Higher helicity invariants and solar dynamo

Modern models of nonlinear dynamo saturation in celestial bodies (specifically, on the Sun) are largely based on the consideration of the balance of magnetic helicity. This physical variable has also a topological meaning: it is associated with the linking coefficient of magnetic tubes. In addition to magnetic helicity, magnetohydrodynamics has a number of topological integrals of motion (the so-called higher helicity moments). We have compared these invariants with magnetic helicity properties and concluded that they can hardly serve as nonlinear constraints on dynamo action.     

Effect of compressibility on the generation of hydrodynamic helicity in the Earth’s liquid core

By the example of a standard three-dimensional model of thermal convection in a rotating spherical shell, it is shown how radial density gradient ?_ρ affects the generation of hydrodynamic helicity χ. For example, the generation of χ weakly depends on ?_ρ inside a Taylor cylinder and, outside the cylinder, the compressibility of the liquid amplifies the generation of χ. The consequences for the geodynamo theory are considered.     

Scale-to-scale stabilization of the magnetic field in the dynamo models

The three-dimensional dynamo model in the fast-rotating plane layer heated from below is considered. The transition from the linear generation of the magnetic field to the nonlinear generation is studied. With the use of the wavelet analysis, it is demonstrated how the spatial spectra of the kinetic and magnetic energies, as well as the hydrodynamic, magnetic, cross-, and current helicity, vary in time. The scenarios of the suppression of α-effect (α-quenching) by the magnetic field are suggested.     

Certain spectral properties of cyclonic turbulence in the Earth’s liquid core

Rapid diurnal rotation of planets results in the appearance of cyclonic thermal turbulence in liquid cores, which is the source of generation of the observed magnetic fields. The model that makes it possible to reproduce characteristic features of small-scale geostrophic flows in the physical and wave spaces is considered in the work. The flows of energy and hydrodynamic helicity as a function of the wavenumber have been estimated. Joint existence of direct and inverse cascades has been indicated. The consequences for the Earth’s core and geodynamo problems have been considered.     

Kinematic dynamos associated with large scale fluid motions

Abstract

A standard approach to the kinematic dynamo problem is that pioneered by Bullard and Gellman (1954), which utilizes the toroidal-poloidal separation and spherical harmonic expansion of the magnetic and velocity fields. In these studies, the velocity field is given as a combination of small number of toroidal and poloidal harmonics, with their radial dependences prescribed by some physical considerations. Starting from the original paper of Bullard and Gellman (1954), a number of authors repeated such analyses on different combination of velocity fields, including the most recent and comprehensive effort by Dudley and James (1989). In this paper, we re-examine the previous kinematic dynamo models, using the computer algebra approach initiated by Kono (1990). This method is particularly suited to this kind of research since different velocity fields can be treated by a single program. We used the distribution of magnetic energies in various harmonics to infer the convergence of the results.

The numerical results obtained in this study for the models of Bullard and Gellman (1954), Lilley (1970), Gubbins (1973), Pekeris et al. (1973), Kumar and Roberts (1975), and Dudley and James (1989) are consistent with the previously reported results, in particular, with the extensive calculation of Dudley and James. In addition, we found that the combination of velocities used by Lilley can support the dynamo action if the radial dependence of the velocity is modified.

We also examined the helicity distributions in these dynamo models, to see if there is any correlation between the helicity and the efficiency of dynamo action. A successful dynamo can result both from the cases in which the helicity distributions are symmetric or antisymmetric with respect to the equator. In both cases, it appears that the dynamo action is efficient if the volume integral of helicity over a hemisphere is large.     

A conserved local cross helicity for non-barotropic MHD

Cross helicity is not conserved in non-barotropic magnetohydro-dynamics (MHD) (as opposed to barotropic or incompressible MHD). Here we show that variational analysis suggests a new kind of local cross helicity which is conserved in the non-barotropic case. This local cross helicity can be integrated to a global non-barotropic cross helicity which was suggested in the work of Webb et al. (2014a,b). The non-barotropic cross helicity reduces to the standard cross helicity under barotropic assumptions. The new local cross helicity is conserved even for topologies for which the variational principle does not apply.     

