Hydromagnetic Dynamo Research Articles

Численное исследование эволюции режимов гидромагнитного динамо во вращающемся сферическом слое при различных начальных условиях

проведено численное исследование влияния начальных условий на характеристики и структуру решений задачи гидромагнитного динамо во вращающемся сферическом слое. Вычислительные эксперименты проводились с помощью разработанного авторами МГД-кода, адаптированного для работы на гибридных вычислительных системах с графическими процессорами. Получены квазистационарные решения с устойчивым уровнем энергии генерируемого магнитного поля. Исследована эволюция решений в зависимости от числа Релея. we simulated the effects of initial conditions on the properties and structure of the hydromagnetic dynamo a rotating spherical layer. We developed an MHD code for the computational experiments adapted for hybrid computing systems with GPUs. We obtained quasi-stationary solutions with the stable energy of the generated magnetic field. The impact of the Rayleigh number on the solutions is also studied.

Arbitrarily high-order accurate simulations of compressible rotationally constrained convection using a transfinite mapping on cubed-sphere grids

We present two major improvements over the Compressible High-ORder Unstructured Spectral difference (CHORUS) code published in Wang et al., “A compressible high-order unstructured spectral difference code for stratified convection in rotating spherical shells,” J. Comput. Phys. 290, 90–111 (2015). The new code is named CHORUS++ in this paper. Subsequently, we perform a series of efficient simulations for rotationally constrained convection (RCC) in spherical shells. The first improvement lies in the integration of the high-order spectral difference method with a boundary-conforming transfinite mapping on cubed-sphere grids, thus ensuring exact geometric representations of spherical surfaces on arbitrary sparse grids. The second improvement is on the adoption of higher-order elements (sixth-order) in CHORUS++ vs third-order elements for the original CHORUS code. CHORUS++ enables high-fidelity RCC simulations using sixth-order elements on very coarse grids. To test the accuracy and efficiency of using elements of different orders, CHORUS++ is applied to a laminar solar benchmark, which is characterized by columnar banana-shaped convective cells. By fixing the total number of solution degrees of freedom, the computational cost per time step remains unchanged. Nevertheless, using higher-order elements in CHORUS++ resolves components of the radial energy flux much better than using third-order elements. To obtain converged predictions, using sixth-order elements is 8.7 times faster than using third-order elements. This significant speedup allows global-scale fully compressible RCC simulations to reach equilibration of the energy fluxes on a small cluster of just 40 cores. In contrast, CHORUS simulations were performed by Wang et al. on supercomputers using approximately 10 000 cores. Using sixth-order elements in CHORUS++, we further carry out global-scale solar convection simulations with decreased rotational velocities. Interconnected networks of downflow lanes emerge and surround broader and weaker regions of upflow fields. A strong inward kinetic energy flux compensated by an enhanced outward enthalpy flux appears. These observations are all consistent with those published in the literature. Furthermore, CHORUS++ can be extended to magnetohydrodynamic simulations with potential applications to the hydromagnetic dynamo processes in the interiors of stars and planets.

Cross-helicity effect onα-type dynamo in non-equilibrium turbulence

Turbulence is typically not in equilibrium, i.e. mean quantities such as the mean energy and helicity are typically time-dependent. The effect of non-stationarity on the turbulent hydromagnetic dynamo process is studied here with the use of the two-scale direct-interaction approximation, which allows one to explicitly relate the mean turbulent Reynolds and Maxwell stresses and the mean electromotive force to the spectral characteristics of turbulence, such as the mean energy, as well as kinetic and cross-helicity. It is demonstrated that the non-equilibrium effects can enhance the dynamo process when the magnetohydrodynamic turbulence is both helical and cross-helical. This effect is based on the turbulent infinitesimal-impulse cross-response functions, which do not affect turbulent flows in equilibrium. The evolution and sources of the cross-helicity in magnetohydrodynamic turbulence are also discussed.

