Test-field method for mean-field coefficients with MHD background

Aims: The test-field method for computing turbulent transport coefficients from simulations of hydromagnetic flows is extended to the regime with a magnetohydrodynamic (MHD) background. Methods: A generalized set of test equations is derived using both the induction equation and a modified momentum equation. By employing an additional set of auxiliary equations, we derive linear equations describing the response of the system to a set of prescribed test fields. Purely magnetic and MHD backgrounds are emulated by applying an electromotive force in the induction equation analogously to the ponderomotive force in the momentum equation. Both forces are chosen to have Roberts flow-like geometry. Results: Examples with an MHD background are studied where the previously used quasi-kinematic test-field method breaks down. In cases with homogeneous mean fields it is shown that the generalized test-field method produces the same results as the imposed-field method, where the field-aligned component of the actual electromotive force from the simulation is used. Furthermore, results for the turbulent diffusivity tensor are given, which are inaccessible to the imposed-field method. For MHD backgrounds, new mean-field effects are found that depend on the occurrence of cross-correlations between magnetic and velocity fluctuations. For strong imposed fields, $\alpha$ is found to be quenched proportional to the fourth power of the field strength, regardless of the type of background studied.Comment: 17 pages, 10 figures, submitted to Astronomy & Astrophysic

Mean--field electrodynamics: Critical analysis of various analytical approaches to the mean electromotive force

There are various analytical approaches to the mean electromotive force $\cal E =$ crucial in mean--field electrodynamics, with $\vec{u}$ and $\vec{b}$ being velocity and magnetic field fluctuations. In most cases the traditional approach, restricted to the second--order correlation approximation, has been used. Its validity is only guaranteed for a range of conditions, which is narrow in view of many applications, e.g., in astrophysics. With the intention to have a wider range of applicability other approaches have been proposed which make use of the so--called $\tau$--approximation, reducing correlations of third order in $\vec{u}$ and $\vec{b}$ to such of second order. After explaining some basic features of the traditional approach a critical analysis of the approaches of that kind is given. It is shown that they lead in some cases to results which are in clear conflict with those of the traditional approach. It is argued that this indicates shortcomings of the $\tau$--approaches and poses serious restrictions to their applicability. These shortcomings do not result from the basic assumption of the $\tau$--approximation. Instead, they seem to originate in some simplifications made in order to derive $\cal E$ without really solving the equations governing $\vec{u}$ and $\vec{b}$. A starting point for a new approach is described which avoids the conflict.Comment: 32 pages, no figures; accepted by Geophys. Astrophys. Fluid Dynam. A quenching formula for \alpha and a section on comparisons with numerical simulations added; references amended; changes in presentation and languag

Fanning out of the ff-mode in presence of nonuniform magnetic fields

We show that in the presence of a harmonically varying magnetic field the fundamental or $f$-mode in a stratified layer is altered in such a way that it fans out in the diagnostic $k\omega$ diagram, but with mode power also within the fan. In our simulations, the surface is defined by a temperature and density jump in a piecewise isothermal layer. Unlike our previous work (Singh et al. 2014) where a uniform magnetic field was considered, we employ here a nonuniform magnetic field together with hydromagnetic turbulence at length scales much smaller than those of the magnetic fields. The expansion of the $f$-mode is stronger for fields confined to the layer below the surface. In some of those cases, the $k\omega$ diagram also reveals a new class of low frequency vertical stripes at multiples of twice the horizontal wavenumber of the background magnetic field. We argue that the study of the $f$-mode expansion might be a new and sensitive tool to determining subsurface magnetic fields with longitudinal periodicity.Comment: 6 pages, 4 figures, submitted to Astrophysical Journal Letter

Small mammal community structure (Rodentia: Muridae) in Punda Maria, Kruger National Park, South Africa : Causes and consequences

