On the formation of axial corner vortices during spin-up in a cylinder of square cross-section

We present experimental and theoretical results for the adjustment of a fluid (homogeneous or linearly stratified), which is initially rotating as a solid body with angular frequency Ω−ΔΩ, to a nonlinear increase ΔΩ in the angular frequency of all bounding surfaces. The fluid is contained in a cylinder of square cross-section which is aligned centrally along the rotation axis, and we focus on the O(Ro−1Ω−1) time scale, where Ro=ΔΩ/Ω is the Rossby number. The flow development is shown to be dominated by unsteady separation of a viscous sidewall layer, leading to an eruption of vorticity that becomes trapped in the four vertical corners of the container. The longer-time evolution on the standard ‘spin-up’ time scale, E−1/2Ω−1 (where E is the associated Ekman number), has been described in detail for this geometry by Foster & Munro (J. Fluid Mech., vol. 712, 2012, pp. 7–40), but only for small changes in the container’s rotation rate (i.e. Ro≪1). In the linear case, for Ro≪E1/2≪1, there is no sidewall separation. In the present investigation we focus on the fully nonlinear problem, Ro=O(1), for which the sidewall viscous layers are Prandtl boundary layers and (somewhat unusually) periodic around the container’s circumference. Some care is required in the corners of the container, but we show that the sidewall boundary layer breaks down (separates) shortly after an impulsive change in rotation rate. These theoretical boundary-layer results are compared with two-dimensional Navier–Stokes results which capture the eruption of vorticity, and these are in turn compared to laboratory observations and data. The experiments show that when the Burger number, S=(N/Ω)2 (where N is the buoyancy frequency), is relatively large – corresponding to a strongly stratified fluid – the flow remains (horizontally) two-dimensional on the O(Ro−1Ω−1) time scale, and good quantitative predictions can be made by a two-dimensional theory. As S was reduced in the experiments, three-dimensional effects were observed to become important in the core of each corner vortex, on this time scale, but only after the breakdown of the sidewall layers

A Mathematical Model for Flash Sintering

A mathematical model is presented for the Joule heating that occurs in a ceramic powder compact during the process of flash sintering. The ceramic is assumed to have an electrical conductivity that increases with temperature, and this leads to the possibility of runaway heating that could facilitate and explain the rapid sintering seen in experiments. We consider reduced models that are sufficiently simple to enable concrete conclusions to be drawn about the mathematical nature of their solutions. In particular we discuss how different local and non-local reaction terms, which arise from specified experimental conditions of fixed voltage and current, lead to thermal runaway or to stable conditions. We identify incipient thermal runaway as a necessary condition for the flash event, and hence identify the conditions under which this is likely to occur.Comment: 14 pages, 9 figure

Tidal controls on the lithospheric thickness and topography of Io from magmatic segregation and volcanism modelling

Tidal heating is expected to impart significant, non-spherically-symmetric structure to Jupiter's volcanic moon Io. A signature of spatially variable tidal heating is generally sought in observations of surface heat fluxes or volcanic activity, an exploration complicated by the transient nature of volcanic events. The thickness of the lithosphere is expected to change over much longer timescales, and so may provide a robust link between surface observations and the tidal heating distribution. To predict long-wavelength lithospheric thickness variations, we couple three-dimensional tidal heating calculations to a suite of one-dimensional models of magmatic segregation and volcanic eruption. We find that the lithospheric thickness could either be correlated with the radially integrated heating rate, or weakly anti-correlated. Lithospheric thickness is correlated with radially integrated heating rate if magmatic intrusions form at a constant rate in the lithosphere, but is weakly anti-correlated if intrusions form at a rate proportional to the flux through volcanic conduits. Utilising a simple isostasy model we show how variations in lithospheric thickness can predict long-wavelength topography. The relationship between lithospheric thickness and topography depends on the difference in chemical density between the lithosphere and mantle. Assuming that this difference is small, we find that long-wavelength topography anti-correlates with lithospheric thickness. These results will allow future observations to critically evaluate models for Io's lithospheric structure, and enable their use in constraining the distribution of tidal heating.Comment: Published in Icaru

Land use modelling and the role of stakeholders in natural protected areas: the case of Doñana national park, Spain

Doñana, a National Park since 1969, a UNESCO site since 1994 among other protected area designations of national and international character, is a coastal dune and marshland ecosystem of outstanding importance for biodiversity and conservation at the mouth of the Guadalaquivir River, Southwest Spain. However, the Doñana natural area is seriously threatened by global change factors such as humanly induced climate change, habitat loss, overexploitation of ecosystem services, and pollution. Not all stakeholders are convinced of the benefits of the national park, and management of Doñana, its environs and watershed are the subject of intense disagreement. This interplay between natural characteristics of great value with intense human pressure makes Doñana a fascinating workshop for the study of global human environment interactions. Here, we discuss the role of stakeholders in the application of a cellular automatabased model to Doñana and its environs and present the results of a series of exercises undertaken with stakeholders to parametrize the model, something often done by researchers without stakeholder engagement. By engaging with stakeholders early in the project, feedback generated from workshops contributes to model development. Stakeholders are therefore contributors of empirical data for the model as well as independent evaluators providing local and specialist knowledge