Исключение интегрального члена в уравнениях одной эредитарной системы, связанной с задачей гидромагнитного динамо

В работе изучается двумерная система интегро-дифференциальных уравнений, которая является простейшей эредитарной моделью двумодового гидромагнитного динамо. Учет пространственной и временной нелокальности взаимодействий в динамо-системах сейчас активно исследуется. В маломодовых приближениях уравнений динамо можно рассматривать только временную нелокальность, т.е. эредитарность (память). Память в исследуемой системе реализована в виде обратной связи, распределенной по всем прошлым состояниям системы. Обратная связь представлена с помощью интегрального члена типа свертки от квадратичной комбинации фазовых переменных с ядром достаточно общего вида. Этот член моделирует подавление турбулентного генератора поля (α-эффекта) квадратичной формой от фазовых переменных. В реальных динамо-системах такое подавление обеспечивается силой Лоренца. Основной результат работы – доказательство возможности исключения интегрального члена для одного класса ядер. Такие ядра являются решениями однородного линейного дифференциального уравнения с постоянными коэффициентами. Доказано, что исследуемую интегро-дифференциальную систему можно заменить дифференциальной системой большей размерности с подходящими начальными условиями на дополнительные фазовые переменные. Если ядро является решением уравнения n-го порядка, то размерность системы может достигать 3n−2 и зависит от начальных условий, которым удовлетворяет ядро. В работе используются классические методы теории дифференциальных уравнений. Приводятся примеры динамических систем, возникающих при некоторых ядрах в результате исключения интегрального члена. Результаты работы можно использовать для верификации вычислительных алгоритмов и программных кодов, разработанных для решения интегро-дифференциальных уравнений.We study a two-dimensional system of integro-differential equations, which is the simplest hereditary model of a two-mode hydromagnetic dynamo. Accounting for the spatial and temporal nonlocality of interactions in dynamo systems is currently being actively studied. In the low-mode approximations of the dynamo equations, one can consider only temporal nonlocality, i.e. heredity (memory). Memory in the system under study is implemented in the form of feedback distributed over all past states of the system. The feedback is represented by a convolution-type integral term of a quadratic combination of phase variables with a fairly general kernel. This term models the quenching of the turbulent field generator (α-effect) by a quadratic form in phase variables. In real dynamo systems, such quenchingn is provided by the Lorentz force. The main result of the work is a proof of the possibility of eliminating the integral term for one class of kernels. Such kernels are solutions of a homogeneous linear differential equation with constant coefficients. It is proved that the studed integro-differential system can be replaced by a higher-dimensional differential system with suitable initial conditions for additional phase variables. If the kernel is a solution to an n-order equation, then the dimension of the system can reach 3n−2 and depends on the initial conditions that the kernel satisfies. The work uses classical methods of the theory of differential equations. Examples are given of dynamical systems that arise for some kernels as a result of the elimination of the integral term. The results of the work can be used to verify computational algorithms and program codes developed for solving integro-differential equations.

Двухмодовая модель гидромагнитного динамо с памятью

Двухмодовая модель гидромагнитного динамо с памятью

Dynamo effect caused by non-stationary turbulence in strongly magnetized, hot, low-density plasma

Context.The large-scale hydromagnetic dynamo mechanism is often assumed to rely on the existence of a resistive phase shift between the kinetic and magnetic components of waves. It is not clear how this mechanism could effectively operate in hot, low-density plasma, where the electrical resistivity is extremely low.Aims.We show that non-stationarity, a common factor in plasma turbulence (e.g., in the interstellar medium caused by random supernova explosions), allows inducing a strong large-scale electromotive force (EMF) by the plasma flow and significantly enhances the dynamo effect.Methods.We adopted the simplest approximation in which plasma evolution is modelled with a set of incompressible magnetohydrodynamic equations with a random, Gaussian, and non-stationary forcing to explicitly demonstrate the role of non-stationarity in the large-scale dynamo process. The EMF was calculated analytically in the limit of large magnetic Prandtl numbers (low magnetic diffusion in comparison with plasma viscosity) and strong magnetic fields for the non-stationary turbulence and the standard diffusive mechanism.Results.We show that the EMF induced by the effects of non-stationarity can typically be expected to dominate the dynamo mechanism (over the diffusive phase shift generation) by several orders of magnitude. This is confirmed by the explicit calculation in two example cases for the interstellar medium in the Milky Way galaxy and hot accretion disks such as those of active galactic nuclei.

