabilities observed in axially premagnetized liner experiments. Simulation results supporting this mechanism are presented. [ABSTRACT FROM AUTHOR]

This research presents an analysis of entropy generation during natural convection in a porous medium using triangular heated cylindrical obstacles with equal spacing. The study consists of three cylindrical obstacles arranged in a triangular pattern. Each cylinder is uniformly spaced from its neighboring cylinders, creating equilateral triangles throughout the arrangement. All of these cylindrical obstacles are heated. The triangular arrangement guarantees an even distribution of obstacles across the experimental space. The governing equations, with entropy, are numerically solved using the finite element method. The study aims to investigate the interactions between several key elements in fluid dynamics: Casson fluid, magnetohydrodynamics, the Darcy–Forchheimer model, entropy, and natural convection. The goal is to gain insights into the individual behaviors of these elements and their interactions in combined systems. The results indicate that the Casson fluid parameter has an impact on the flow and heat transfer characteristics, while the Hartmann and Nusselt numbers exhibit control mechanisms for the intensity of natural convection and affect the patterns of isotherms, streamlines, and entropy. [ABSTRACT FROM AUTHOR]

In wall-bounded turbulent flows, both velocity and scalar fluctuations exhibit inhomogeneity and anisotropy. This study investigates the statistical properties of the small-scale scalar fluctuations in a turbulent channel flow at R e τ ≈ 585 using direct numerical simulations with and without a magnetic field. The influence of the Hartmann, Ha , and Prandtl, Pr , numbers on turbulent velocity and passive scalar fields is examined at Ha = 0 , 20, and 40 and Pr = 0.7 and 1.4. Small-scale dynamics of the passive scalar and velocity fields are studied, analyzing their probability density functions and higher-order moments, as well as their gradients. We observed that the magnetic field substantially changes flow dynamics such as the typical cliff-and-ramp type structures. The presence of the magnetic field led to statistical anisotropy, even at small-scale gradient fields. The findings reveal that the skewness of the normal derivative of scalar fluctuations remains at the order of 2. We investigated mixing characteristics by analyzing scalar dissipation rates. Scalar dissipation rates near the wall remain close to unity and decrease sharply toward the channel center, reaching a minimum value. Moreover, an increase in scalar dissipation rates leads to a decrease in the corresponding mixing timescale of the flow. This could suggest a connection between an increase in the Lorentz force and potential adjustments in the mixing timescale, potentially contributing to enhance overall mixing. Additionally, we argue that combined effects of strong intermittency and persistency of anisotropy at small scales can influence the mixing characteristics of magnetohydrodynamic turbulent flow. [ABSTRACT FROM AUTHOR]

The visual boundary recurrence plot (VBRP) method is used in this analysis to study time series of fluctuating velocities in turbulent magnetohydrodynamic channel flow that were studied in our previous study using the theory of the recurrence plots. The VBRP is a new graphical tool, which visualizes each point of the recurrence plot with colors depending on whether the neighboring points are recurrent or not and enhances, thus, the study of the stability of the textures of the recurrence plots, viewing them as geometrical shapes. We calculate the VBRPs of the turbulent velocity time series of a simulated channel flow monitored at constant streamwise and spanwise positions and at a number of positions along the wall-normal direction. We further estimate the visual boundary recurrence plot rates to indicate the change of the dynamics of the flow. The results highlight the flow dynamics under the influence of the magnetic field and identify additional correlations/similarities between the flow point positions within the channel. In this study, we show that these areas correspond to perturbations due to strikes that are created close to the boundary and move toward the centerline. It also seems that we have more often creation of streaks in the case of absence of magnetic field. [ABSTRACT FROM AUTHOR]

