In this work, three-dimensional numerical investigations into flow manipulation have been conducted using the principles of magnetohydrodynamics, followed by the analysis of the phenomenon of species mixing in a Carreau–Yasuda-type fluid. The flow control has been implemented by employing Lorentz forces to guide the conducting fluid along desired routes throughout a compact mixing chamber. The Lorentz forces were generated using electrode arrays placed in a magnetic field. We have demonstrated that different flow patterns can be created by using different electrode configurations with minor variation in the applied electrode potentials. Results show that the mixing performance of the device depends on the electrode configuration and rheology of the fluid – shear thinning, Newtonian or shear thickening. Effects of fluid rheology on different aspects of flow and mixing have been thoroughly investigated.

In gamma-ray binaries neutron star is orbiting a companion that produces a strong stellar wind. We demonstrate that observed properties of ‘stellar wind’–‘pulsar wind’ interaction depend both on the overall wind thrust ratio, as well as more subtle geometrical factors: the relative direction of the pulsar’s spin, the plane of the orbit, the direction of motion, and the instantaneous line of sight. Using fully 3D relativistic magnetohydrodynamical simulations we find that the resulting intrinsic morphologies can be significantly orbital phase-dependent: a given system may change from tailward-open to tailward-closed shapes. As a result, the region of unshocked pulsar wind can change by an order of magnitude over a quarter of the orbit. We calculate radiation maps and synthetic light curves for synchrotron (X-ray) and inverse-Compton emission (GeV-TeV), taking into account $\gamma $–$\gamma $ absorption. Our modelled light curves are in agreement with the phase-dependent observed light curves of LS5039.

MHD avalanches involve small, narrowly localized instabilities spreading across neighbouring areas in a magnetic field. Cumulatively, many small events release vast amounts of stored energy. Straight cylindrical flux tubes are easily modelled, between two parallel planes, and can support such an avalanche: one unstable flux tube causes instability to proliferate, via magnetic reconnection, and then an ongoing chain of like events. True coronal loops, however, are visibly curved, between footpoints on the same solar surface. With 3D MHD simulations, we verify the viability of MHD avalanches in the more physically realistic, curved geometry of a coronal arcade. MHD avalanches thus amplify instability across strong solar magnetic fields and disturb wide regions of plasma. Contrasting with the behaviour of straight cylindrical models, a modified ideal MHD kink mode occurs, more readily and preferentially upwards in the new, curved geometry. Instability spreads over a region far wider than the original flux tubes and than their footpoints. Consequently, sustained heating is produced in a series of ‘nanoflares’ collectively contributing substantially to coronal heating. Overwhelmingly, viscous heating dominates, generated in shocks and jets produced by individual small events. Reconnection is not the greatest contributor to heating, but is rather the facilitator of those processes that are. Localized and impulsive, heating shows no strong spatial preference, except a modest bias away from footpoints, towards the loop’s apex. Remarkable evidence emerges of ‘campfire’ like events, with simultaneous, reconnection-induced nanoflares at separate sites along coronal strands, akin to recent results from Solar Orbiter. Effects of physically realistic plasma parameters, and the implications for thermodynamic models, with energetic transport, are discussed.

We present results from 3D MHD simulations of the magnetospheres from massive stars with a dipole magnetic axis that has an arbitrary obliquity angle (β) to the stars rotation axis. As an initial direct application, we examine the global structure of co-rotating disks for tilt angles β=0, 45 and 90 degrees using ζ Pup stellar parameters as a prototype. We find that for models with rapid stellar rotation (∼ 0.5 critical rotation), accumulation surfaces closely resemble the form predicted by the analytic Rigidly Rotating Magnetosphere (RRM) model, but with a mass distribution and outer disk termination set by centrifugal breakout processes. However, some significant differences are found including warping resulting from the dynamic nature of the MHD models in contrast to static RRM models. These MHD models can be used to synthesize rotational modulation of photometric absorption and H-alpha emission for a direct comparison with observations.