Nonlinear turbulent dynamo induced by fluctuations of the Lorentz force.

The turbulent hydromagnetic dynamo is a process of magnetic field amplification by a chaotic flow of an electrically conducting fluid, responsible for generation of the magnetic fields of planets and stars. Here we demonstrate a curious effect of the Lorentz force, which can act to intensify the magnetic fields, counterintuitively in light of the Lenz law according to which the Lorentz force acts to retard motions and saturate the dynamo-induced magnetic field. However, the net effect of its small-scale fluctuations in a turbulent flow is far from obvious and it is shown that it can lead to amplification rather than saturation of the magnetic energy through creation of negative turbulent diffusivity.

Possible Role of Non-Stationarity of Magnetohydrodynamic Turbulence in Understanding of Geomagnetic Excursions

The natural simplifying assumptions often put forward in the theoretical investigations of the magnetohydrodynamic turbulence are that the turbulent flow is statistically isotropic, homogeneous and stationary. Of course, the natural turbulence in the planetary interiors, such as the liquid core of the Earth is neither, which has important consequences for the dynamics of the planetary magnetic fields generated via the hydromagnetic dynamo mechanism operating in the interiors of the planets. Here we concentrate on the relaxation of the assumption of statistical stationarity of the turbulent flow and study the effect of turbulent wave fields in the Earth’s core, which induces non-stationarity, on the turbulent resistivity in the non-reflectionally symmetric flow and the geodynamo effect. It is shown that the electromotive force, including the so-called α-effect and the turbulent magnetic diffusivity η¯, induced by non-stationary turbulence, evolves slowly in time. However, the turbulent α¯ coefficient, responsible for the dynamo action and η¯ evolve differently in time, thus creating periods of enhanced and suppressed turbulent diffusion and dynamo action somewhat independently. In particular, periods of enhanced α¯ may coincide with periods of suppressed diffusion, leading to a stable and strong field period. On the other hand, it is shown that when enhanced diffusion occurs simultaneously with suppression of the α-effect, this leads to a sharp drop in the intensity of the large-scale field, corresponding to a geomagnetic excursion.

An internal heating mechanism operating in ultra-short-period planets orbiting magnetically active stars

Context. Rocky planets with orbital periods shorter than ~1 day have been discovered by the method of transits and their study can provide information on Earth-like planets not available from bodies on longer period orbits. Aims. A new mechanism for the internal heating of such ultra-short-period planets is proposed based on the gravitational perturbation produced by a non-axisymmetric quadrupole moment of their host stars. Such a quadrupole is due to the magnetic flux tubes in the stellar convection zone, unevenly distributed in longitude and persisting for many stellar rotations as observed in young late-type stars. Methods. The rotation period of the host star evolves from its shortest value on the zero-age main sequence (ZAMS) to longer periods due to the loss of angular momentum through a magnetized wind. If the stellar rotation period comes close to twice the orbital period of the planet, the quadrupole leads to a spin-orbit resonance that excites oscillations of the star-planet separation. As a consequence, a strong tidal dissipation is produced inside the planet that converts the energy of the oscillations into internal heat. The total heat released inside the planet scales as a−8, where a is the orbit semimajor axis, and it is largely independent of the details of the planetary internal dissipation or the lifetime of the stellar magnetic flux tubes. Results. We illustrate the operation of the mechanism by modeling the evolution of the stellar rotation and of the innermost planetary orbit under the action of the stellar wind and the tides in the cases of CoRoT-7, Kepler-78, and K2-141 whose present orbital periods range between 0.28 and 0.85 days. If the spin-orbit resonance occurs, the maximum power dissipated inside the planets ranges between 1018 and 1019 W, while the total dissipated energy is on the order of 1030−1032 J over a time interval as short as (1−4.5) × 104 yr. Conclusions. Our illustrative models suggest that, if their host stars started their evolution on the ZAMS as fast rotators with periods between 0.5 and 1.0 days, the resonance occurred after about 40 Myr since the host stars settled on the ZAMS in all the three cases. This huge heating over such a short time interval produces a complete melting of the planetary interiors and may shut off their hydromagnetic dynamos. These may initiate a successive phase of intense internal heating owing to unipolar magnetic star-planet interactions and affect the composition and the escape of their atmospheres, producing effects that could be observable during the entire lifetime of the planets.

