Forward plane-wave electromagnetic model in three dimensions using hybrid finite volume–integral equation scheme

We present a concept of the hybrid finite volume–integral equation technique for solving Maxwell's equation in a quasi-static form. The divergence correction was incorporated to improve the convergence and stability of the governing linear system equations which pose a challenge on the discretization of the curl–curl Helmholtz equation. A staggered finite volume approach is applied for discretizing the system of equations on a structured mesh and solved in a secondary field technique. The bi-conjugate gradient stabilizer was utilized with block incomplete lower-upper factorization preconditioner to solve the system of equation. To obtain the electric and magnetic fields at the receivers, we use the integral Green tensor scheme. We verify the strength of our hybrid technique with benchmark models relative to other numerical algorithms. Importantly, from the tested models, our scheme was in close agreement with the semi-analytical solution. It also revealed that the use of a quasi-analytical boundary condition helps to minimize the runtime for the linear system equation. Furthermore, the integral Green tensor approach to compute at the receivers demonstrates better accuracy compared with the conventional interpolation method. This adopted technique can be applied efficiently to the inversion procedure.     

Sun–Earth geometry,geomagnetic activity,and planetary F2 layer ion density: Part I: Signatures of magnetic reconnection

Our previous quantitative analyses have shown that geomagnetic activity and planetary ion density of the F2 layer of the ionosphere seem to share the same parent cause, the solar wind, whose entry into geospace is controlled by the Sun–Earth geometry. The thrust of this paper is four fold: (a) to establish the reality of this not clearly recognized connection, (b) to demonstrate that geomagnetic activity varies seasonally with three separate and independent components, viz. a semiannual, an annual and a Sun–Earth-distance determined component, all of which can be accurately derived from solar–terrestrial geometry alone, (c) to evaluate the contribution of each of these components which, taken together, appear to represent the steady-state signatures of the mechanism of magnetopause reconnection, and (d) to highlight the fact that the currently used planetary geomagnetic indices are deficient and therefore need to be revised. Since detailed understanding of the precise mechanism of the entry of solar wind energy into geospace is still lacking, no mechanism is suggested to show how solar wind energy is transported to the F2 layer (including low and equatorial latitudes). Magnetospheric electric fields, precipitation of energetic neutrals produced through charge exchange reactions with ions in the ring current and radiation belt particles, Joule heating, etc., may all be involved, but the energy for all such processes still comes from the solar wind. Apart from the three components of the reconnection mechanism mentioned above, a steady component due to the viscous interaction mechanism should also be present.     

A forward particle tracking Eulerian–Lagrangian Localized Adjoint Method for solution of the contaminant transport equation in three dimensions

The contaminant transport equation is solved in three dimensions using the Eulerian–Lagrangian Localized Adjoint Method (ELLAM). Trilinear and finite volume test functions defined by the characteristics of the governing equation are employed and compared. Integrations are simplified by forward tracking of integration points along the characteristics. The resulting equations are solved using a preconditioned conjugate gradient method. The algorithm is coupled to a block-centered finite difference approximation of the groundwater flow equation similar to that used in the popular MODFLOW code. The ELLAM is tested by comparison with 1D and 3D analytic solutions. The method is then applied with random, spatially correlated hydraulic conductivities in a simulation of a tracer experiment performed on Cape Cod, Massachusetts. The linear test function ELLAM was found to perform better than the finite volume ELLAM. Both ELLAM formulations were found to be robust, computationally efficient and relatively straightforward to implement. When compared to traditional particle tracking and characteristics codes commonly used with MODFLOW, the ELLAM retains the computational advantages of traditional characteristic methods with the added advantage of good mass conservation.     

Advected fields in maps: II. Dynamo action in the stretch–fold–shear map

The growth of magnetic field is considered in the stretch–fold–shear map in the limit of weak diffusion. Numerical results are given for insulating, perfectly conducting and periodic boundary conditions. The resulting eigenvalue branches and magnetic fields are related to eigenvalue branches for perfect dynamo action, obtained for zero diffusion using a complex variable formulation.

The effect of diffusion on these perfect dynamo modes depends on their structure, growth rate and the diffusive boundary conditions employed. In some cases, the effect of diffusion is a small perturbation, giving a correction going to zero in the limit of weak diffusion, with a scaling exponent given analytically. In other cases weak diffusion can entirely destroy a perfect dynamo branch. Diffusive boundary layers can also generate entirely new branches.

These different cases are elucidated, and within the framework of the asymptotic approximations used (which do not constitute a rigorous proof), it is seen that for all three boundary conditions employed, the stretch–fold–shear map is a fast dynamo.     

