The influence of an externally enforced compositional gradient on the onset of convection of a mixture of two components in a rotating fluid spherical shell is studied for Ekman numbers E = 10−3 and E = 10−6, Prandtl numbers σ = 0.1, 0.001, Lewis numbers τ = 0.01, 0.1, 0.8, and radius ratio η = 0.35. The Boussinesq approximation of the governing equations is derived by taking the denser component of the mixture for the equation of the concentration. Differential and internal heating, an external compositional gradient, and the Soret and Dufour effects are included in the model. By neglecting these two last effects, and by considering only differential heating, it is found that the critical thermal Rayleigh number Rec depends strongly on the direction of the compositional gradient. The results are compared with those obtained previously for pure fluids of the same σ. The influence of the mixture becomes significant when the compositional Rayleigh number Rc is at least of the same order of magnitude as the known Rec computed without mixture. For positive and sufficiently large compositional gradients, Rec decreases and changes sign, indicating that the compositional convection becomes the main source of instability. Then the critical wave number mc decreases, and the drifting waves slow down drastically giving rise to an almost stationary pattern of convection. Negative gradients delay the onset of convection and determine a substantial increase of mc and ωc for Rc sufficiently high. Potential laws are obtained numerically from the dependence of Rec and of the critical frequency ωc on Rc, for the moderate and small Ekman numbers explored.Postprint (published version

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This study considers the onset of stress-free Boussinesq thermal convection in rotating spherical shells with aspect ratio η = ri/ro = 0.9 (ri and ro being the inner and outer radius), Prandtl numbers Pr ∈ [10 −4 , 10 −1 ], and Taylor numbers Ta ∈ [10 4 , 10 12 ]. We are particularly interested in the form of the convective cell pattern that develops, and in its time scales, since this may have observational consequences. For a fixed Ta < 10 9 and by decreasing Pr from 0.1 to 10 −4 a transition between spiralling columnar (SC) and equatorially-attached (EA) modes, and a transition between EA and equatorially antisymmetric or symmetric polar (AP/SP) weakly multicellular modes are found. The latter modes are preferred at very low Pr. Surprisingly, for Ta > 3 × 10 9 the unicellular polar modes become also preferred at moderate Pr ∼ 10 −2 because two new transition curves between EA and AP/SP and between AP/SP and SC modes are born at a triple-point bifurcation. The dependence on Pr and Ta of the transitions is studied to estimate the type of modes, and their critical parameters, preferred at different stellar regimes.

Experiments on the magnetised spherical Couette system are presently being carried out at Helmholtz‐Zentrum Dresden‐Rossendorf (HZDR). A liquid metal (GaInSn) is confined within two differentially rotating spheres and exposed to a magnetic field parallel to the axis of rotation. Intermittent chaotic flows, corresponding to the radial jet instability, are described. The relation of these chaotic flows with unstable regular (periodic and quasiperiodic) solutions obtained at the same range of parameters is investigated.

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After considering heating sector, one realises that there is no clear and consensual way to quantify or qualify the thermal comfort of the different technologies available to satisfy the heating demand of a home. This contribution tries to call attention to this by means of an experimental study of the thermal comfort provided by two very different technologies, an electrical heater and a heat pump. To do so, a test matrix is developed by considering [2]. Some experiments are carried out in a climate chamber constructed following [1]. The variables registered are used to determine the comfort variables defined in [3] for each technology. After both technologies are compared and some conclusions are drawn.