Mean-field concept and direct numerical simulations of rotating magnetoconvection and the geodynamo

Mean-field theory describes magnetohydrodynamic processes leading to large-scale magnetic fields in various cosmic objects. In this study magnetoconvection and dynamo processes in a rotating spherical shell are considered. Mean fields are defined by azimuthal averaging. In the framework of mean-field theory, the coefficients which determine the traditional representation of the mean electromotive force, including derivatives of the mean magnetic field up to the first order, are crucial for analyzing and simulating dynamo action. Two methods are developed to extract mean-field coefficients from direct numerical simulations of the mentioned processes. While the first method does not use intrinsic approximations, the second one is based on the second-order correlation approximation. There is satisfying agreement of the results of both methods for sufficiently slow fluid motions. Both methods are applied to simulations of rotating magnetoconvection and a quasi-stationary geodynamo. The mean-field induction effects described by these coefficients, e.g., the α-effect, are highly anisotropic in both examples. An α²-mechanism is suggested along with a strong γ-effect operating outside the inner core tangent cylinder. The turbulent diffusivity exceeds the molecular one by at least one order of magnitude in the geodynamo example. With the aim to compare mean-field simulations with corresponding direct numerical simulations, a two-dimensional mean-field model involving all previously determined mean-field coefficients was constructed. Various tests with different sets of mean-field coefficients reveal their action and significance. In the magnetoconvection and geodynamo examples considered here, the match between direct numerical simulations and mean-field simulations is only satisfying if a large number of mean-field coefficients are involved. In the magnetoconvection example, the azimuthally averaged magnetic field resulting from the numerical simulation is in good agreement with its counterpart in the mean-field model. However, this match is not completely satisfactory in the geodynamo case anymore. Here the traditional representation of the mean electromotive force ignoring higher than first-order spatial derivatives of the mean magnetic field is no longer a good approximation.     

Amplification of disturbances on a channel flow

Abstract

The stability of a rotating, stationary flow of zero potential vorticity in a slowly varying channel is examined using the method of multiple scales. This technique can be applied when the variations of the basic flow occur on a length scale which is much larger than the one associated with the perturbation. To lowest order the disturbance is described by a propagating part multiplied by a slowly changing amplitude. It is shown that when the phase speed of a disturbance approaches zero, the growth of the amplitude becomes unbounded. This happens when a perturbation superimposed upon a flow which is slightly sub/supercritical, or which alters from a super- to a subcritical state, propagates over a shoaling bottom. If, however, the change of the basic flow is from a sub- to a supercritical state, the phase speed is quite large and the amplitude of the perturbation will just show minor variations along the channel. The same holds true if the steady flow is only moderately affected by the changing topography. The problem has also been analyzed using wave-action formalism, and the outcome of this alternative approach to the stability problem proved to conform to the previously obtained results. Finally, an interpretation of the calculated growth rates is undertaken in terms of “convective” amplification and “absolute” instability.     

Storing and retrieving changes in a sequence of polygons

Abstract

Several notions of optimality are introduced for two-dimensional geometric versioning of polygons. The storage required for a series of versions is minimized by determining references and restating versions from the references. Structural properties are presented as well as algorithms which yield optimal or near-optimal references for some of the optimality notions. Several of the algorithms are shown to be efficient.     

Pre‐Glacial Landform Inheritance in a Glaciated Shield Landscape

We seek to quantify glacial erosion in a low relief shield landscape in northern Sweden. We use GIS analyses of digital elevation models and field mapping of glacial erosion indicators to explore the geomorphology of three granite areas with the same sets of landforms and of similar relative relief, but with different degrees of glacial streamlining. Area 1, the Parkajoki district, shows no streamlining and so is a type area for negligible glacial erosion. Parkajoki retains many delicate pre‐glacial features, including tors and saprolites with exposure histories of over 1 Myr. Area 2 shows the onset of significant glacial erosion, with the development of glacially streamlined bedrock hills. Area 3 shows extensive glacial streamlining and the development of hill forms such as large crag and tails and roches moutonnées. Preservation of old landforms is almost complete in Area 1, due to repeated covers of cold‐based, non‐erosive ice. In Area 2, streamlined hills appear but sheet joint patterns indicate that the lateral erosion of granite domes needed to form flanking cliffs and to give a streamlined appearance is only of the order of a few tens of metres. The inheritance of large‐scale, pre‐glacial landforms, notably structurally controlled bedrock hills and low relief palaeosurfaces, remains evident even in Area 3, the zone of maximum glacial erosion. Glacial erosion here has been concentrated in valleys, leading to the dissection and loss of area of palaeosurfaces. Semi‐quantitative estimates of glacial erosion on inselbergs and palaeosurfaces and in valleys provide mean totals for glacial erosion of 8 ± 8 m in Area 1 and 27 ± 11 m in Area 3. These estimates support previous views that glacial erosion depths and rates on shields can be low and that pre‐glacial landforms can survive long periods of glaciation, including episodes of wet‐based flow.     

