Remark on the Mean Energy of the Fluctuating Magnetic Field in Mean-field Magnetohydrodynamics

A relation between the mean square of the fluctuating magnetic field, B′ , and the square of the mean magnetic field, B̄ , is derived for the case of homogeneous isotropic turbulence. The second order correlations approximation is used under the assumption that the space and time scales L̄ and T̄ of the mean field are large compared with the scales L and T of the fluctuations. BOCHNER 's theorem manifests itself as a guarantee for the ratio B̄′²|B̄² to be non-negative.     

On the turbulent decay of strong magnetic fields and the development of sunspot areas

This paper deals with the conception that two-dimensional turbulence is present in a sunspot where the magnetic field is strong. This conception is based upon the incapacity of even a strong magnetic field to influence an arbitrary two-dimensional turbulence, if the magnetic field is parallel to a constant direction and the motion occurs in planes orthogonal to it. It is, moreover, shown that such a two-dimensional turbulence provides for a turbulent decay of the magnetic field. The decay rate possesses nearly the same dependence on the scales as for three-dimensional turbulence. Finally, the turbulent decay is studied by investigating a simple model and comparing the results with those deduced by Bumba from the observed decay of sunspot groups areas. By means of our conception even a good quantitative agreement is stated.     

Dynamos with a flat α-effect distribution

Abstract

In order to obtain a better insight into the excitation conditions of magnetic fields in flat objects, such as galaxies, we have calculated critical dynamo numbers of different magnetic field modes for spherical dynamos with a flat α-effect distribution. A simple but realistic approximation formula for the rotation curve is employed. In most cases investigated a stationary quadrupole-type solution is preferred. This is a consequence of the flat distribution of the α-effect. Non-axisymmetric fields are in all cases harder to excite than axisymmetric ones. This seems to be the case particularly for flat objects in combination with a realistic rotation curve for galaxies. The question of whether non-axisymmetric (bisymmetric) fields, which are observed in some galaxies, can be explained as dynamos generated by an axisymmetric αω-effect is therefore still open.     

How well developed is the dynamo theory of flat objects?

Abstract

The existing models of disk dynamos are reviewed and an attempt is made to assess the reliability of their predictions. We analyze key questions such as whether the infinitely extended layer is a proper approximation of the finite disk, or whether it overlooks the possibility of ‘‘forgotten modes'', i.e. whether there is a guarantee that, when the model is used in applications, the mode it predicts as the most easily excited is truly such.

What we find is that all existing models of disk dynamos have shortcomings in these respects, so that the analysis of improved models is worth the effort.     

Tritium balance in macro‐scale river basins analysed through distributed hydrological modelling

The recession of bomb tritium in river discharge of large basins indicates a contribution of slowly moving water. For an appropriate interpretation it is necessary to consider different runoff components (e.g. direct runoff and ground water components) and varying residence times of tritium in these components. The spatially distributed catchment model (tracer aided catchment model, distributed; TAC^D) and a tritium balance model (TRIBIL) were combined to model process‐based tritium balances in a large German river basin (Weser 46 240 km²) and seven embedded sub‐basins. The hydrological model (monthly time step, 2 × 2 km²) estimated the three major runoff components: direct runoff, fast‐moving and slow‐moving ground water for the period of 1950 to 1999. The model incorporated topography, land use, geomorphology, geology and hydro‐meteorological data. The results for the different basins indicated a contribution of direct runoff of 30–50% and varying amounts for fast and slow ground water components. Combining these results with the TRIBIL model allowed us to estimate the residence time of the components. Mean residence times of 8 to 14 years were found for the fast ground water component, 21 to 93 years for the slow ground water component and 14 to 50 years for an overall mean residence time within these basins. Balance calculations for the Weser basin indicate an over‐estimation of loss of tritium through evapotranspiration (more than 60%) and decay (10%). About 28% were carried in stream‐flow where direct runoff contributed about 12% and ground water runoff 13% in relation to precipitation input over the studied 50‐year period. Neighbouring basins and nuclear power plants contributed about 1% each over this time period. Copyright © 2007 John Wiley & Sons, Ltd.     