Tracing magnetic helicity from the solar corona to the interplanetary space

On October 14, 1995, a C1.6 long duration event (LDE) started in active region (AR) NOAA 7912 at approximately 5:00 UT and lasted for about 15 h. On October 18, 1995, the Solar Wind Experiment and the Magnetic Field Instrument (MFI) on board the Wind spacecraft registered a magnetic cloud (MC) at 1 AU, which was followed by a strong geomagnetic storm. We identify the solar source of this phenomenon as AR 7912. We use magnetograms obtained by the Imaging Vector Magnetograph at Mees Solar Observatory, as boundary conditions to the linear force-free model of the coronal field, and, we determine the model in which the field lines best fit the loops observed by the Soft X-ray Telescope on board Yohkoh. The computations are done before and after the ejection accompanying the LDE. We deduce the loss of magnetic helicity from AR 7912. We also estimate the magnetic helicity of the MC from in situ observations and force-free models. We find the same sign of magnetic helicity in the MC and in its solar source. Furthermore, the helicity values turn out to be quite similar considering the large errors that could be present. Our results are a first step towards a quantitative confirmation of the link between solar and interplanetary phenomena through the study of magnetic helicity.     

Magnetic Helicity in fast dynamos

The behaviour of magnetic helicity in kinematic dynamos at large magnetic Reynolds number is considered. Hughes, et al . [ Phys. Lett. A 223 , 167-172 (1996)] observe that the relative helicity tends to zero in the limit of large magnetic Reynolds number. This paper gives upper bounds on the helicity, by relating the helicity spectrum to the energy spectrum. These bounds are confirmed by numerical simulation and the distribution of helicity over scales is considered. Although it is found that the total helicity becomes small in the limit of high conductivity, there can remain significant, but cancelling, helicity at large and small scales of the field. This is illustrated by considering the evolution of helicity in the stretch-twist-fold dynamo picture.     

Integrating the LISFLOOD‐FP 2D hydrodynamic model with the CAESAR model: implications for modelling landscape evolution

Landscape evolution models (LEMs) simulate the geomorphic development of river basins over long time periods and large space scales (100s–1000s of years, 100s of km²). Due to these scales they have been developed with simple steady flow models that enable long time steps (e.g. years) to be modelled, but not shorter term hydrodynamic effects (e.g. the passage of a flood wave). Nonsteady flow models that incorporate these hydrodynamic effects typically require far shorter time steps (seconds or less) and use more expensive numerical solutions hindering their inclusion in LEMs. The recently developed LISFLOOD‐FP simplified 2D flow model addresses this issue by solving a reduced form of the shallow water equations using a very simple numerical scheme, thus generating a significant increase in computational efficiency over previous hydrodynamic methods. This leads to potential convergence of computational cost between LEMs and hydrodynamic models, and presents an opportunity to combine such schemes. This paper outlines how two such models (the LEM CAESAR and the hydrodynamic model LISFLOOD‐FP) were merged to create the new CAESAR‐Lisflood model, and through a series of preliminary tests shows that using a hydrodynamic model to route flow in an LEM affords many advantages. The new model is fast, computationally efficient and has a stronger physical basis than a previous version of the CAESAR model. For the first time it allows hydrodynamic effects (tidal flows, lake filling, alluvial fans blocking valley floor) to be represented in an LEM, as well as producing noticeably different results to steady flow models. This suggests that the simplification of using steady flow in existing LEMs may bias their findings significantly. Copyright © 2013 John Wiley & Sons, Ltd.     