Renormalization group analysis of the turbulent hydromagnetic dynamo: Effect of anisotropy

The turbulent hydromagnetic dynamo is a process of magnetic field generation by chaotic flow of an electrically conducting fluid (plasma, liquid iron etc.). It is responsible for generation of large-scale magnetic fields of astrophysical objects such as planets, stars, accretion discs, galaxies, galaxy clusters etc. In particular, the dynamical process of induction of large-scale fields is strongly nonlinear and the effect of the Lorentz force is crucial. The aim of the analysis presented here is to provide analytic expressions for the large-scale electromotive force (EMF) in the limit of rapid rotation, with inclusion of both types of nonlinearities - the effect of the Lorentz force (hitherto scarcely considered) and the nonlinear evolution of turbulent fluctuations. The renormalization group technique is applied to extract the final expression for the mean EMF from the full nonlinear dynamical equations (Navier-Stokes, induction equation) and the mean-field equations are studied in order to demonstrate amplification and saturation of the mean magnetic field in two simplifying limits, that is the limit of a thin disc and a limit of a narrow spherical gap.

Renormalization Group Analysis of the Turbulent Hydromagnetic Dynamo: The Effect of Nonstationarity

Abstract The turbulent hydromagnetic dynamo is a process of magnetic field generation by chaotic flow of an electrically conducting fluid (plasma, liquid iron, etc.). It is responsible for generation of large-scale magnetic fields of astrophysical objects such as planets, stars, accretion disks, galaxies, galaxy clusters, etc. In particular, the dynamical process of induction of large-scale fields by highly conducting plasma has been very difficult to understand, as very low resistivity is not capable of creating a phase shift between magnetic and kinetic components of waves, making their interaction ineffective for generation of a large-scale electromotive force (EMF). The aim of the analysis presented here is to demonstrate that when the typically invoked statistical stationarity of turbulence is relaxed, large-scale magnetic fields can be very effectively generated by low-resistivity plasma. The renormalization group technique is applied to extract the final expression for the mean EMF from the fully nonlinear dynamical equations (Navier–Stokes, induction equation), and the mean field equations are solved for a force-free mode. Nonstationarity is shown to strongly enhance the process of large-scale EMF generation via wave interactions, and the dynamo effect induced by nonstationarity is proved to be effective. The results are also used to demonstrate the influence of magnetic fields and nonstationarity on energy and helicity spectra of turbulent flows.

A Part II of the Reports on the Ongoing HMD Technology Research

The report continues reporting of results of an ongoing research verifying a hypothetic energy generation mechanism for reengineering of Gritskevich’s Hydro Magnetic Dynamo (HMD). The HMD technology is a patented technology for electric power generation. It was invented in Russia and deployed in a semi-industrial scale (1.5 MW power unit) in Armenia in 1992. After its successful exploitation during 5 years no more units were assembled. Nowadays the technology needs verification of its physical mechanisms for its successful reengineering. The aim of the report is to present current results of an ongoing theoretical and experimental research of hypothetic physical mechanisms providing energy generation in the unit. It is written without disclosure of its construction and technical details. Thus the theory of hypothetic energy generation mechanisms is described in a general way. The reported experimental results provide only partial support for the theory. They should be independently reproduced and verified.

