Helicity Generation Research Articles

ON THE MECHANISM OF THE UPFLOW HELICITY GENERATION DUE TO INHOMOGENEOUS FRICTION ON THE UNDERLYING SURFACE

Inhomogeneous friction on the underlying surface leads to horizontal divergence, vertical motions, and helicity generation. The paper presents an analytical model that allows one to establish some general laws and estimate the amplitudes of the corresponding perturbations depending on the values of the parameters. In particular, the possibility of generating noticeable vertical motions and a contribution to helicity that goes far beyond the boundaries of the boundary layer is shown.

The role of slow magnetostrophic waves in the formation of the axial dipole in planetary dynamos

The preference for the axial dipole in planetary dynamos is investigated through the analysis of wave motions in spherical dynamo models. Our study focuses on the role of slow magnetostrophic waves, which are generated from localized balances between the Lorentz, Coriolis and buoyancy (MAC) forces. Since the slow waves are known to intensify with increasing field strength, simulations in which the field grows from a small seed towards saturation are useful in understanding the role of these waves in dynamo action. Axial group velocity measurements in the energy-containing scales show that fast inertial waves slightly modified by the magnetic field and buoyancy are dominant under weak fields. However, the dominance of the slow waves is evident for strong fields satisfying ∣ωM/ωC∣∼ 0.1, where ωM and ωC are the frequencies of the Alfvén and inertial waves respectively. A MAC wave window of azimuthal wavenumbers is identified in which helicity generation by the slow waves strongly correlates with dipole generation. Analysis of the magnetic induction equation suggests a poloidal–poloidal field conversion in the formation of the dipole. Finally, the attenuation of slow waves may result in polarity reversals in a strongly driven Earth's core.

Contactless generation and trapping of hydrodynamic knots in sessile droplets by acoustic screw dislocations

Helicity is an important quantity in fluid mechanics that indicates the presence of linked or knotted hydrodynamic vortex filaments. Such flow structures are not only promising elementary structures to study mass and momentum transfer in turbulent flows but also potent analogs for other topological problems arising in particle physics, liquid crystals, and plasma physics. However, experimental studies of knots and links are highly challenging due to the limited control over helicity generation and difficult observation of the resulting fast-paced multiscale flow evolution. In this paper, we propose using acoustic streaming to link hydrodynamic filaments in fluids. The method is contactless, almost instantaneous, and relatively insensitive to viscosity. Importantly, it allows starting from quite arbitrary three-dimensional flow structures without relying on external boundary conditions. We demonstrate our approach by using an acoustic screw dislocation to link two hydrodynamic vortex filaments in a sessile droplet. We observe an inversion of the flow chirality (measured by the hydrodynamic helicity) as the topological charge of the screw dislocation is increased. Combined with recent progress in acoustic field synthesis, this work opens a window to study more complex hydrodynamic knots and links topology at a broader range of space and time scales.

Helicity inversion and generation of orthogonal, degenerate index states of generic C points

We discuss a technique to invert the helicity of generic C points and generate its orthogonal state of polarization in a single step through a fork grating (FG). It is experimentally demonstrated that the beam in each of its diffraction orders possesses a degenerate C point index state. The diffraction phenomenon reported is helicity-dependent, in which left and right-handed ellipse field singularities are separated. The orthogonal polarization state of the input singularity is produced in one of the first diffracted orders of the grating. For every singularity that the grating produces, its orthogonal polarization state is also available in one of its diffraction orders. In contrast to a half-wave plate, where helicity inversion is accompanied by index inversion, a FG inverts helicity without inverting the index. Therefore, a FG can be used to perform multi-functions under generic C point illumination.

On magnetic helicity generation and transport in a nonlinear dynamo driven by a helical flow

The relationship between nonlinear large-scale dynamo action and the generation and transport of magnetic helicity is investigated at moderate values of the magnetic Reynolds number ( $Rm$ ). The model consists of a helically forced, sheared flow in a Cartesian domain. The boundary conditions are periodic in the horizontal and impenetrable for the vertical. The magnetic field is required to be vertical at the upper and lower boundaries. There are two consequences of this choice; one is that the magnetic helicity is not gauge invariant, the second is that fluxes of magnetic helicity are allowed in and out of the domain. We select the winding gauge, define all the contributions to the evolution of the helicity in this gauge and measure these contributions for various solutions of the dynamo equations. We vary $Rm$ and the shear strength, and find a rich landscape of dynamo solutions including travelling waves, pulsating waves and non-wave-like solutions. We find that, at the $Rm$ considered, the main contribution to the growth of magnetic helicity comes from processes throughout the volume of the fluid and that boundary terms respond by limiting the growth. We find that, in this magnetic Reynolds number regime, helicity conservation is not a strong constraint on large-scale dynamo action. We speculate on what may happen at higher $Rm$ .