Analysis on small-earthquake composite fault plane solutions from 1961 to 1999 in Xinfengjiang reservoir area

Introduction XFJ reservoir has been about 40 years since its water loading in 1959 and has induced a great number of earthquakes. The largest one was the M = 6.1 earthquake occurred on March 19, 1962. Since then, a large amount of seismologists in our country have made many researches on the in-duced earthquake. In the paper, we have studied XFJ reservoir earthquakes and their relation with water cyclic fluctuation by using the mechanism solutions of small earthquakes occurred in these 40 y…     

Dynamic analysis of offshore wind turbine in clay considering soil–monopile–tower interaction

A comprehensive study is performed on the dynamic behavior of offshore wind turbine (OWT) structure supported on monopile foundation in clay. The system is modeled using a beam on nonlinear Winkler foundation model. Soil resistance is modeled using American Petroleum Institute based cyclic p–y and t–z curves. Dynamic analysis is carried out in time domain using finite element method considering wind and wave loads. Several parameters, such as soil–monopile–tower interaction, rotor and wave frequencies, wind and wave loading parameters, and length, diameter and thickness of monopile affecting the dynamic characteristics of OWT system and the responses are investigated. The study shows soil–monopile–tower interaction increases response of tower and monopile. Soil nonlinearity increases the system response at higher wind speed. Rotor frequency is found to have dominant role than blade passing frequency and wave frequency. Magnitude of wave load is important for design rather than resonance from wave frequency.     

Geoeffectiveness of solar flares in magnetic crochet (sfe) production: II—Dependence on the detection method

During magnetic active periods, disturbances in the geomagnetic field can act as natural noise masking other magnetic variations of small amplitude. In this paper, the influence of these perturbations on the observation of the effects on Earth of solar flares (sfe) has been studied. The diurnal and monthly values of detected sfe have been obtained, as well as the temporal variation of the relative occurrence of events. These numbers show how the irregular distribution of the magnetic observatories is an important limitation in the efficiency of the detection method. Some considerations about the actual method used at the International Service on Rapid Magnetic Variations are finally presented.     

Epistemological dimensions of the water–energy–food nexus approach: reply to discussions of “Challenges in operationalizing the water–energy–food nexus”*

ABSTRACT

We thank the authors, Varis and Keskinen, and Nauditt, for their constructive contributions. We endorse their key comments, further referring to recent literature and events, including the UN 2018 High Level Political Forum on sustainable development. Here, we elaborate on the epistemological perspective of the water–energy–food nexus conceptualization, assessment, discourse and operationalization.     

Variations in the large-scale polar solar magnetic flux: The average annual series of the Π index in 1858–2006

A long series of the known Π index of the solar corona structure has been proposed. It seems that this index, which characterizes the limb extension of polar coronal plume systems, is of importance because it is related to the large-scale polar solar magnetic flux. Solar corona photographs and drawings during total solar eclipses, collected for 13 solar activity cycles from different sources (78 eclipses), as well as H-alpha map data on the drift of the high-latitude belt of filaments before polarity reversal of the polar magnetic field have been used. Daily solar corona images, obtained on the SOHO spacecraft (using an EIT ultraviolet telescope), have been additionally used.     

Depth–energy and depth–force relationships in open channel flows. II: Analytical findings for power-law cross-sections

In a recent work [Valiani A, Caleffi V. Depth–energy and depth–force relationships in open channel flows: analytical findings. Adv Water Resour 2008;31(3):447–54], the authors analytically inverted the depth–specific energy and depth–total force relationships for flows in open channels with wide rectangular cross-sections.     

Helicity–vorticity turbulent pumping of magnetic fields in the solar convection zone

We study the effect of turbulent drift of a large-scale magnetic field that results from the interaction of helical convective motions and differential rotation in the solar convection zone. The principal direction of the drift corresponds to the direction of the large-scale vorticity vector. Thus, the effect produces a latitudinal transport of the large-scale magnetic field in the convective zone wherever the angular velocity has a strong radial gradient. The direction of the drift depends on the sign of helicity and it is defined by the Parker–Yoshimura rule. The analytic calculations are done within the framework of mean-field magnetohydrodynamics using the minimal τ-approximation. We estimate the magnitude of the drift velocity and find that it can be a few m/s near the base of the solar convection zone. The implications of this effect for the solar dynamo are illustrated on the basis of an axisymmetric mean-field dynamo model with a subsurface shear layer. The model shows that near the bottom of the convection zone the helicity–vorticity pumping results mostly from the kinetic helicity contributions. We find that the magnetic helicity contributions to the pumping effect are dominant at the subsurface shear layer. There the magnitude of the drift velocity is found to be a few cm/s. We find that the helicity–vorticity pumping effect can have an influence on the features of the sunspot time–latitude diagram, producing a fast drift of the sunspot activity maximum at the rise phase of the cycle and a slow drift at the decay phase of the cycle.     