Self-excitation in a helical liquid metal flow: the Riga dynamo experiments

The homogeneous dynamo effect is at the root of magnetic field generation in cosmic bodies, including planets, stars and galaxies. While the underlying theory had increasingly flourished since the middle of the 20th century, hydromagnetic dynamos were not realized in the laboratory until 1999. On 11 November 1999, this situation changed with the first observation of a kinematic dynamo in the Riga experiment. Since that time, a series of experimental campaigns has provided a wealth of data on the kinematic and the saturated regime. This paper is intended to give a comprehensive survey about these experiments, to summarize their main results and to compare them with numerical simulations.

РОЛЬ КОНВЕКТИВНОЇ ЗОНИ У ЗБУДЖЕННІ МАГНІТНОЇ АКТИВНОСТІ СОНЦЯ

The sources of energy of solar activity are analyzed. The primary source of solar energy is the core of the Sun, where as a result of the reactions of thermonuclear fusion, energy is released in the form of γ-quanta and neutrino particles that propagate outward. At approaching the surface, the temperature is rapidly decreasing and at the same time the opacity of the substance of the radiation zone steadily increases, resulting in the creation of conditions for the emergence of a convective energy transfer at a distance from surface of about 0.3 radius of the Sun. Above this boundary lies a layer called the convection zone. The existence and localization of the convection zone of the Sun is determined by two reasons: the first – the structural (radiative) temperature gradient increases due to increased opacity when the temperature drops; the second – the adiabatic gradient of the temperature of the floating elements reduces its value in the zones of partial ionization of hydrogen and helium. It is the convection zone that plays the role of the landfill, where the main processes are born, which are responsible for the cyclic manifestations of the Sun’s activity. However, part of the convective flow of energy coming from the interior of the Sun, accumulates and is carried upwards in the “magnetic form”. An important specific property of magnetic energy transfer is manifested in cyclic changes in most of the phenomena generated by magnetic fields, which are called magnetic activity of the Sun. The main mechanism providing the cyclic nature of the fluctuations of magnetic activity is the turbulent dynamo, localized in the convection zone. The most favorable place for the generation of a toroidal magnetic field, on which the intensity of spot formation depends, are the deep layers near the bottom of the convection zone, covering the layer of permeable convection (convective overshoot layer) and the tachocline. Overshoot creates the necessary conditions for the formation of a layer of long retention maintenance of magnetic fields, whereas in the tachocline, due to the sharp decrease in angular velocity in the presence of a weak poloidal field, a powerful toroidal field is effectively generated. Parker buoyancy of this field dominates over the effects of anti-buoyancy. Therefore, eventually, toroidal field rises to the surface and forms magnetic bipolar groups of sunspots. An important factor of physical processes in the deep layers is also the meridional flow directed to the equator, which, within the framework of the hydromagnetic dynamo model, provides the migration of toroidal fields from high latitudes to low ones. The author’s recent studies on the role of the deep layers of the solar convection zone in explaining the observed phenomenon of double peaks of the cycle of sunspots are noted.

Large-Scale HydroMagnetic Dynamo by Lehnert Waves in Nonresistive Plasma

A new mechanism of large-scale magnetic fields generation is studied, which is based on creation of mean electromotive force through interactions between distinct Lehnert (magneto-Coriolis) waves. ...

Inertial effects on thermochemically driven convection and hydromagnetic dynamos in a spherical shell

We investigate the thermochemical convection and hydromagnetic dynamos in a spherical shell using the so-called codensity formulation with different buoyancy sources: the secular cooling from the mantle, the buoyancy sources due to the solidification at the inner core boundary and the combination of the two sources. Numerical simulations of the fully non-linear problem are performed using the PARODY code. In the thermochemical regime, we find that when the Prandtl numbers are lower than Ekman numbers, inertial convection is preferred, while the large-scale columnar convection is preferred otherwise. Unlike the large-scale convection, the inertial convection is found to be almost independent of the nature of driving buoyancy source. Moreover, the codensity field evolves to a new, radially symmetric stationary state. At the Ekman numbers much smaller than the Prandtl numbers, we have obtained the westward equatorial zonal flow in the chemically driven regime, while for the other cases zonal flows are eastward near the equator. In the dynamo regime, inertial convection is preferred when the Prandtl numbers are lower than Ekman numbers and the generated dipolar magnetic fields oscillate from the polar region to the mid-latitudes and back. In this case, the generated magnetic fields are independent of the type of buoyancy source. At the Prandtl numbers greater than Ekman numbers, both dipolar and hemispherical dynamos are found.