Biogeochemical responses to late-winter storms in the Sargasso Sea,III—Estimates of export production using 234Th:238U disequilibria and sediment traps

Direct measurements of new production and carbon export in the subtropical North Atlantic Ocean appear to be too low when compared to geochemical-based estimates. It has been hypothesized that episodic inputs of new nutrients into surface water via the passage of mesoscale eddies or winter storms may resolve at least some of this discrepancy. Here, we investigated particulate organic carbon (POC), particulate organic nitrogen (PON), and biogenic silica (BSiO₂) export using a combination of water column ²³⁴Th:²³⁸U disequilibria and free-floating sediment traps during and immediately following two weather systems encountered in February and March 2004. While these storms resulted in a 2–4-fold increase in mixed layer NO₃ inventories, total chlorophyll a and an increase in diatom biomass, the systems were dominated by generally low ²³⁴Th:²³⁸U disequilibria, suggesting limited particle export. Several ²³⁴Th models were tested, with only those including non-steady state and vertical upwelling processes able to describe the observed ²³⁴Th activities. Although upwelling velocities were not measured directly in this study, the ²³⁴Th model suggests reasonable rates of 2.2–3.7 m d^?1.Given the uncertainties associated with ²³⁴Th derived particle export rates and sediment traps, both were used to provide a range in sinking particle fluxes from the upper ocean during the study. ²³⁴Th particle fluxes were determined applying the more commonly used steady state, one-dimensional model with element/²³⁴Th ratios measured in sediment traps. Export fluxes at 200 m ranged from 1.91±0.20 to 4.92±1.22 mmol C m^?2 d^?1, 0.25±0.08 to 0.54±0.09 mmol N m^?2 d^?1, and 0.22±0.04 to 0.50±0.06 mmol Si m^?2 d^?1. POC export efficiencies (Primary Production/Export) were not significantly different from the annual average or from time periods without storms, although absolute POC fluxes were elevated by 1–11%. This increase was not sufficient, however, to resolve the discrepancy between our observations and geochemical-based estimates of particle export. Comparison of PON export rates with simultaneous measurements of NO₃^? uptake derived new production rates suggest that only a fraction, <35%, of new production was exported as particles to deep waters during these events. Measured bSiO₂ export rates were more than a factor of two higher (p<0.01) than the annual average, with storm events contributing as much as 50% of annual bSiO₂ export in the Sargasso Sea. Furthermore it appears that 65–95% (average 86±14%) of the total POC export measured in this study was due to diatoms.Combined these results suggest that winter storms do not significantly increase POC and PON export to depth. Rather, these storms may play a role in the export of bSiO₂ to deep waters. Given the slower remineralization rates of bSiO₂ relative to POC and PON, this transport may, over time, slowly decrease water column silicate inventories, and further drive the Sargasso Sea towards increasing silica limitation. These storm events may further affect the quality of the POC and PON exported, given the large association of this material with diatoms during these periods.     

Methods of analyzing radio polarization data

Abstract

Methods of estimating the strength and direction of galactic magnetic fields from radio polarization measurements are reviewed. Particular attention is paid to the analysis of the Faraday rotation in order to derive the large scale magnetic field structure. Ways in which an axisymmetric spiral field structure can be observationally distinguished from a bisymmetric spiral structure are described, as are the ways in which field symmetric with respect to the galactic plane can be distinguished from those that are antisymmetric.     

Modeling the total and polarized emission in evolving galaxies: “Spotty” magnetic structures

Future radio observations with the Square Kilometre Array (SKA) and its precursors will be sensitive to trace spiral galaxies and their magnetic field configurations up to redshift z ≈ 3. We suggest an evolutionary model for the magnetic configuration in star‐forming disk galaxies and simulate the magnetic field distribution, the total and polarized synchrotron emission, and the Faraday rotation measures for disk galaxies at z ≲ 3. Since details of dynamo action in young galaxies are quite uncertain, we model the dynamo action heuristically relying only on well‐established ideas of the form and evolution of magnetic fields produced by the mean‐field dynamo in a thin disk. We assume a small‐scale seed field which is then amplified by the small‐scale turbulent dynamo up to energy equipartition with kinetic energy of turbulence. The large‐scale galactic dynamo starts from seed fields of 100 pc and an averaged regular field strength of 0.02 μG, which then evolves to a “spotty” magnetic field configuration in about 0.8 Gyr with scales of about one kpc and an averaged regular field strength of 0.6 μG. The evolution of these magnetic spots is simulated under the influence of star formation, dynamo action, stretching by differential rotation of the disk, and turbulent diffusion. The evolution of the regular magnetic field in a disk of a spiral galaxy, as well as the expected total intensity, linear polarization and Faraday rotation are simulated in the rest frame of a galaxy at 5GHz and 150 MHz and in the rest frame of the observer at 150 MHz. We present the corresponding maps for several epochs after disk formation. Dynamo theory predicts the generation of large‐scale coherent field patterns (“modes”). The timescale of this process is comparable to that of the galaxy age. Many galaxies are expected not to host fully coherent fields at the present epoch, especially those which suffered from major mergers or interactions with other galaxies. A comparison of our predictions with existing observations of spiral galaxies is given and discussed (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)