Scale dependence of kinetic helicity and selection of the axial dipole in rapidly rotating dynamos

The dominant polarity of the magnetic field in rapidly rotating spherical dynamos is the axial dipole. Studies of the onset of magnetoconvection in the limit of vanishing Ekman number have proposed that the dipole is favored over other polarities because its equatorial symmetry generates kinetic helicity that would be otherwise absent in nonmagnetic convection. This study explores the effect of the magnetic field in the selection of the axial dipole in rapidly rotating, supercritical dynamos. The strength of convection is such that the axial dipole grows from a starting seed field in the nonlinear dynamo but fails to grow in the kinematic dynamo at the same parameters. The magnetic field is shown to excite convection over a range of length scales larger than the energy injection scale and at the same time extract energy from smaller scales through the Lorentz force in order to feed itself. This leads to substantial helicity generation in a range of length scales and helicity loss in smaller scales, both relative to nonmagnetic convection. The crossover point between the helicity surplus and deficit regions is displaced to smaller length scales as the rotation rate is increased (by decreasing the Ekman number). The helicity deficit occurs in the region of the spectrum where the Lorentz force approximately balances the Coriolis force in the vorticity equation, so that energy may be drawn from these scales via vortex stretching. The timescale for the increase in convection intensity relative to the nonmagnetic state approximately coincides with the timescale for the formation of the axial dipole, which indicates that the Lorentz force has an important role in polarity selection. Crucially, the dipole forms from a chaotic state well before the saturation of the dynamo, implying that planetary dynamos choose their polarity during their nonlinear growth phase. The generation of the toroidal part of the dipole field is primarily through the classical Omega effect, although the pattern of the zonal flow switches from spherical harmonic degree l = 1 to l = 3 in the presence of the magnetic backreaction.

Magnetic helicity generation in the frame of Kazantsev model

Using a magnetic dynamo model, suggested by Kazantsev (J. Exp. Theor. Phys. 1968, vol. 26, p. 1031), we study the small-scale helicity generation in a turbulent electrically conducting fluid. We obtain the asymptotic dependencies of dynamo growth rate and magnetic correlation functions on magnetic Reynolds numbers. Special attention is devoted to the comparison of a longitudinal correlation function and a function of magnetic helicity for various conditions of asymmetric turbulent flows. We compare the analytical solutions on small scales with numerical results, calculated by an iterative algorithm on non-uniform grids. We show that the exponential growth of current helicity is simultaneous with the magnetic energy for Reynolds numbers larger than some critical value and estimate this value for various types of asymmetry.

Helicity of Convective Flows from Localized Heat Source in a Rotating Layer

AbstractExperimental and numerical study of the steady-state cyclonic vortex from isolated heat source in a rotating fluid layer is described. The structure of laboratory cyclonic vortex is similar to the typical structure of tropical cyclones from observational data and numerical modelling including secondary flows in the boundary layer. Differential characteristics of the flow were studied by numerical simulation using CFD software FlowVision. Helicity distribution in rotating fluid layer with localized heat source was analysed. Two mechanisms which play role in helicity generation are found. The first one is the strong correlation of cyclonic vortex and intensive upward motion in the central part of the vessel. The second one is due to large gradients of velocity on the periphery. The integral helicity in the considered case is substantial and its relative level is high.

Облачно-разрешающий численный анализ процесса генерации спиральности в условиях тропического циклогенеза

Облачно-разрешающий численный анализ процесса генерации спиральности в условиях тропического циклогенеза

Evaluation of helicity generation in the tropical storm Gonu

Helicity is a valuable dynamical concept for the study of rotating flows. Consequently helicity flux, indicative of the source or sink of helicity, owns comparable importance. In this study, while reviewing the existing methods, a mathematical relation between helicity and helicity-flux is introduced, discussed and examined. The computed values of helicity and helicity fluxes in an actual case, using the classical and this proposed method are compared. The down-stream helicity flux including sources and sinks of helicity is considered for the tropical storm Gonu that occurred over the coasts of Oman and Iran on June 2–7, 2007. Results show that the buoyancy, through the upper troposphere down to a height within boundary layer, is the main source in producing helicity, and surface friction from earth surface up to a height within boundary layer, is the main dissipating element of helicity. The dominance of buoyancy forcing over the dissipative friction forcing results in generation of vortex or enhancement of it after bouncing the land. Furthermore, the increase (decrease) of helicity results in an increase (decrease) in the height of the level in which maximum helicity flux occurs. It is suggested that the maximum helicity flux occurs at the top of the turbulent boundary layer, so that the height of boundary layer could be obtained.