Magnetic and velocity fields in a dynamo operating at extremely small Ekman and magnetic Prandtl numbers

AbstractNumerical simulations of the geodynamo are becoming more realistic because of advances in computer technology. Here, the geodynamo model is investigated numerically at the extremely low Ekman and magnetic Prandtl numbers using the PARODY dynamo code. These parameters are more realistic than those used in previous numerical studies of the geodynamo. Our model is based on the Boussinesq approximation and the temperature gradient between upper and lower boundaries is a source of convection. This study attempts to answer the question how realistic the geodynamo models are. Numerical results show that our dynamo belongs to the strong-field dynamos. The generated magnetic field is dipolar and large-scale while convection is small-scale and sheet-like flows (plumes) are preferred to a columnar convection. Scales of magnetic and velocity fields are separated, which enables hydromagnetic dynamos to maintain the magnetic field at the low magnetic Prandtl numbers. The inner core rotation rate is lower than that in previous geodynamo models. On the other hand, dimensional magnitudes of velocity and magnetic fields and those of the magnetic and viscous dissipation are larger than those expected in the Earth’s core due to our parameter range chosen.

Energy geodynamo parameters compatible with analytical, numerical, paleomagnetic models and observations

A hydromagnetic dynamo is only possible at a sufficiently powerful convection. In the Earth’s core, it is probably the nonthermal convection very much in excess of its critical level with the molecular transporr coefficients. However, in the case of medium- or large-scale fields, the critical energy level caused by the turbulent tranport coefficients is likely to be slightly below the actual level. This probably explains both the 22-year success of this type of simplified geodynamo models and the energy scaling laws for hydromagnetic fields, which generalize these models. Also the review of energy-dependent analytical and observational estimates of vortex fields, hydromagnetic scale sizes, and velocities in the core is presented. These typical parameters are partly in a new way linked to the observed and more ancient magnetic variations. New, albeit, simplified and self-evident, substantiation is given to the paleomagnetic hypothesis about the predominance of the axial dipole under a certain time averaging. In (Pozzo et al., 2012) and more recent works, it is shown that the adiabatic heat flow and electrical conductivity in the Earth’s core are severalfold higher than the generally accepted estimates. Here, the dynamo supporting Braginsky’s convection (Braginsky, 1963) (under the crystallization of the heavy fraction of a liquid onto the solid core) started less than 1 Ga ago, whereas the more ancient geodynamo was supported by the compositional convection of another type. The known mechanisms implementing this convection, which differ by the scenarios of magnetic evolution, are reviewed. This may help identify the sought mechanism through the most ancient paleomagnetic estimates of the field’s intensity and through the numerical models. The probable mechanisms of generation and their absence for the primordial and recent magnetic field of the studied terrestrial planets are discussed.

Magnetic field dynamos and magnetically triggered flow instabilities

The project A2 of the LIMTECH Alliance aimed at a better understanding of those magnetohydrodynamic instabilities that are relevant for the generation and the action of cosmic magnetic fields. These comprise the hydromagnetic dynamo effect and various magnetically triggered flow instabilities, such as the magnetorotational instability and the Tayler instability. The project was intended to support the experimental capabilities to become available in the framework of the DREsden Sodium facility for DYNamo and thermohydraulic studies (DRESDYN). An associated starting grant was focused on the dimensioning of a liquid metal experiment on the newly found magnetic destabilization of rotating flows with positive shear. In this survey paper, the main results of these two projects are summarized.

Symbolic Computations in Simulations of Hydromagnetic Dynamo

The compilation of spectral models of geophysical fluid dynamics and hydromagnetic dynamo involves the calculation of a large number of volume integrals from complex combinations of basis fields. In this paper we describe the automation of this computation with the help of systems of symbolic computations.