Internal flow structures in columnar jointed basalt from Hrepphólar, Iceland: II. Magnetic anisotropy and rock magnetic properties

The anisotropy of magnetic susceptibility (AMS) and rock magnetic properties were measured on specimens from a basalt plate that was cut from a vertical section of a basalt column from Hrepphólar, Iceland. Macroscopic structures are clearly distinguishable in the plate, including banding inferred to represent viscous fingering parallel to the vertical axis of the column. Rock magnetic experiments indicate that the dominant ferromagnetic (sensu lato) mineral is titanomagnetite, Fe _3?x Ti _x O₄, with a Ti-composition of x?=?~0.6. Magnetic properties are related to the position within the plate and reveal a dominant volume fraction of single domain titanomagnetite in the center of the basalt column, with multidomain titanomagnetite away from the center. The AMS determined by low-field measurements shows an inconclusive relationship with the visual structures, which arises from variation of the grain size (i.e., single domain versus multidomain) across the column. In contrast, the AMS measured with a high-field torsion magnetometer avoids the complication of magnetic domain state, as is demonstrated in this contribution, and additionally allows for the separation of ferrimagnetic from paramagnetic sub-fabrics. Both sub-fabrics display a clear relationship with the macroscopic structures and support the hypothesis that vertical flow of melt took place during development of the Hrepphólar columnar basalt. Maximum susceptibility axes of the ferrimagnetic sub-fabric are grouped near the vertical axis of the column. The paramagnetic sub-fabric varies systematically across the column in coincidence with internal structure. The shape of the magnetic susceptibility ellipsoid varies across the basalt column, showing an increasingly prolate fabric toward its center.     

Distribution of magnetic energy in αΩ-dynamos,I: The method

Abstract

In this paper a method for solving the equation for the mean magnetic energy <BB> of a solar type dynamo with an axisymmetric convection zone geometry is developed and the main features of the method are described. This method is referred to as the finite magnetic energy method since it is based on the idea that the real magnetic field B of the dynamo remains finite only if <BB> remains finite. Ensemble averaging is used, which implies that fields of all spatial scales are included, small-scale as well as large-scale fields. The method yields an energy balance for the mean energy density ε ≡ B ²/8π of the dynamo, from which the relative energy production rates by the different dynamo processes can be inferred. An estimate for the r.m.s. field strength at the surface and at the base of the convection zone can be found by comparing the magnetic energy density and the outgoing flux at the surface with the observed values. We neglect resistive effects and present arguments indicating that this is a fair assumption for the solar convection zone. The model considerations and examples presented indicate that (1) the energy loss at the solar surface is almost instantaneous; (2) the convection in the convection zone takes place in the form of giant cells; (3) the r.m.s. field strength at the base of the solar convection zone is no more than a few hundred gauss; (4) the turbulent diffusion coefficient within the bulk of the convection zone is about 10¹⁴cm²s^?1, which is an order of magnitude larger than usually adopted in solar mean field models.     

Dynamics of solar protons in the Earth’s magnetosphere during magnetic storms in November 2004–January 2005

The processes of penetration, trapping, and acceleration of solar protons in the Earth’s magneto-sphere during magnetic storms in November 2004 and January 2005 are studied based on the energetic particle measurements on the CORONAS-F and SERVIS-1 satellites. Acceleration of protons by 1–2 orders of magnitude was observed after trapping of solar protons with an energy of 1–15 MeV during the recovery phase of the magnetic storm of November 7–8, 2004. This acceleration was accompanied by an earthward shift of the particle flux maximum for several days, during which the series of magnetic storms continued. The process of relativistic electron acceleration proceeded simultaneously and according to a similar scenario including acceleration of protons. At the end of this period, the intensification was terminated by the process of precipitation, and a new proton belt split with the formation of two maximums at L ～ 2 and 3. In the January 2005 series of moderate storms, solar protons were trapped at L = 3.7 during the storm of January 17–18. However, during the magnetic storm of January 21, these particles fell in the zone of quasi-trapping, or precipitated into the atmosphere, or died in the magnetosheath. At the same time, the belts that were formed in November at L ～ 2 and 3 remained unchanged. Transformations of the proton (and electron) belts during strong magnetic storms change the intensity and structure of belts for a long time. Thus, the consequences of changes during the July 2004 storm did not disappear until November disturbances.     