Compressible magnetohydrodynamic (MHD) turbulence is a common feature of astrophysical systems such as the solar atmosphere and interstellar medium. Such systems are rife with shock waves that can redistribute and dissipate energy. For an MHD system, three broad categories of shocks exist (slow, fast, and intermediate); however, the occurrence rates of each shock type are not known for turbulent systems. Here, we present a method for detecting and classifying the full range of MHD shocks applied to the Orszag–Tang vortex. Our results show that the system is dominated by fast and slow shocks, with far less-frequent intermediate shocks appearing most readily near magnetic reconnection sites. We present a potential mechanism that could lead to the formation of intermediate shocks in MHD systems, and study the coherency and abundances of shocks in compressible MHD turbulence.

This paper presents a study of a novel type of magnetic nozzle that allows for three-dimensional (3-D) steering of a plasma plume. Numerical simulations were performed using Tech-X’s USim® software to quantify the nozzle’s capabilities. A 2-D planar magnetic nozzle was applied to plumes of a nominal pulsed inductive plasma (PIP) source with discharge parameters similar to those of Missouri S&T’s Missouri Plasmoid Experiment (MPX). Argon and xenon plumes were considered. Simulations were verified and validated through a mesh convergence study as well as comparison with available experimental data. Periodicity was achieved over the simulation run time and phase angle samples were taken to examine plume evolution over pulse cycles. The resulting pressure, velocity, and density fields were analysed for nozzle angles from 0° to 14°. It was found that actual plume divergence was small compared to the nozzle angle. Even with an offset angle of 14° for the magnetic nozzle, the plume vector angle was only about 2° for argon and less than 1° for xenon. The parameters that had the most effect on the vectoring angle were found to be the coil current and inlet velocity.

High-resolution direct numerical simulations are performed to study the turbulent shear flow of liquid metal in a cylindrical container. The flow is driven by an azimuthal Lorentz force induced by the interaction between the radial electric currents injected through electrodes placed at the bottom wall and a magnetic field imposed in the axial direction. All physical parameters, are aligned with the experiment by Messadek & Moreau (J. Fluid Mech. vol. 456, 2002, pp. 137–159). The simulations recover the variations of angular momentum, velocity profiles, boundary layer thickness and turbulent spectra found experimentally to a very good precision. They further reveal a transition to small scale turbulence in the wall side layer when the Reynolds number based on Hartmann layer thickness $R$ exceeds 121, and a separation of this layer for $R \geq 145.2$. Ekman recirculations significantly influence these quantities and determine global dissipation. This phenomenology well captured by the 2-D PSM model (Pothérat, Sommeria & Moreau, J. Fluid Mech. vol. 424, 2000, pp. 75–100) until small-scale turbulence appears and incurs significant extra dissipation only captured by 3-D simulations. Secondly, we recover the theoretical law for the cutoff scale separating large quasi-two-dimensional (Q2-D) scales from small three-dimensional ones (Sommeria & Moreau, J. Fluid Mech. vol. 118, 1982, pp. 507–518), and thus establish its validity in sheared magnetohydrodynamics (MHD) turbulence. We further find that three-componentality and three-dimensionality appear concurrently and that both the frequency corresponding to the Q2-D cutoff scale and the mean energy associated with he axial component of velocity scale with the true interaction parameter $N_t$, respectively, as $0.063 N_t^{0.37}$ and $0.126N_t^{-0.92}$.

