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The shear flow instabilities under the presence of magnetic fields in the primordial disk can greatly facilitate the formation of density structures that serve as seeds prior to the onset of the gravitational Jeans instability. We evaluate the effects of the Parker, magnetorotational and kinematic dynamo instabilities by comparing the properties of these instabilities. We calculate the mass spectra of coagulated density structures by the above mechanism in the radial direction for an axisymmetric magnetohydrodynamic (MHD) torus equilibrium and power density profile models. Our local three-dimensional MHD simulation indicates that the coupling of the Parker and magnetorotational instability creates spiral arms and gas blobs in an accretion disk, reinforcing the theory and model. Such a mechanism for the early structure formation may be tested in a laboratory. The recent progress in experiments involving shear flows in rotating tokamak, field reversed configuration (FRC) and laser plasmas may become a key element to advance in nonlinear studies. [ABSTRACT FROM AUTHOR]

The possibility of generating a magnetic field at a large distance (10–15 kpc) from the center of the galaxy has been investigated. The magnetic field can be generated both by the dynamo mechanism, considering nonlinear effects, and by magnetorotational instability. Presumably, the nonlinear effects of the dynamo mechanism play a more significant role at this distance. [ABSTRACT FROM AUTHOR]

The existence of magnetic fields in spiral galaxies is beyond doubt and is confirmed by both observational data and theoretical models. Their generation occurs due to the dynamo mechanism action associated with the properties of turbulence. Most studies consider magnetic fields at moderate distances to the center of the disk, since the dynamo number is small in the marginal regions, and the field growth should be suppressed. At the same time, the computational results demonstrate the possibility of magnetic field penetration into the marginal regions of galaxies. In addition to the action of the dynamo, magnetorotational instability (MRI) can serve as one of the mechanisms of the field occurrence. This research is devoted to the investigation of MRI impact on galactic magnetic field generation and solving the occurring eigenvalue problems. The problems are formulated assuming that the perturbations may possibly increase. In the present work, we consider the eigenvalue problem, picturing the main field characteristics in the case of MRI occurrence, where the eigenvalues are firmly connected with the average vertical scale of the galaxy, to find out whether MRI takes place in the outer regions of the galaxy. The eigenvalue problem cannot be solved exactly; thus, it is solved using the methods of the perturbation theory for self-adjoint operators, where the eigenvalues are found using the series with elements including parameters characterizing the properties of the interstellar medium. We obtain linear and, as this is not enough, quadratic approximations and compare them with the numerical results. It is shown that they give a proper precision. We have compared the approximation results with those from numerical calculations and they were relatively close for the biggest eigenvalue. [ABSTRACT FROM AUTHOR]

A concise review is given of astrophysically motivated experimental and theoretical research on Taylor–Couette flow. The flows of interest rotate differentially with the inner cylinder faster than the outer, but are linearly stable against Rayleigh's inviscid centrifugal instability. At shear Reynolds numbers as large as 106 , hydrodynamic flows of this type (quasi-Keplerian) appear to be nonlinearly stable: no turbulence is seen that cannot be attributed to interaction with the axial boundaries, rather than the radial shear itself. Direct numerical simulations agree, although they cannot yet reach such high Reynolds numbers. This result indicates that accretion-disc turbulence is not purely hydrodynamic in origin, at least insofar as it is driven by radial shear. Theory, however, predicts linear magnetohydrodynamic (MHD) instabilities in astrophysical discs: in particular, the standard magnetorotational instability (SMRI). MHD Taylor–Couette experiments aimed at SMRI are challenged by the low magnetic Prandtl numbers of liquid metals. High fluid Reynolds numbers and careful control of the axial boundaries are required. The quest for laboratory SMRI has been rewarded with the discovery of some interesting inductionless cousins of SMRI, and with the recently reported success in demonstrating SMRI itself using conducting axial boundaries. Some outstanding questions and near-future prospects are discussed, especially in connection with astrophysics. This article is part of the theme issue 'Taylor–Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (part 2)'. [ABSTRACT FROM AUTHOR]

