We present the first detailed 3D hydrodynamic implicit large eddy simulations of turbulent convection of carbon burning in massive stars. Simulations begin with radial profiles mapped from a carbon-burning shell within a 15 M 1D stellar evolution model. We consider models with 128 3 , 256 3 , 512 3 , and 1024 3 zones. The turbulent flow properties of these carbon-burning simulations are very similar to the oxygen-burning case. We performed a mean field analysis of the kinetic energy budgets within the Reynolds-averaged Navier-Stokes framework. For the upper convective boundary region, we find that the numerical dissipation is insensitive to resolution for linear mesh resolutions above 512 grid points. For the stiffer, more stratified lower boundary, our highest resolution model still shows signs of decreasing sub-grid dissipation suggesting it is not yet numerically converged. We find that the widths of the upper and lower boundaries are roughly 30 per cent and 10 per cent of the local pressure scaleheights, respectively. The shape of the boundaries is significantly different from those used in stellar evolution models. As in past oxygen-shell-burning simulations, we observe entrainment at both boundaries in our carbon-shell-burning simulations. In the large Péclet number regime found in the advanced phases, the entrainment rate is roughly inversely proportional to the bulk Richardson number, Ri B (∝Ri B −α , 0.5 α 1.0). We thus suggest the use of Ri B as a means to take into account the results of 3D hydrodynamics simulations in new 1D prescriptions of convective boundary mixing.Key words: convection -hydrodynamics -turbulence -stars: evolution -stars: interiorsstars: massive. I N T RO D U C T I O N1D stellar evolution codes are currently the only way to simulate the entire lifespan of a star. This comes at the cost of having to replace complex, inherently 3D processes, such as convection, rotation, and magnetic activity, with generally simplified mean-field models. An essential question is 'how well do these 1D models represent reality?' Answers can be found both in empirical and theoretical works. On the empirical front, we can investigate full star models, by comparing them to observations of stars under a range of conditions, as well as testing the basic physics that goes into models of multidimensional phenomena by studying relevant laboratory work and E-mail: a.j.cristini@keele.ac.uk (AC); r.hirschi@keele.ac.uk (RH); wdarnett@gmail.com (DA) data from meteorology and oceanography (remembering that stars are much bigger than planets, and are composed of high-energy density plasma). On the theoretical side, multidimensional simulations can be used to test 1D models under astrophysical conditions that can be recreated in terrestrial laboratories only in small volumes, e.g. in National Ignition Facility (NIF) (Kuranz et al. 2011) and z-pinch device (Miernik et al. 2013) experiments. Astronomical testsThe results from the astronomical validation studies are mixed. Observations of stars confirm the gener...
Convective boundary mixing is one of the major uncertainties in stellar evolution. In order to study its dependence on boundary properties and turbulence strength in a controlled way, we computed a series of 3D hydrodynamical simulations of stellar convection during carbon burning with a varying boosting factor of the driving luminosity. Our 3D implicit large eddy simulations were computed with the prompi code. We performed a mean field analysis of the simulations within the Reynolds-averaged Navier-Stokes framework. Both the vertical RMS velocity within the convective region and the bulk Richardson number of the boundaries are found to scale with the driving luminosity as expected from theory: ∝ 1/3 and Ri B ∝ −2/3 , respectively. The positions of the convective boundaries were estimated through the composition profiles across them, and the strength of convective boundary mixing was determined by analysing the boundaries within the framework of the entrainment law. We find that the entrainment is approximately inversely proportional to the bulk Richardson number, Ri B (∝ Ri − B , ∼ 0.75). Although the entrainment law does not encompass all the processes occurring at boundaries, our results support the use of the entrainment law to describe convective boundary mixing in 1D models, at least for the advanced phases. The next steps and challenges ahead are also discussed.
This paper describes the potential environmental changes caused by tidal power installations with illustration for schemes in the eastern Irish Sea, focussing mainly on major estuarine barrages. The generic impacts in the near-field and far-field are discussed. Results from a 0-D and a 2-D model are presented: the former allows rapid calculations to be made for a large range of options while the latter allows the full effect on 2D hydrodynamics to be investigated. It is shown that there may be a significant change in tidal amplitude at the coast of Northern Ireland. The bed stress in the Bristol Channel will be significantly reduced if a Severn barrage is constructed. Some effects on the tidal mixing are expected although the location of tidal fronts in the Irish and Celtic Seas will not be changed significantly. The largest environmental impact is expected to be on the amount of inter-tidal area retained after construction of an estuarine barrage. It is shown that the loss of mudflats can be substantially reduced by using a dual-mode (ebb and flood generation) scheme with an increased number of turbines over the lowest-cost option.
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