We analyse linear stability of interfacial waves in an idealised model of an aluminium reduction cell consisting of two stably stratified liquid layers which carry a vertical electric current in a collinear external magnetic field. If the product of electric current and magnetic field exceeds a certain critical threshold depending on the cell design, the electromagnetic coupling of gravity wave modes can give rise to a self-amplifying rotating interfacial wave which is known as the metal pad instability. Using the eigenvalue perturbation method, we show that, in the inviscid limit, rectangular cells of horizontal aspect ratios $\alpha =\sqrt {m/n}$, where $m$ and $n$ are any two odd numbers, can be destabilised by an infinitesimally weak electromagnetic interaction while cells of other aspect ratios have finite instability thresholds. This fractal distribution of critical aspect ratios, which form an absolutely discontinuous dense set of points interspersed with aspect ratios with non-zero stability thresholds, is confirmed by accurate numerical solution of the linear stability problem. Although the fractality vanishes when viscous friction is taken into account, the instability threshold is smoothed out gradually and its principal structure, which is dominated by the major critical aspect ratios corresponding to moderate values of $m$ and $n$, is well-preserved up to relatively large dimensionless viscous friction coefficients $\gamma \sim 0.1$. With a small viscous friction, the most stable are cells with $\alpha ^{2}\approx 2.13$ which have the highest stability threshold corresponding to the electromagnetic interaction parameter $\beta \approx 4.7$.

We study the nonlinear mode competition of various spiral instabilities in magnetised Taylor–Couette flow. The resulting finite-amplitude mixed-mode solution branches are tracked using the annular-parallelogram periodic domain approach developed by Deguchi & Altmeyer (Phys. Rev. E, vol. 87, 2013, 043017). Mode competition phenomena are studied in both the anticyclonic and cyclonic Rayleigh-stable regimes. In the anticyclonic sub-rotation regime, with the inner cylinder rotating faster than the outer, Hollerbach et al. (Phys. Rev. Lett., vol. 104, 2010, 044502) found competing axisymmetric and non-axisymmetric magneto-rotational linearly unstable modes within the parameter range where experimental investigation is feasible. Here we confirm the existence of mode competition and compute the nonlinear mixed-mode solutions that result from it. In the cyclonic super-rotating regime, with the inner cylinder rotating slower than the outer, Deguchi (Phys. Rev. E, vol. 95, 2017, 021102) recently found a non-axisymmetric purely hydrodynamic linear instability that coexists with the non-axisymmetric magneto-rotational instability discovered a little earlier by Rüdiger et al. (Phys. Fluids, vol. 28, 2016, 014105). We show that nonlinear interactions of these instabilities give rise to rich pattern-formation phenomena leading to drastic angular momentum transport enhancement/reduction.

The combination of strong magnetic fields and fast rotation is often invoked as a characteristic of the central engine for outstanding sources such as GRBs, hypernovae, and superluminous supernovae. However, the actual properties of the magnetic field during the collapse of the stellar progenitor are very uncertain, since they depend on the evolution of the star and can be affected by complex dynamo processes occurring in the central proto-neutron star. Using 3D relativistic MHD models we show that higher-order multipolar fields can lead to the onset of a supernova, although they tend to produce less energetic explosions and less collimated outflows. Quadrupolar fields efficiently extract angular momentum from the central core, but the rotational energy is partly stored in the equatorial regions, rather than powering up the polar outflows. Finally, our results show a strong magnetic quenching of the hydrodynamic non-axisymmetric instabilities that are associated to the emission of GWs.

We study the long-term heating due to magnetic field decay in the core of neutron star. Two cases for the nucleonic core are considered: normal and strongly superconducting. We give simple scaling relations (depending on the internal stellar temperature and the averaged magnetic field in the core) to estimate the magnetic field decay rate for the most important dissipation processes. Comparison to properties of observed neutron stars suggests that heating due to the magnetic field decay is (at least partially) responsible for the thermal states of middle-aged magnetars and highly-magnetized isolated neutron stars with ages of 1 — 10 Myr.

In a collisionless shock, there are no binary collisions to isotropize the flow. It is therefore reasonable to ask to which extent the magnetohydrodynamics (MHD) jump conditions apply. Following up on recent works which found a significant departure from MHD in the case of parallel collisionless shocks, we here present a model allowing to compute the density jump for collisionless shocks. Because the departure from MHD eventually stems from a sustained downstream anisotropy that the Vlasov equation alone cannot specify, we hypothesize a kinetic history for the plasma, as it crosses the shock front. For simplicity, we deal with non-relativistic pair plasmas. We treat the cases of parallel and perpendicular shocks. Non-MHD behavior is more pronounced for the parallel case where, according to MHD, the field should not affect the shock at all.