Feedback of mesoscale ocean currents on atmospheric winds in high-resolution coupled models and implications for the forcing of ocean-only models

The repercussions of surface ocean currents for the near-surface wind and the air-sea momentum flux are investigated in two versions of a global climate model with eddying ocean. The focus is on the effect of mesoscale ocean current features at scales of less than 150 km, by considering high-pass filtered, monthly-mean model output fields. We find a clear signature of a mesoscale oceanic imprint in the wind fields over the energetic areas of the oceans, particularly along the extensions of the western boundary currents and the Antarctic Circumpolar Current. These areas are characterized by a positive correlation between mesoscale perturbations in the curl of the surface currents and the wind curl. The coupling coefficients are spatially non-uniform and show a pronounced seasonal cycle. The positive feedback of mesoscale current features on the near-surface wind acts in opposition to their damping effect on the wind stress. A tentative incorporation of this feedback in the surface stress formulation of an eddy-permitting global ocean-only model leads to a gain in the kinetic energy of up to 10 %, suggesting a fundamental shortcoming of present ocean model configurations

Dietary Protein and Bone Health Across the Life-Course : an updated systematic review and meta-analysis over 40 years

Abstract Purpose: This systematic review and meta-analysis analysed the relationship between dietary protein and bone health across the life-course. Methods: The PubMed database was searched for all relevant human studies from the 1st 4 January 1976 to 22nd January 2016, including all bone outcomes except calcium metabolism. Results: The searches identified 127 papers for inclusion, including 74 correlational studies, 23 fracture or osteoporosis risk studies and 30 supplementation trials. Protein intake accounted for 0 - 4% of areal BMC and areal BMD variance in adults and 0-14% of areal BMC variance in children and adolescents. However, when confounder adjusted (5 studies) adult lumbar spine and femoral neck BMD associations were not statistically significant. There was no association between protein intake and relative risk (RR) of osteoporotic fractures for total (RR(random) = 0.94; 0.72 to 1.23, I2=32%), animal (RR (random) = 0.98; 0.76 to 1.27, I2 = 46%) or vegetable protein (RR (fixed)= 0.97 (0.89 to 1.09, I2 = 15%). In total protein supplementation studies, pooled effect sizes were not statistically significant for LSBMD (total n=255, MD(fixed)=0.04 g/cm2 (0.00 to 0.08, P=0.07), I2=0%) or FNBMD (total n=435, MD(random)=0.01 g/cm2 (-0.03 to 0.05, P=0.59), I2=68%). Conclusions: There appears to be little benefit of increasing protein intake for bone health in healthy adults but there is also clearly no indication of any detrimental effect, at least within the protein intakes of the populations studied (around 0.8-1.3 g/Kg/day). More studies are urgently required on the association between protein intake and bone health in children and adolescents. Key Words: Aging, Epidemiology, IGF-1, Nutrition, Osteoporosis, Die

What Next-Generation 21 cm Power Spectrum Measurements Can Teach Us About the Epoch of Reionization

A number of experiments are currently working towards a measurement of the 21 cm signal from the Epoch of Reionization. Whether or not these experiments deliver a detection of cosmological emission, their limited sensitivity will prevent them from providing detailed information about the astrophysics of reionization. In this work, we consider what types of measurements will be enabled by a next-generation of larger 21 cm EoR telescopes. To calculate the type of constraints that will be possible with such arrays, we use simple models for the instrument, foreground emission, and the reionization history. We focus primarily on an instrument modeled after the $\sim 0.1~\rm{km}^2$ collecting area Hydrogen Epoch of Reionization Array (HERA) concept design, and parameterize the uncertainties with regard to foreground emission by considering different limits to the recently described "wedge" footprint in k-space. Uncertainties in the reionization history are accounted for using a series of simulations which vary the ionizing efficiency and minimum virial temperature of the galaxies responsible for reionization, as well as the mean free path of ionizing photons through the IGM. Given various combinations of models, we consider the significance of the possible power spectrum detections, the ability to trace the power spectrum evolution versus redshift, the detectability of salient power spectrum features, and the achievable level of quantitative constraints on astrophysical parameters. Ultimately, we find that $0.1~\rm{km}^2$ of collecting area is enough to ensure a very high significance ($\gtrsim30\sigma$) detection of the reionization power spectrum in even the most pessimistic scenarios. This sensitivity should allow for meaningful constraints on the reionization history and astrophysical parameters, especially if foreground subtraction techniques can be improved and successfully implemented.Comment: 27 pages, 18 figures, updated SKA numbers in appendi