Vortex structure of swirl flows

The paper presents some results of investigations related to the problem of studying the mechanisms of vorticity generation and the conditions for formation and stability of determinate vortex structures. This problem is one of particular importance in the field of fundamental investigations of complex vortex flows. At the same time the problems of studying the physics and topology of complex vortex and swirl flows are topical for diagnostics of some hazardous geophysical processes such as hurricanes, tornados, tsunami, change in the direction of oceanic currents, etc. It is shown that the main mechanism for appearance of steady-state vortex structures in swirl and curved flows is connected with the process of helicity generation. The equation of helicity generation rate for dynamical liquid system is obtained to determine the critical conditions for flow field alteration. The convenience of theoretical analysis on the base of helicity generation rate equation consists in a possibility to predict the appearance of steady large-scale structures from solution of a single scalar equation written with respect to the scalar value of helicity. Application of developed model of vortex motion in swirl flows is demonstrated for two hydro-mechanical systems: in case of Taylor instability in annular channel, and for flow of coolant in collector of nuclear reactor. The paper describes a new approach for prediction of conditions for appearance of large-scale steady-state vortex structures in complicated vortex and swirl flows.

The fluctuating α-effect and Waldmeier relations in the nonlinear dynamo models

We study the possibility of reproducing the statistical relations of the sunspot activity cycle, such as the so-called Waldmeier relations, the cycle period–amplitude and the cycle rise rate–amplitude relations, by means of the mean-field dynamo models with fluctuating α-effect. The dynamo model takes into account the long-term fluctuations of the α-effect and two types of nonlinear feedback of the mean field on the α-effect, namely, the algebraic quenching and the dynamic quenching due to the magnetic helicity generation. We found that the models are able to reproduce qualitatively and quantitatively the inclination and dispersion across the Waldmeier relations with 20% fluctuations of the α-effect. The models with dynamic quenching are in better agreement with observations than the models with algebraic α-quenching. We compare the statistical distributions of the modelled parameters, such as the amplitude, period, and the rise and decay rates of the sunspot cycles with observations.

Helicity generation and subcritical behaviour in rapidly rotating dynamos

AbstractNumerical dynamo models based on convection-driven flow in a rapidly rotating spherical shell frequently give rise to strong, stable, dipolar magnetic fields. Dipolar dynamos can be subcritical in the sense that strong magnetic fields are sustained at a Rayleigh number lower than that required for a dynamo to grow from a small seed field. In this paper we find subcritical behaviour in dynamos in line with previous studies. We explore the action of Lorentz force in a rotating dynamo which gives rise to a strong preference for dipolar modes over quadrupolar modes, and also makes subcritical behaviour more likely to occur. The coherent structures that arise in rapidly rotating convection are affected by the magnetic field in ways which strongly increase their helicity, particularly if the magnetic field is dipolar. As helicity enhances dynamo action, an existing magnetic field can hold itself up, which leads to subcritical behaviour in the dynamo. We investigate this mechanism by means of the asymptotic small Ekman number theory of rapidly rotating magnetoconvection, and compare our results with fully nonlinear dynamo simulations. There are also other mechanisms which can promote subcritical behaviour. When Reynolds stresses are significant, zonal flows can lower the helicity and disrupt the onset of dynamo action, but an established dipole field can suppress the zonal flow, and hence boost the helicity. Subcriticality means that a slow gradual reduction in Rayleigh number can lead to a catastrophic collapse of the dynamo once a critical Rayleigh number is reached. While there is little evidence that the Earth is currently in a subcritical regime, this may have implications for the long-term evolution of the geodynamo.

Magnetic helicity evolution inside a hexagonal convective cell

AbstractMagnetic helicity has received considerable attention in the area of fluid dynamics. Recently, this quantity is attracting the interest of solar physicists and much research has been carried out related to magnetic helicity generation and transport through different solar layers, starting from the interior and the convection zone, towards the photosphere, the corona and finally into the heliosphere. Taking into account the global importance of supergranular cells in convection theories, we study the motion of magnetic features into such a geometrical element simplified as hexagonal cell and we analyse the results in terms of the accumulated magnetic helicity. We compute the emergence of a bipole inside the hexagonal cell and its motion from the centre of the cell towards its sides and its vertices, where the magnetic elements are considered to be sinking down. Multiple bipoles are also considered and phenomena such as cancellation, coalescence and fragmentation are also investigated. We find that the most important process for the accumulation of magnetic helicity is the shear motion between the polarities. The magnetic helicity accumulation changes its trend when one polarity reaches the side of the hexagon, and later the vertex. It has zero value when there is no shear motion inside the hexagonal cell, and it is constant when there is no shear between the two polarities during their motion along the cell sides.