Based on the theory of magnetohydrodynamics, a mathematical model of air arc in the arc extinguishing chamber of a DC miniature circuit breaker was established. By coupling external circuit characteristics and contact movement process, the motion process of the arc was simulated and analyzed. On this basis, the effects of breaking speed, time constant, and magnetic field on the arc motion characteristics were studied. The study showed that increasing the breaking speed appropriately and adding appropriate magnetic field can improve the breaking performance of DC miniature circuit breakers. The research results can provide reference for the optimization design of DC miniature circuit breakers. [ABSTRACT FROM AUTHOR]

We prove a continuation criterion for the free boundary problem of three-dimensional incompressible ideal magnetohydrodynamic (MHD) equations in a bounded domain, which is analogous to the theorem given in Beale, Kato, and Majda [Commun. Math. Phys. 94, 61–66 (1984)]. We combine the energy estimates of our previous works [C. Hao and T. Luo, Arch. Ration. Mech. Anal. 212(3), 805–847 (2014)] on incompressible ideal MHD and some analogous estimates in Ginsberg [SIAM J. Math. Anal. 53, 3366–3384 (2021); arXiv:1811.06154] to show that the solution can be continued as long as the curls of the magnetic field and velocity, the second fundamental form and injectivity radius of the free boundary and some norms of the pressure remain bounded, provided that the Taylor-type sign condition holds. [ABSTRACT FROM AUTHOR]

3D non-linear magnetohydrodynamics simulations of a double tearing mode with the JOREK code are presented in the context of trying to better understand the benign termination of runaway electron beams observed in some experiments. It is shown that the non-linear behavior qualitatively depends on the resistivity η via its effect on how fast secondary, non-linearly destabilized, tearing modes grow relative to the primary mode. Within a certain range of η, a violent and global relaxation is observed, consistent with the "Kadomtsev-predicted" reconnection region extending from almost the very center up to the edge of the plasma. [ABSTRACT FROM AUTHOR]

We characterize the plasma flows generated during the ablation stage of an over-massed exploding planar wire array, fielded on the COBRA pulsed-power facility (1 MA peak current, 250 ns rise time). The planar wire array is designed to provide a driving magnetic field (80 – 100 T) and current per wire distribution (about 60 kA), similar to that in a 10 MA cylindrical exploding wire array fielded on the Z machine. Over-massing the arrays enables continuous plasma ablation over the duration of the experiment without implosion. The requirement to over-mass on the Z machine necessitates wires with diameters of 75 – 100 μ m , which are thicker than wires usually fielded on wire array experiments. To test ablation with thicker wires, we perform a parametric study by varying the initial wire diameter between 33 and 100 μm. The largest wire diameter (100 μm) array exhibits early closure of the cathode-wire gap, while the gap remains open over the duration of the experiment for wire diameters between 33 and 75 μm. Laser plasma interferometry and time-gated extreme-ultraviolet (XUV) imaging are used to probe the plasma flows ablating from the wires. The plasma flows from the wires converge to generate a pinch, which appears as a fast-moving (V ≈ 100 kms − 1 ) column of increased plasma density ( n ¯ e ≈ 2 × 10 18 cm − 3 ) and strong XUV emission. Finally, we compare the results with three-dimensional resistive-magnetohydrodynamic (MHD) simulations performed using the code GORGON, the results of which reproduce the dynamics of the experiment reasonably well. [ABSTRACT FROM AUTHOR]

The Kelvin–Helmholtz instability (KHI) stems from the velocity shear in a single continuous fluid or a velocity difference across the interface between two distinct fluids. The effect of the transverse magnetic field on the KHI of the supersonic mixing layer is investigated by numerical method. An algorithm with corner-transport-upwind and constrained-transport is used to solve the equations of magnetohydrodynamic (MHD). The evolutions of vorticity, pressure, and shock-vortex structure of the supersonic mixing layer with and without the magnetic field are studied qualitatively and quantitively. The suppression mechanism of the transverse magnetic field on the KHI is analyzed from the aspects of magnetic pressure and magnetic tension, respectively. The results show that the transverse magnetic field has a significant influence on the evolution of shock-vortex structure in the supersonic mixing layer. The magnetic pressure makes the vorticity deposition at the shear layer, and the magnetic tension produces an anti-bending torque on the shear layer. Under these two kinds of effects, the instability of the shear layer is suppressed effectively, and a long-standing banded structure of the shear layer is formed and teared later, which results in a "fishhook-like" structure occurred. Moreover, the transverse magnetic field inhibits the formation of the high-convection Mach value (Mc) regions, which effectively inhibits the formation of shocklets. In addition, with the effect of the magnetic field, a premature laminar-turbulent transition is stimulated at the core region of the vortex structure. [ABSTRACT FROM AUTHOR]