The population dynamics of small mammal populations in Punda Maria, Kruger National Park, South Africa was investigated with respect to community size and structure, seed predation and dispersal of several trees. Species populations, community structure and habitat attributes were measured at six sites comprising of 3 habitat types (2 sites per habitat); namely Acaciagrassland, North-facing and South-facing sloped sites. Seasonal variation was investigated at the Acacia sites during late summer (April) and winter months (July). Five habitat attributes were measured; percentages of total cover and herbage, plant litter depth (cm), height of dominant vegetation type measured (m) and edaphic condition were recorded at 15 randomly selected traps per site. Almonds (Prunus dulcis), baobabs (Adansonia digitata), mopane (Colophospermum mopane), and Acacia tortilis seeds were used in the predation and dispersal experiment. North- and South-facing sites were dominated by Aethomys sp. while Acacia sites were dominated by Mastomys natalensis. Seed predation was high at the North-facing slopes, with a significant difference in predation on A. tortilis seeds. Seed dispersal activity was low; no , scatter hoarding was identified; only larder hoarding was observed by Aethomys sp. and M. natalensis at North-facing sites and Acacia sites respectively. Trampling by megaherbivore activity impacted vegetation structure and has negatively affected rodent population and ground activity, particularly at the Acacia sites

Feeding preferences of Tripneustes gratilla Linnaeus Echinodermata Echinodea and the prospect for sea urchin aquaculture in South Africa

Sea urchin aquaculture for human food is a major industry, and there are prospects for the industry in South Africa. Feeding preferences of the sea urchin Tripneustes gratilla were tested by two different methods; a touch-preference test and a 48-hour consumption test. A touchpreference is established when the sea urchins' lantern teeth touched an algal species. The 48-hour consumption test was performed with paired combinations using four species of fresh algae. It was hypothesized that the preferred species would be similar in the touch-preference test and the consumption test. Five algal species were used in the touch-preference test; namely, Ecklonia maxima (kelp), Gigartina polycarpa, Grateloupia capensi, Porphyra capensis, and U/va rigida. Four of these species were used in the paired consumption test; namely, E. maxima, G. polycarpa, P. capensis and U. rigida. We found that E. maxima was most preferred in the touch-test followed by P. capensis and U. rigida. This result did not correlate with our consumption test. Here, U. rigida was significantly most preferred followed by E. maxima. Overall, the result is significant in relation to the prospect of echinoculture in South Africa as Ulva may provide a valuable alternate feed or supplement to this new industry. Due to the increase in time provided for the paired consumption test, we found that the paired consumption test was more conclusive in providing a preference for Tripneustes gratilla. Our results agree with literature which suggests that Tripneustes gratilla is a genera list feeder; however, Tripneustes gratilla shows definite preferences. Ulva spp. has been grown on a number of abalone farms in South Africa. Integrated aquaculture using T. gratilla and U. rigida as a biofilter and alternate feed is a very promising idea for echinoculture in South Africa

Properties of pp- and ff-modes in hydromagnetic turbulence

With the ultimate aim of using the fundamental or $f$-mode to study helioseismic aspects of turbulence-generated magnetic flux concentrations, we use randomly forced hydromagnetic simulations of a piecewise isothermal layer in two dimensions with reflecting boundaries at top and bottom. We compute numerically diagnostic wavenumber-frequency diagrams of the vertical velocity at the interface between the denser gas below and the less dense gas above. For an Alfv\'en-to-sound speed ratio of about 0.1, a 5% frequency increase of the $f$-mode can be measured when $k_xH_{\rm p}=3$-$4$, where $k_x$ is the horizontal wavenumber and $H_{\rm p}$ is the pressure scale height at the surface. Since the solar radius is about 2000 times larger than $H_{\rm p}$, the corresponding spherical harmonic degree would be 6000-8000. For weaker fields, a $k_x$-dependent frequency decrease by the turbulent motions becomes dominant. For vertical magnetic fields, the frequency is enhanced for $k_xH_{\rm p}\approx4$, but decreased relative to its nonmagnetic value for $k_xH_{\rm p}\approx9$.Comment: 17 pages, 22 figures, Version accepted in MNRA