Helicity generation and α-effect by Tayler instability with z-dependent differential rotation

Aims.We investigate the instability of toroidal magnetic fields resulting from the action of z-dependent differential rotation on a given axial field in a cylindrical enclosure where, in particular, the helicity of the resulting nonaxisymmetric flow is of interest. We probe the idea that helicity is related to the external field and the differential rotation as .

Thermal convection and the dynamo during rapid rotation

A dynamo model for an incompressible liquid in a rectangular rapidly rotating box is considered. The model is based on a pseudospectral method adapted for multiprocessor technology. The effect of rotation in Boussinesq models on some of the basic characteristics of flows is studied: the spatial form of fields, helicity generation, and spectra of fields. A mechanism stabilizing the magnetic field rise associated with the transition of the system to a nonlinear regime is analyzed separately. The results obtained in the paper provide deeper insights into the processes of magnetoconvection in the cores of planets.

Numerical simulation of helical-vortex effects in Rayleigh-Bénard convection

Abstract. A numerical approach is substantiated for searching for the large-scale alpha-like instability in thermoconvective turbulence. The main idea of the search strategy is the application of a forcing function which can have a physical interpretation. The forcing simulates the influence of small-scale helical turbulence generated in a rotating fluid with internal heat sources and is applied to naturally induced fully developed convective flows. The strategy is tested using the Rayleigh-Bénard convection in an extended horizontal layer of incompressible fluid heated from below. The most important finding is an enlargement of the typical horizontal scale of the forming helical convective structures accompanied by a cells merging, an essential increase in the kinetic energy of flows and intensification of heat transfer. The results of modeling allow explaining how the helical feedback can work providing the non-zero mean helicity generation and the mutual intensification of horizontal and vertical circulation, and demonstrate how the energy of the additional helical source can be effectively converted into the energy of intensive large-scale vortex flow.

Magnetic helicity generation from the cosmic axion field

The coupling between a primordial magnetic field and the cosmic axion field generates a helical component of the magnetic field around the time in which the axion starts to oscillate. If the energy density of the seed magnetic field is comparable to the energy density of the universe at that time, then the resulting magnetic helicity is about vertical bar H{sub B} vertical bar {approx_equal}(10{sup -20}G){sup 2} kpc and remains constant after its generation. As a corollary, we find that the standard properties of the oscillating axion remain unchanged even in the presence of very strong magnetic fields.

Helicity Generation and Signature in Solar Atmosphere

AbstractTo fully understand the origin, evolution and topology of solar magnetic fields, one should comprehend their magnetic helicity. Observationally, non-zero helicity reveals itself in the patterns of electric currents inside active regions, superpenumbral sunspot whirls, the shape of coronal loops and the fine structure of chromospheric filaments. Some patterns may bear information about deep sub-photospheric processes (e.g., dynamo, turbulent convection). Others may originate at or near the photosphere. This presentation reviews the observations of magnetic and current helicity on the Sun, discusses the possible mechanisms of helicity generation, and compares them with the observations.

Amplification of Interstellar Magnetic Fields by Supernova‐driven Turbulence

Several lines of evidence suggest that magnetic fields grow rapidly in protogalactic and galactic environments. However, mean field dynamo theory has always suggested that the magnetic fields grow rather slowly, taking of order a Hubble time to reach the observed values. The theoretical difficulties only become worse when the system has a high magnetic Reynolds number, as is the case for galactic and protogalactic environments. The discrepancy can be reconciled if fast processes for amplifying the magnetic field could operate. Following the 2001 work of Balsara and coworkers, we show that an interstellar medium that is dominated by realistic energy input from supernova explosions will naturally become a strongly turbulent medium with large positive and negative values of the kinetic helicity. Even though the medium is driven by compressible motions, the kinetic energy in this high Mach number flow is mainly concentrated in solenoidal rather than compressible motions. These results stem from the interaction of strong shocks with each other and with the interstellar turbulence they self-consistently generate in our model. Moreover, this interaction also generates large kinetic helicities of either sign. The turbulent flow that we model has two other characteristics of a fast dynamo: magnetic energy growth independent of scale and a growth time that is comparable to the eddy turnover time. This linear phase of growth permits the field to grow rapidly until the magnetic energy reaches about 1% of the kinetic energy. At that stage, other astrophysical processes for producing magnetic fields can take over. Energetics, power spectra, statistics, and structures of the turbulent flow are studied here. Shock-turbulence interaction is shown to be a very general mechanism for helicity generation and magnetic field amplification, with applicability to damped Ly? systems, protogalaxies, the Galaxy, starburst galaxies, the intracluster medium, and molecular clouds.