Rigorous new limits on magnetic helicity dissipation in the solar corona

Abstract

The Cauchy-Schwarz inequality is employed to find geometry-independent limits on the magnetic helicity dissipation rate in a resistive plasma. These limits only depend upon the total energy of the plasma, the energy dissipation rate, and a mean diffusion coefficient. For plasmas isolated from external energy sources, limits can also be set on the minimum time necessary to dissipate a net amount of helicity ΔH. As evaluated in the context of a solar coronal loop, these limits strongly suggest that helicity decay occurs on a diffusion timescale which is far too great to be relevant to most coronal processes. Furthermore, rapid reconnection is likely to approximately conserve magnetic helicity. The dilliculties involved in determining the free energy residing in a magnetic structure (given the constraint of magnetic helicity conservation) are discussed.     

地球磁尾中不同类型磁结构的磁螺度演化特征

在二维三分量MHD数值模拟的基础上 ,对地球磁尾不同类型磁结构的形成作磁螺度分析 .研究表明 ,对于由晨昏电场产生的磁尾驱动重联过程 ,通过系统边界输运的磁螺度通量是引起系统总磁螺度变化的直接原因 .不同的初始磁螺度密度分布和磁螺度通量输运 ,可以引起中性片区域磁螺度密度分布的不同演化 ,从而导致具有不同拓扑位形磁结构的形成 .     

Writhe in the stretch-twist-fold dynamo

This article looks at the influence of writhe in the stretch-twist-fold dynamo. We consider a thin flux tube distorted by simple stretch, twist, and fold motions and calculate the helicity and energy spectra. The writhe number assists in the calculations, as it tells us how much the internal twist changes as the tube is distorted. In addition it provides a valuable diagnostic for the degree of distortion. Non mirror-symmetric dynamos typically generate magnetic helicity of one sign on large-scales and the opposite sign on small scales. The calculations presented here confirm the hypothesis that the large-scale helicity corresponds to writhe and the small scale corresponds to twist. In addition, the writhe helicity spectrum exhibits an interesting oscillatory behavior. The technique of calculating Fourier spectra for the writhe helicity may be useful in other areas of research, for example, the study of highly coiled molecules.     

Origin and structures of solar eruptions Ⅱ: Magnetic modeling

The topology and dynamics of the three-dimensional magnetic field in the solar atmosphere govern various solar eruptive phenomena and activities, such as flares, coronal mass ejections, and filaments/prominences. We have to observe and model the vector magnetic field to understand the structures and physical mechanisms of these solar activities. Vector magnetic fields on the photosphere are routinely observed via the polarized light, and inferred with the inversion of Stokes profiles. To analyze these vector magnetic fields, we need first to remove the 180° ambiguity of the transverse components and correct the projection effect. Then, the vector magnetic field can be served as the boundary conditions for a force-free field modeling after a proper preprocessing. The photospheric velocity field can also be derived from a time sequence of vector magnetic fields.Three-dimensional magnetic field could be derived and studied with theoretical force-free field models, numerical nonlinear force-free field models, magnetohydrostatic models, and magnetohydrodynamic models. Magnetic energy can be computed with three-dimensional magnetic field models or a time series of vector magnetic field. The magnetic topology is analyzed by pinpointing the positions of magnetic null points, bald patches, and quasi-separatrix layers. As a well conserved physical quantity,magnetic helicity can be computed with various methods, such as the finite volume method, discrete flux tube method, and helicity flux integration method. This quantity serves as a promising parameter characterizing the activity level of solar active regions.     

"THREE DIMENSIONAL MATHEMATICAL MODEL OF SEDIMENT TRANSPORT IN ESTUARINE REGIONS-- A CASE STUDY OF THE HAIHE RIVER MOUTH" Yuchuan Bai,Huanting SHEN and Shixiong HU

The paper presents the 3D finite element simulation of tidal flow and Sediment transport in the estuarine region of the Haihe river. The proposed model adopts sigma-transformation of the hydrodynamic and sediment transport equations. The hydrodynamic and sediment transport models are verified in case of a simple test problem for which analytical solutions are available. Finally the models are applied to muddy Haihe river estuary of North China and it is claimed that hydrodynamic and sediment transport models give a reliable comparison with the observed field data. However, there are certain discrepancies, and some reasonable questions regarding the present state-of-art, in the modeling of three-dimensional multilevel hydrodynamics and sediment transport, which are provided below for answer.     