Subcritical instabilities (i.e. finite-amplitude instabilities that occur without any linear instability) in magnetohydrodynamic (MHD) flows are studied by computing finite-amplitude equilibrium solutions of viscous–resistive MHD equations. The plane Couette flow magnetised by a uniform spanwise current is used as a model flow. Solutions are found for broad sub- and super-Alfvénic flow regimes by controlling the magnetic Mach number, but their existence is greatly influenced by the magnetic Prandtl number. When that number is unity, and the walls are perfectly insulating, the solution branch found in the super-Alfvénic regime cannot be continued towards the sub-Alfvénic regime; the boundary between those regimes is called the Chandrasekhar state, where Chandrasekhar (Proc. Natl Acad. Sci. USA, vol. 42, 1956, pp. 273–276) proved the non-existence of a linear ideal instability. Thus, the result may seem to suggest that the Chandrasekhar theorem holds even when diffusivity and nonlinearity are present. This is certainly true, but only when the perturbation magnetic field on the boundary is small. The boundary effects add more complexity to the nonlinear analysis of the Chandrasekhar state. The Chandrasekhar theorem is known to work for flows bounded by perfectly conducting walls. However, somewhat paradoxically, when the walls are perfectly conducting, our large-Reynolds-number computational results show that the nonlinear solutions do exist in the Chandrasekhar state. We give a theoretical reasoning for this curious phenomenon, using a large-Reynolds-number asymptotic analysis. For small magnetic Prandtl numbers, we also show that the solution can be continued for infinitesimally small magnetic Mach number, where the flow is significantly sub-Alfvénic.

The wake structure of an incompressible, conducting, viscous fluid past an electrically insulating sphere affected by a transverse magnetic field is investigated numerically over flow regimes including steady and unsteady laminar flows at Reynolds numbers up to 300. For a steady axisymmetric flow affected by a transverse magnetic field, the wake structure is deemed to be a double plane symmetric state. For a periodic flow, unsteady vortex shedding is first suppressed and transitions to a steady plane symmetric state and then to a double plane symmetric pattern. Wake structures in the range $210<Re\leqslant 300$ without a magnetic field have a symmetry plane. An angle $\unicode[STIX]{x1D703}$ exists between the orientation of this symmetry plane and the imposed transverse magnetic field. For a given transverse magnetic field, the final wake structure is found to be independent of the initial flow configuration with a different angle $\unicode[STIX]{x1D703}$. However, the orientation of the symmetry plane tends to be perpendicular to the magnetic field, which implies that the transverse magnetic field can control the orientation of the wake structure of a free-moving sphere and change the direction of its horizontal motion by a field–wake–trajectory control mechanism. An interesting ‘reversion phenomenon’ is found, where the wake structure of the sphere at a higher Reynolds number and a certain magnetic interaction parameter ($N$) corresponds to a lower Reynolds number with a lower $N$ value. Furthermore, the drag coefficient is proportional to $N^{2/3}$ for weak magnetic fields or to $N^{1/2}$ for strong magnetic fields, where the threshold value between these two regimes is approximately $N=4$.

We present the linear theory of two-dimensional incompressible magneto-Rayleigh–Taylor instability in a system composed of a linear elastic (Hookean) layer above a lighter semi-infinite ideal fluid with magnetic fields present, above and below the layer. As expected, magnetic field effects and elasticity effects together enhance the stability of thick layers. However, the situation becomes more complicated for relatively thin slabs, and a number of new and unexpected phenomena are observed. In particular, when the magnetic field beneath the layer dominates, its effects compete with effects due to elasticity, and counteract the stabilising effects of the elasticity. As a consequence, the layer can become more unstable than when only one of these stabilising mechanisms is acting. This somewhat unexpected result is explained by the different physical mechanisms for which elasticity and magnetic fields stabilise the system. Implications for experiments on magnetically driven accelerated plates and implosions are discussed. Moreover, the relevance for triggering of crust-quakes in strongly magnetised neutron stars is also pointed out.