Taylor-Couette flow (TCF) is often used as a simplified model for complex rotating flows in the interior of stars and accretion discs. The flow dynamics in these objects is influenced by magnetic fields. For example, quasi-Keplerian flows in Taylor-Couette geometry become unstable to a travelling or standing wave in an external magnetic field if the fluid is conducting; there is an instability even when the flow is hydrodynamically stable. This magnetorotational instability leads to the development of chaotic states and, eventually, turbulence, when the cylinder rotation is sufficiently fast. The transition to turbulence in this flow can be complex, with the coexistence of parameter regions with spatio-temporal chaos and regions with quasi-periodic behaviour, involving one or two additional modulating frequencies. Although the unstable modes of a periodic flow can be identified with Floquet analysis, here we adopt a more flexible equation-free data-driven approach. We analyse the data from the transition to chaos in the magnetized TCF and identify the flow structures related to the modulating frequencies with dynamic mode decomposition; this method is based on approximating nonlinear dynamics with a linear infinite-dimensional Koopman operator. With the use of these structures, one can construct a nonlinear reduced model for the transition. [ABSTRACT FROM AUTHOR]

Abstract—The use of a special technique for processing variations of the geomagnetic field at several mid-latitude observatories allowed us to identify a series of jerks over a 17-year period, from 2004 to 2020. To interpret the our experimental results showing that jerks follow with a quasi period of 3‒4 years, a probable mechanism of the occurrence of rapid changes in the geomagnetic field caused by unstable processes in the Earth's core is proposed. [ABSTRACT FROM AUTHOR]

The use of a special technique for processing variations of the geomagnetic field at several mid-latitude observatories allowed us to identify a series of jerks over more than a decade, from 2004 to 2020. To interpret the experimental results showing that jerks follow with a quasi-period of 3–4 years, a mechanism for the occurrence of rapid changes in the geomagnetic field caused by unstable processes in the Earth's core is proposed. [ABSTRACT FROM AUTHOR]

Instability modes of viscoelastic Taylor–Couette flow in the Keplerian regime are investigated using both linear stability analysis and experimental detection of critical states. A generalised Rayleigh criterion has been derived and it allows to separate the zone of potential purely elastic instability modes and the zone of stability. The analogy between the instability of viscoelastic Taylor–Couette flow in the Keplerian regime and the magnetorotational instability (MRI) of conducting magnetic fluids is established. Viscoelastic stress tensor can be represented by a tensor product of magnetic-like vectors. This allows to use the Velikhov-Chandrasekhar criterion of the MRI to predict the elasto-rotational instability (ERI). ERI modes obtained in linear stability and in the experiments are assumed to represent the MRI analogue modes as they are observed in the stable zone according to generalised Rayleigh discriminant. [ABSTRACT FROM AUTHOR]

Decades ago S. Lundquist, S. Chandrasekhar, P. H. Roberts and R. J. Tayler first posed questions about the stability of Taylor–Couette flows of conducting material under the influence of large-scale magnetic fields. These and many new questions can now be answered numerically where the nonlinear simulations even provide the instability-induced values of several transport coefficients. The cylindrical containers are axially unbounded and penetrated by magnetic background fields with axial and/or azimuthal components. The influence of the magnetic Prandtl number P m on the onset of the instabilities is shown to be substantial. The potential flow subject to axial fields becomes unstable against axisymmetric perturbations for a certain supercritical value of the averaged Reynolds number R m ¯ = R e ⋅ R m (with R e the Reynolds number of rotation, R m its magnetic Reynolds number). Rotation profiles as flat as the quasi-Keplerian rotation law scale similarly but only for P m ≫ 1 while for P m ≪ 1 the instability instead sets in for supercritical R m at an optimal value of the magnetic field. Among the considered instabilities of azimuthal fields , those of the Chandrasekhar-type, where the background field and the background flow have identical radial profiles, are particularly interesting. They are unstable against nonaxisymmetric perturbations if at least one of the diffusivities is non-zero. For P m ≪ 1 the onset of the instability scales with R e while it scales with R m ¯ for P m ≫ 1 . Even superrotation can be destabilized by azimuthal and current-free magnetic fields; this recently discovered nonaxisymmetric instability is of a double-diffusive character, thus excluding P m = 1 . It scales with R e for P m → 0 and with R m for P m → ∞ . The presented results allow the construction of several new experiments with liquid metals as the conducting fluid. Some of them are described here and their results will be discussed together with relevant diversifications of the magnetic instability theory including nonlinear numerical studies of the kinetic and magnetic energies, the azimuthal spectra and the influence of the Hall effect. [ABSTRACT FROM AUTHOR]