Variations in the critical frequency of the ionospheric F-region during magnetic storms in 2008–2012 at auroral latitudes

Fifty-one magnetic storms occurred during the last solar half-cycle of transition from the epoch minimum to the epoch maximum are considered. Ionospheric (foF2) and magnetic (X component) data from Sodankyla observatory, Finland, were used for the analysis, as well as values of the ΣKp indices of magnetic activity. The dependence of variations in the critical frequency foF2 was studied before, during, and after each storm. It has been revealed that a major effect (ME) takes place for all of the storms analyzed. It consists in the following: the first maximum in foF2 values occurs several days before the onset of the active phase of a storm, then foF2 attains its minimum during the active phase, and the second maximum occurred after the active phase. Five principals, the most frequent types of variation in foF2 during a storm, have been revealed. However, special cases (30%) in which an ME exists but shifts rightward several days along the time axis are observable. Ionospheric “memory” (inertia) from 8–9 h to 2 days has been revealed. It has been ascertained that the occurrence of the first ME maximum can be considered a magnetic storm precursor. Such a precursor potentially can be used for forecasting the beginning of magnetic storm development, which is important for space weather problems.     

A spatial windowing technique to account for finite dimensions in 2.5D dynamic soil–structure interaction problems

The dynamic interaction between a layered halfspace and quasi translationally invariant structures such as roads, railway tracks, tunnels, dams, and lifelines can be modelled using a computationally efficient 2.5D approach, assuming invariance of the geometry in the longitudinal direction. This assumption is not always fulfilled in practice, however. Even for elongated structures, full 3D computations may be required for an accurate solution of the dynamic soil–structure interaction problem. This paper presents a spatial windowing technique for elastodynamic transmission and radiation problems that allows accounting for the finite length of a structure, still maintaining the computational efficiency of a 2.5D formulation. The proposed technique accounts for the diffraction occurring at the structure's edges, but not for its modal behaviour resulting from reflections of waves at its boundaries. Numerical examples of a barrier for vibration transmission and a surface foundation are discussed to demonstrate the accuracy and applicability of the proposed methodology. Full 3D calculations are performed to provide a rigorous validation for each of these examples. It is demonstrated that the proposed technique is appropriate as long as the response is not dominated by the resonant behaviour of individual modes of the structure.     

Explosive lava–water interactions II: self-organization processes among volcanic rootless eruption sites in the 1783–1784 Laki lava flow, Iceland

We have applied quantitative geospatial analyses to rootless eruption sites in the Hnúta and Hrossatungur groups of the 1783–1784 Laki lava flow to establish how patterns of spatial distribution can be used to obtain information about rootless cone emplacement processes and paleo-environments. This study utilizes sample-size-dependent nearest neighbor (NN) statistics and Voronoi tessellations to quantify the spatial distribution of rootless eruption sites and validate the use of statistical NN analysis as a remote sensing tool. Our results show that rootless eruption sites cluster in environments with abundant lava and water resources, but competition for limited groundwater in these clusters can cause rootless eruption sites to develop repelled distributions. This pattern of self-organization can be interpreted within the context of resource availability and depletion. Topography tends to concentrate lava (fuel) and water (coolant) within topographic lows, thereby promoting explosive lava–water interactions in these regions. Given an excess supply of lava within broad sheet lobes, rootless eruption sites withdraw groundwater from their surroundings until there is insufficient water to maintain analogs to explosive molten fuel–coolant interactions. Rootless eruption sites may be modeled as a network of water extraction wells that draw down the water table in their vicinity. Rootless eruptions at locations with insufficient groundwater may either fail to initiate or terminate before explosive activity has ceased at nearby locations with a greater supply of water, thus imparting a repelled distribution to observed rootless eruption sites.     

Height stratification and polar reversal of the Sun’s magnetic fields in cycles 21–23

Using calculations of the magnetic field in the solar atmosphere in the potential approximation, it is shown that, (1) as distance R from the Sun’s center grows, the area of the positive magnetic field (S _+field) in 10-deg latitude zones tends to 100% (0%) in the neighborhood of the solar minimum. At the distance R = 2.5R _⊙(R _⊙ is the solar radius), these values of the positive field are observed during ≈(12–55) Carrington rotations (CRs) for solar minima between neighboring cycles; (2) polar magnetic field reversals can occur repeatedly. Note that a polar reversal at large heights ends by 6–16 Carrington rotations earlier than on the Sun’s surface. On the Sun’s surface, a field polar reversal begins earlier at lower latitudes than at high ones; (3) for each longitude at different Rs and separately for each solar hemisphere the radial component of the field was averaged on synoptic maps in the 0°–40° latitude range. It is established that the T _R rotation periods of the boundaries between the sectors (areas of longitudes with the same sign of the averaged field) can be shorter than, longer than, and equal to Carrington solar rotation period T _CR. It turned out that boundaries with T _R < T _CR are observed at all heights, while boundaries with T _R > T _CR are observed at relatively small heights.