We perform a numerical study of the scaling laws of tearing modes in different parameter regimes of incompressible fluid electron magnetohydrodynamics, both in the small and large wavelength limits, as well as for the fastest growing mode that can be destabilized in a large aspect ratio current sheet. We discuss the relevance of these results, also for the interpretation of the "electron-only reconnection regime," recently identified in spacecraft measures and in numerical simulations of solar wind turbulence. We restrict here to a single parameter study, in which we selectively consider only one non-ideal effect among electron inertia, perpendicular resistivity, and perpendicular electron viscosity, and we also consider the cases in which a proportionality exists between the parallel and the perpendicular dissipative coefficients. While some known theoretical results are thus confirmed, in other regimes and/or wavelength limits, corrections are proposed with respect to some theoretical estimates already available in the literature. In other cases, the scalings are provided for the first time. All numerical results are justified in terms of heuristic arguments based on the measurement of the scaling laws of some new microscopic scales associated with the gradients of the eigenfunctions. The alternative scalings we have found are consistent with this interpretation. [ABSTRACT FROM AUTHOR]

Several studies pointed out the joint role of resistivity η and viscosity ν in determining the dynamics and the emergence of helical regimes of reversed-field pinch (RFP) plasmas. In this framework, the self-consistent time evolution of the η and ν coefficients still lacks of a fully satisfying modeling, being constrained by many approximations. In this work, the hypothesis of a flat viscosity profile is relaxed: A viscosity profile inspired by the Braginskii perpendicular viscosity is implemented in the code. This choice is motivated by the fact that the magnetohydrodynamics field instabilities relevant for the RFP configuration dynamics (resistive-kink/tearing modes) are active in the direction perpendicular to the magnetic field. Such a non-monotonous profile causes a localized damping of plasma flow in the regions, where the viscosity is stronger, close to the plasma edge. This results in the reduction of the flow shear, in turn allowing the enhancement of edge magnetic field modes amplitude. The impact on the magnetic topology and on connection length to the wall is also analyzed. [ABSTRACT FROM AUTHOR]

The stability of the n = 1 resistive wall modes (RWMs) dominated by the pressure-driven infernal components is investigated using the ideal magnetohydrodynamics (MHD) code AEGIS for the advanced tokamak scenarios. Here, n is the toroidal mode number. In the advanced tokamak scenarios, due to the large fraction of bootstrap current contribution, the profile of safety factor q is deeply reversed in magnetic shear in the central core region and locally flattened within the edge pedestal. Consequently, the pressure-driven infernal components develop in the corresponding flat-q regions of both core and edge. However, the edge infernal components dominate the n = 1 RWM structure and lead to lower βN limits for the advanced tokamak scenarios. In the framework of ideal MHD, the edge rotation is found the most critical to the stabilization due to the dominant influence of the edge infernal components, which should be maintained sufficiently large in magnitude and range in order for the rotation alone to fully suppress the n = 1 RWM in typical advanced tokamak scenarios. [ABSTRACT FROM AUTHOR]