We study local instabilities of a differentially rotating viscous flow of electrically conducting incompressible fluid subject to an external azimuthal magnetic field. In the presence of the magnetic field, the hydrodynamically stable flow can demonstrate non-axisymmetric azimuthal magnetorotational instability (AMRI) both in the diffusionless case and in the double-diffusive case with viscous and ohmic dissipation. Performing stability analysis of amplitude transport equations of short-wavelength approximation, we find that the threshold of the diffusionless AMRI via the Hamilton-Hopf bifurcation is a singular limit of the thresholds of the viscous and resistive AMRI corresponding to the dissipative Hopf bifurcation and manifests itself as the Whitney umbrella singular point. A smooth transition between the two types of instabilities is possible only if the magnetic Prandtl number is equal to unity, Pm = 1. At a fixed Pm ≠ = 1, the threshold of the double-diffusive AMRI is displaced by finite distance in the parameter space with respect to the diffusionless case even in the zero dissipation limit. The complete neutral stability surface contains three Whitney umbrella singular points and two mutually orthogonal intervals of self-intersection. At these singularities, the double-diffusive system reduces to a marginally stable system which is either Hamiltonian or parity-time-symmetric. [ABSTRACT FROM AUTHOR]

The last decades have seen a number of liquid metal experiments on the interaction of magnetic fields with the flow of electrically conducting fluids. The opaqueness of liquid metals requires non-optical methods for inferring the velocity structure of the flow. Quite often, such experiments are carried out in the presence of high electrical currents to generate the necessary magnetic fields. Depending on the specific purpose, these currents can reach several kiloamperes. The utilized switching mode power supply can then influence seriously the measurement system by electromagnetic interference. A recent experiment on the azimuthal magnetorotational instability (AMRI) has shown that a hydrodynamically stable Taylor–Couette flow becomes unstable under the influence of a high azimuthal magnetic field. An electrical current along the axis of the experiment with up to 20 kA generates the necessary field to destabilize the flow. We present experimental results of this AMRI experiment carried out at the PROMISE facility with an enhanced power supply. For this setup, we discuss the elaborate measures that were needed to obtain a reasonable signal-to-noise ratio of the ultrasonic Doppler velocimetry (UDV) system. In dependence on various parameter variations, some typical features of the observed instability, such as the energy content, the wavelength, and the frequency are analyzed and compared with theoretical predictions. [ABSTRACT FROM AUTHOR]

This paper demonstrates an equivalence between rotating magnetized shear flows and a stressed elastic beam. This results from finding the same form of dynamical equations after an asymptotic reduction of the axis-symmetric magnetorotational instability (MRI) under the assumption of almostcritical driving. The analysis considers the MRI dynamics in a non-dissipative near-equilibrium regime. Both the magnetic and elastic systems reduce to a simple one-dimensional wave equation with a non-local nonlinear feedback. Under transformation, the equation comprises a large number of mean-field interacting Duffing oscillators. This system was the first proven example of a strange attractor in a partial differential equation. Finding the same reduced equation in two natural applications suggests the model might result from other applications and could fall into a universal class based on symmetry. [ABSTRACT FROM AUTHOR]

Abstract: Static instability or divergence threshold of both potential and circulatory systems with kinematic constraints depends singularly on the constraintsʼ coefficients. Particularly, the critical buckling load of the kinematically constrained Zieglerʼs pendulum as a function of two coefficients of the constraint is given by the Plücker conoid of degree . This simple mechanical model exhibits a structural instability similar to that responsible for the Velikhov–Chandrasekhar paradox in the theory of magnetorotational instability. [Copyright &y& Elsevier]