Investigating the impact of initial soil moisture conditions on total infiltration by using an adapted double-ring infiltrometer

ABSTRACT

This study presents an adaptation of the double-ring infiltrometer (DRI) device, which allows several infiltration experiments to be conducted at the same location. Hence, it becomes possible to use the DRI method to investigate infiltration behaviour under different initial soil moisture conditions. The main feature is the splitting of the inner ring into two parts. While the lower part remains in the soil throughout the investigation period, the upper part is attached to the lower one just before the infiltration experiment. This method was applied to eight test sites in an Alpine catchment, covering different land-use/cover types. The results demonstrated the applicability of the adapted system and showed correlations between total water infiltration and initial soil moisture conditions on pastures, independent of the underlying soil type. In contrast, no correlation was found at forest sites or wetlands. Thus, the study emphasizes the importance of paying special attention to the impact of initial soil moisture conditions on the infiltration—and consequently the runoff behaviour—at managed areas. Given the differences in the total infiltrated water of between 30 and 1306 mm, consideration of the interplay between initial soil moisture conditions, land-use/cover type, and soil properties in rainfall–runoff models is a prerequisite to predict runoff production accurately.

EDITOR Z.W. Kundzewicz; ASSOCIATE EDITOR not assigned     

Vertical structure of the Venus cloud top from the VeRa and VIRTIS observations onboard Venus Express

We investigate the Venus cloud top structure by joint analysis of the data from Visual and Thermal Infrared Imaging Spectrometer (VIRTIS) and the atmospheric temperature sounding by the Radio Science experiment (VeRa) onboard Venus Express. The cloud top altitude and aerosol scale height are derived by fitting VIRTIS spectra at 4–5 μm with temperature profiles taken from the VeRa radio occultation. Our study shows gradual descent of the cloud top from 67.2 ± 1.9 km in low latitudes to 62.8 ± 4.1 km at the pole and decrease of the aerosol scale height from 3.8 ± 1.6 km to 1.7 ± 2.4 km. These changes correlate with the mesospheric temperature field. In the cold collar and high latitudes the cloud top position remarkably coincides with the sharp minima in temperature inversions suggesting importance of radiative cooling in their maintenance. This behaviour is consistent with the earlier observations. Spectral trend of the cloud top altitude derived from a comparison with the earlier observations in 1.6–27 μm wavelength range is qualitatively consistent with sulphuric acid composition of the upper cloud and suggests that particle size increases from equator to pole.     

Determination of Electromagnetic Source Direction as an Eigenvalue Problem

Low-frequency solar and interplanetary radio bursts are generated at frequencies below the ionospheric plasma cutoff and must therefore be measured in space, with deployable antenna systems. The problem of measuring both the general direction and polarization of an electromagnetic source is commonly solved by iterative fitting methods such as linear regression that deal simultaneously with both directional and polarization parameters. We have developed a scheme that separates the problem of deriving the source direction from that of determining the polarization, avoiding iteration in a multi-dimensional manifold. The crux of the method is to first determine the source direction independently of concerns as to its polarization. Once the source direction is known, its direct characterization in terms of Stokes vectors, in a single iteration if desired, is relatively simple. This study applies the source-direction determination to radio signatures of flares received by STEREO. We studied two previously analyzed radio type III bursts and found that the results of the eigenvalue decomposition technique are consistent with those obtained previously by Reiner et al. (Solar Phys. 259, 255, 2009). For the type III burst observed on 7 December 2007, the difference in travel times from the derived source location to STEREO A and B is the same as the difference in the onset times of the burst profiles measured by the two spacecraft. This is consistent with emission originating from a single, relatively compact source. For the second event of 29 January 2008, the relative timing does not agree, suggesting emission from two sources separated by 0.1 AU, or perhaps from an elongated region encompassing the apparent source locations.