Turbulent structures in a concentric annular pipe within a uniform transverse magnetic field are examined for a liquid metal flow. Large-eddy simulations are performed to study the effect of magnetic field on turbulence suppression and heat transfer within this geometry. At the characteristic Prandtl number of liquid metals, the smallest scales based on temperature fluctuations are much larger than those of the velocity, which allows to resolve all the temperature scales with sufficient accuracy. The calculations are run at Reynolds number 8900 for three different Hartmann numbers, H a = 40 , 60 , 120. The comparison with available direct numerical simulation data shows encouraging agreement. The main findings of this work show a circumferential dependency of the flow characteristics on the local orientation of the magnetic field, with increased anisotropy observed at all Hartmann numbers studied. Anisotropic effects of the magnetic field are predominant for Ha = 60 and Ha = 120 causing turbulence to deviate from its conventional state. At these Hartmann numbers, a partial redistribution of the turbulent kinetic energy from the axial and radial components to the azimuthal component is observed. This effect, observed here for the first time, appears to be related to the appearance of coexisting quasi two-dimensional (2D) and three-dimensional (3D) turbulence states. Moreover, large skin friction increments are also observed at Ha = 60 and Ha = 120, while coherent structures stretching and streak suppression are found for all three Hartmann numbers. [ABSTRACT FROM AUTHOR]

In magneto-inertial fusion, the ratio of the characteristic fuel length perpendicular to the applied magnetic field R to the α-particle Larmor radius ϱ α is a critical parameter setting the scale of electron thermal-conduction loss and charged burn-product confinement. Using a previously developed deep-learning-based Bayesian inference tool, we obtain the magnetic-field fuel-radius product B R ∝ R / ϱ α from an ensemble of 16 magnetized liner inertial fusion (MagLIF) experiments. Observations of the trends in BR are consistent with relative trade-offs between compression and flux loss as well as the impact of mix from 1D resistive radiation magneto-hydrodynamics simulations in all but two experiments, for which 3D effects are hypothesized to play a significant role. Finally, we explain the relationship between BR and the generalized Lawson parameter χ. Our results indicate the ability to improve performance in MagLIF through careful tuning of experimental inputs, while also highlighting key risks from mix and 3D effects that must be mitigated in scaling MagLIF to higher currents with a next-generation driver. [ABSTRACT FROM AUTHOR]

Current interchange tearing modes (CITMs) have been proposed to explain an intermittent eruption of electric current toward a divertor at an edge region of a tokamak device. Extended magnetohydrodynamic (MHD) simulations combined with the Scrape-Off-Layer diffusion model, which has been developed by the authors [Miura et al., Phys. Plasmas 24, 092111 (2017)], are carried out in order to study the growth of a CITM under influences of two-fluid and gyro-viscous effects, or non-ideal MHD effects. Numerical simulations both with and without an externally imposed azimuthal flow show that the growth of a CITM is observed for a relatively small flow velocity, and that a CITM can be a candidate mechanism for the intermittent eruption of the current in a tokamak, whether the growth is under influences of non-ideal MHD effects or not. The growth can be suppressed when an externally imposed azimuthal flow is sufficiently large to cause a finite radial displacement because such a displacement prevents a transition from an interchange to a tearing mode that is the key process of a CITM. Furthermore, it is also found that a stripe pattern similar to so-called streamers is formed in the course of the CITM growth. The basic nature of this streamer-like structure is also presented. [ABSTRACT FROM AUTHOR]

One of the most pressing issues in contemporary applied mathematics is the regulation of energy transfer via the application of external forces. The processes of heat transfer are affected by magnetic force, which has many practical uses in industry, engineering, and medicine. This research explores the magnetohydrodynamics (MHD) three-dimensional stable axisymmetric boundary layer over a permeable moving plate, which consists of water as a base liquid and binary distinct nanoparticles to generate a hybrid nanofluid. In all of these, flow beyond the boundary layer area might be calculated by a small crosswise velocity. As a result of its high thermal conductivity, a pair of distinct kinds of nanoparticles have been considered, namely alumina and copper, which are integrated into the base water. The mathematical model is built within a boundary of specified geometry and then converted into a set of ordinary differential equations (ODEs). Resultant ODEs are solved numerically using the technique of three-stage Lobatto IIIa in bvp4c solver in 2017, MATLAB software. Results revealed that two branches exist in certain ranges of moving parameter. The impacts of an increasing physical parameter on profiles of velocities and temperature with skin friction as well as with heat transfer rate are represented in graphs. Furthermore, as the volume fraction of copper increases, so does the skin friction coefficient in the positive direction of λ. The effect of viscous dissipation on the temperature profile in the z -direction has the same rising results as observed in the x -direction. According to the results of the temporal stability analysis, the upper branch is realizable and stable. [ABSTRACT FROM AUTHOR]