The magnetorotational instability (MRI) triggers turbulence and enables outward transport of angular momentum in hydrodynamically stable rotating shear flows, e.g., in accretion disks. What laws of differential rotation are susceptible to the destabilization by axial, azimuthal, or helical magnetic field? The answer to this question, which is vital for astrophysical and experimental applications, inevitably leads to the study of spectral and geometrical singularities on the instability threshold. The singularities provide a connection between seemingly discontinuous stability criteria and thus explain several paradoxes in the theory of MRI that were poorly understood since the 1950s. [ABSTRACT FROM AUTHOR]

Cosmic magnetic fields, including the fields of planets, stars, and galaxies, are produced by the hydromagnetic dynamo effect in moving electrically conducting fluids. They also play an active role in cosmic structure formation by enabling outward transport of angular momentum in accretion disks via the magnetorotational instability. The last 10 years have seen tremendous efforts in studying both effects in liquid metal experiments. This paper is focused on the numerical attempts that were undertaken to understand, optimize, and analyze those experiments. [ABSTRACT FROM AUTHOR]

Abstract: The problem of instabilities responsible for magnetic turbulence in collisionless laboratory rotating plasma is investigated. It is shown that the standard mechanism of driving the magnetorotational instability (MRI), due to negative rotation frequency gradient, disappears in such a plasma. Instead of it, a new driving mechanism due to plasma pressure gradient is predicted. [Copyright &y& Elsevier]

We have constructed self-consistent temperature and density profiles of irradiated active protoplanetary disks, using a two-dimensional radiative transfer calculation. By means of these profiles we have studied the stabilization of the convective instability by radiative heating and the magnetorotational instability (MRI) via ohmic dissipation, taking into account the effect of dust particle growth. Simple chemistry such as ionization by cosmic rays and recombination on dust grains are used to calculate the ionization degree of gas in the disks. Our results show that the dust growth stabilizes the convective instability due to the 2D effect of radiative transfer, while it enhances the MRI through the decrease in the recombination of ions on the dust grains. In addition, the influences of the dust settling toward the midplane of the disks on the instabilities are discussed. [ABSTRACT FROM AUTHOR]

Abstract: Instabilities responsible for magnetic turbulence in laboratory rotating plasma are investigated. It is shown that the plasma compressibility gives a new driving mechanism in addition to the known Velikhov effect due to the negative rotation frequency gradient. This new mechanism is related to the perpendicular plasma pressure gradient, while the density gradient gives an additional drive depending also on the pressure gradient. It is shown that these new effects can manifest themselves even in the absence of the equilibrium magnetic field, which corresponds to nonmagnetic instabilities. [Copyright &y& Elsevier]

Abstract: It is shown that the magnetorotational instability (MRI) can be driven in nonmagnetized plasma. In this case, in contrast to the case of strongly magnetized plasma, radial derivative of plasma rotation frequency should be positive for such a driving. The characteristic wave lengths of MRI in nonmagnetized plasma are of the same order of magnitude as those for the Weibel instability. [Copyright &y& Elsevier]

In this paper, regarding the recent detection of significant azimuthal magnetic field in some accretion disks such as protostellar (Donati et al. in Nature 438:466, 2005), the multi-fluid model has been employed to analysis the stability of Keplerian rotational viscous dusty plasma system in a current-free helical magnetic field structure. Using the fluid-Maxwell equations, the general dispersion relation of the excited modes in the system has been obtained by applying the local approximation method in the linear perturbation theory. The typical numerical analysis of the obtained dispersion relation in the high-frequency regime shows that the presence of azimuthal magnetic field component in Keplerian flow has a considerable role in the stability conditions of the system. It also shows that the magnetic field helicity has a stabilization role against the magnetorotational instability (MRI) in the system due to contraction of the unstable wavelength region and decreasing the maximum growth rate of the instability. In this sense, the stabilization role of the viscosity term is more considerable for HMRI (instability in the presence of azimuthal magnetic field component) than the corresponding MRI (instability in the absence of azimuthal magnetic field component). Moreover, considering the discovered azimuthal magnetic field in these systems, the MRI can be arisen in the over-all range of dust grains construction values in contract with traditional MRI. This investigation can greatly contribute to better understanding the physics of some astrophysical phenomena, such as the main source of turbulence and angular momentum transport in protostellar and the other sufficiently ionized astrophysical disks, where the azimuthal magnetic field component in these systems can play a significant role. [ABSTRACT FROM AUTHOR]