The angular momentum transport by unstable toroidal magnetic fields

We demonstrate with a nonlinear MHD code that angular momentum can be transported due to the magnetic instability of toroidal fields under the influence of differential rotation, and that the resulting effective viscosity may be high enough to explain the almost rigid-body rotation observed in radiative stellar cores. Only stationary current-free fields and only those combinations of rotation rates and magnetic field amplitudes which provide maximal numerical values of the viscosity are considered. We find that the dimensionless ratio of the effective over molecular viscosity, $\nu_T/\nu$;, linearly grows with the Reynolds number of the rotating fluid multiplied with the square-root of the magnetic Prandtl number - which is of order unity for the considered red sub-giant KIC 7341231. For the considered interval of magnetic Reynolds numbers - which is restricted by numerical constraints of the nonlinear MHD code - there is a remarkable influence of the magnetic Prandtl number on the relative importance of the contributions of the Reynolds stress and the Maxwell stress to the total viscosity, which is magnetically dominated only for Pm $\gtrsim$ 0.5. We also find that the magnetized plasma behaves as a non-Newtonian fluid, i.e. the resulting effective viscosity depends on the shear in the rotation law. The decay time of the differential rotation thus depends on its shear and becomes longer and longer during the spin-down of a stellar core.Comment: Revised version. 7 pages, 9 figures; accepted for publication in A&

The eddy heat-flux in rotating turbulent convection

The three components of the heat-flux vector $F =\rho C_p are numerically computed for a stratified rotating turbulent convection using the NIRVANA code in a flat box. The latitudinal component$F_\theta$proves to be negative (positive) in the northern (southern) hemisphere so that the heat always flows towards the poles. As a surprise, the radial heat-flux$F_r$peaks at the equator rather than at the poles (Taylor numbers O(10^6)). The same behavior is observed for the radial turbulence intensity$ which for \emph{free} turbulence is also believed to peak at the poles (see Eq. (19) below). As we can show, however, the consequences of this unexpected result (also obtained by Kaepylae, Korpi and Tuominen 2004) for the theory of differential rotation are small as mainly the F_\theta$is responsible to solve the `Taylor number puzzle'. In all our simulations the azimuthal component$F_\phi$proves to be negative so that the rotating turbulence produces an westwards directed azimuthal heat-flux which should be observable. Fluctuations with higher temperature are expected to be anticorrelated with their own angular velocity fluctuations. We find this rotation-induced result as understandable as the$F_\phi$ is closely related to the radial \Lambda-effect which is known to be also negative in stratified and rapidly rotating convection zones.Comment: 8 pages, 9 figures, Astron. Astrophys. (subm.

Understanding the impact of crop and food production on the water environment ‐using sugar as a model

The availability of fresh water and the quality of aquatic ecosystems are important global concerns, and agriculture plays a major role. Consumers and manufacturers are increasingly sensitive to sustainability issues related to processed food products and drinks. The present study examines the production of sugar from the growing cycle through to processing to the factory gate, and identifies the potential impacts on water scarcity and quality and the ways in which the impact of water use can be minimised. We have reviewed the production phases and processing steps, and how calculations of water use can be complicated, or in some cases how assessments can be relatively straightforward. Finally, we outline several ways that growers and sugar processors are improving the efficiency of water use and reducing environmental impact, and where further advances can be made. This provides a template for the assessment of other crops

The exceptional Herbig Ae star HD101412: The first detection of resolved magnetically split lines and the presence of chemical spots in a Herbig star

We obtained high-resolution, high signal-to-noise UVES and a few lower quality HARPS spectra revealing the presence of resolved magnetically split lines. HD101412 is the first Herbig Ae star for which the rotational Doppler effect was found to be small in comparison to the magnetic splitting. The measured mean magnetic field modulus varies from 2.5 to 3.5kG, while the mean quadratic field was found to vary in the range of 3.5 to 4.8kG. To determine the period of variations, we used radial velocity, equivalent width, line width, and line asymmetry measurements of variable spectral lines of several elements, as well as magnetic field measurements. The most pronounced variability was detected for spectral lines of He I and the iron peak elements, whereas the spectral lines of CNO elements are only slightly variable. From spectral variations and magnetic field measurements we derived a potential rotation period P_rot=13.86d, which has to be proven in future studies with a larger number of observations. It is the first time that the presence of element spots is detected on the surface of a Herbig Ae/Be star. Our previous study of Herbig Ae stars revealed a trend towards stronger magnetic fields for younger Herbig Ae stars, confirmed by statistical tests. This is in contrast to a few other (non-statistical) studies claiming that magnetic Herbig Ae stars are progenitors of the magnetic Ap stars. New developments in MHD theory show that the measured magnetic field strengths are compatible with a current-driven instability of toroidal fields generated by differential rotation in the stellar interior. This explanation for magnetic intermediate-mass stars could be an alternative to a frozen-in fossil field.Comment: 7 pages, 6 figures, 1 table, to appear in Astronomische Nachrichte