Factors contributing to the conservation of magnetic helicity

The magnetic helicity is often considered a quasi-invariant in the magnetohydrodynamic evolution of a plasma. While in general this is not the case, this invariance phenomenon occurs in many relevant situations, so that it is interesting to look for physical parameters that may detract from the maximum theoretical decay rate of helicity. The size of the Lorentz force is the main one: based on it, we find that several means of the magnetic energy, the transfer rate between kinetic and magnetic energies, and the variation of the angular momentum tend to slow down the evolution of magnetic helicity.     

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.     

Strömungsdynamische Untersuchungen im Zürich- und im Luganersee Ein Vergleich von Feldmessungen mit Resultaten theoretischer Modelle

Density distribution and temperature and current data which were measured in Lake of Zürich and Lake of Lugano in two summer field programs are scrutinized and interpreted by means of hydrodynamic models. Barotropic surface seiches and baroclinic internal seiches are studied using a one-and two-layer model and measured data permit identification of the respective resonant periods. Wind induced barotropic and baroclinic circulation dynamics is also studied by means of three-dimensional finite difference models of the hydrodynamic viscous equations on the rotating earth. In general the predictions of these models agree favorably with observed data.     

Issues in Eulerian–Lagrangian modeling of sediment transport under saltation regime

The saltation regime is very important for understanding the sediment transport mechanism. However,there is no consensus on a model for the saltation regime. This study answers several questions raised with respect to the Eulerian-Lagrangian modeling of sediment transport. The first question is why the previous saltation models that use different combinations of hydrodynamic forces yielded acceptable results? The second question is which shear lift model(i.e. a shear lift expression and its coefficient) is more appropriate? Another important question is which hydrodynamic forces have greater contributions to the saltation characteristics of a sediment particle? The last question is what are the contributions of the turbulence fluctuations as well as effects of using two-and three-dimensional(2 D and 3 D) models on the simulation results? In order to fairly answer these questions, a systematic study was done by considering different scenarios. The current study is the first attempt to clearly discuss these issues. A comprehensive 3 D saltation model for non-cohesive sediment was developed that includes all the hydrodynamic forces acting on the particle. The random nature of sediment transport was included using turbulent flow and bed-particle collision models. The eddy interaction model was applied to generate a3 D turbulent flow field. Bed-particle collisions were considered using the concept of a contact zone and a corresponding contact point. The validation of the model was done using the available experimental data for a wide range of sediment size(0.03 to 4.8 cm). For the first question, the results indicated that some of the hydrodynamic effects show opposing trends and some have negligible effects. With these opposing effects it is possible to adjust the coefficients of different models to achieve acceptable agreement with the same experimental data while omitting some aspects of the physics of the process. A suitable model for the shear lift force was developed by linking the lift coefficient to the drag coefficient and the contributions of the hydrodynamic forces and turbulence fluctuations as well as the consequences of using of 2 D and 3 D models were studied. The results indicate that the shear lift force and turbulent flow fluctuations are important factors for the saltation of both sand and gravel, and they cannot be ignored.     

水平螺旋度与沙尘暴的动力学关系研究

应用2002～2006年高空流场和地面观测资料,计算近地面至500 hPa水平螺旋度的大小.结果表明：水平螺旋度负值中心值越大,500 hPa到近地面风速越大,西风增强,风速垂直切变越大,辐合上升运动越强,形成沙尘暴的强度就越强.水平螺旋度负值中心常常在河西走廊附近最强,导致其下游东南方发生沙尘暴.水平螺旋度负值中心与其下游沙尘暴发生强度有一致的对应关系：当水平螺旋度负值中心≤-200 m²/s²时,未来24小时内该区下游将有沙尘天气出现,当≤-600 m²/s²时,6小时内该区下游将有能见度小于500 m的强沙尘暴天气出现,当≤-1000 m²/s²时,6小时内该区下游将有能见度小于50 m的特强沙尘暴天气出现.