The Richtmyer–Meshkov instability (RMI) is caused by an incident planar shock wave impinging on the heavy-gas-density interface. We have numerically investigated the RMI controlled by different transverse magnetic-field strengths based on the ideal compressible magnetohydrodynamics (MHD) equations. The MHD equations are solved by the corner transport upwind + constrained transport algorithm, which guarantees a divergence-free constraint on the magnetic field. We discuss the flow characteristics and shock patterns in both classical hydrodynamic and MHD situations and verify our conclusions by comparing the experimental results with the numerical results. The results show that the magnetic field modifies the pressure-gradient distribution, and the baroclinic vorticity splits and attaches to the MHD shock waves. In addition, the results indicate that the interaction of shock wave and density interface changes the distribution of magnetic-field energy and distorts the magnetic induction line in the region of magnetic-field energy accumulation. The distortion of the magnetic induction lines alters the magnetic field gradient and creates a magnetic tension that produces a torque opposing that generated by the shear force on the vorticity layer, so the Kelvin–Helmholtz instability is effectively suppressed and no Kelvin–Helmholtz vortex appears on the vorticity layer. The result is that the interface instability is suppressed. [ABSTRACT FROM AUTHOR]

We develop an improved lattice-Boltzmann numerical scheme to solve magnetohydrodynamic (MHD) equations in the regime of low magnetic Reynolds numbers, grounded on the central-moment (CM) and multi-relaxation-time (MRT) collision models. The simulation of the magnetic induction equation within the lattice-Boltzmann approach to MHD has been usually devised along the lines of the simplest phenomenological description—the single relaxation time (SRT) model to solve the complete induction equation. In order to deal with well-known stability difficulties of the SRT framework for larger magnetic relaxation time scales, we introduce, alternatively, a MRT technique for the solution of the magnetic induction equation, which proves to be efficient in extending the domain of applicability of the lattice-Boltzmann method to MHD problems. We also put forward a novel and practical boundary condition method to cope with the subtleties of magnetic Boltzmann-like distributions on curved boundaries. As supporting applications, we discuss the performance of the CM–MRT algorithm to describe the complex dynamics of the 3D Orszag–Tang vortex problem and open issues related to transient flow regimes in MHD pipe flows, subject to uniform and non-uniform magnetic fields. [ABSTRACT FROM AUTHOR]

Collisionless magnetic reconnection typically requires kinetic treatment that is, in general, computationally expensive compared to fluid-based models. In this study, we use the magnetohydrodynamics with an adaptively embedded particle-in-cell (MHD-AEPIC) model to study the interaction of two magnetic flux ropes. This innovative model embeds one or more adaptive PIC regions into a global MHD simulation domain such that the kinetic treatment is only applied in regions where the kinetic physics is prominent. We compare the simulation results among three cases: (1) MHD with adaptively embedded PIC regions, (2) MHD with statically (or fixed) embedded PIC regions, and (3) a full PIC simulation. The comparison yields good agreement when analyzing their reconnection rates and magnetic island separations as well as the ion pressure tensor elements and ion agyrotropy. In order to reach good agreement among the three cases, large adaptive PIC regions are needed within the MHD domain, which indicates that the magnetic island coalescence problem is highly kinetic in nature, where the coupling between the macro-scale MHD and micro-scale kinetic physics is important. [ABSTRACT FROM AUTHOR]