Convection in an ideal gas at high Rayleigh numbers

Numerical simulations of convection in a layer filled with ideal gas are presented. The control parameters are chosen such that there is a significant variation of density of the gas in going from the bottom to the top of the layer. The relations between the Rayleigh, Peclet and Nusselt numbers depend on the density stratification. It is proposed to use a data reduction which accounts for the variable density by introducing into the scaling laws an effective density. The relevant density is the geometric mean of the maximum and minimum densities in the layer. A good fit to the data is then obtained with power laws with the same exponent as for fluids in the Boussinesq limit. Two relations connect the top and bottom boundary layers: The kinetic energy densities computed from free fall velocities are equal at the top and bottom, and the products of free fall velocities and maximum horizontal velocities are equal for both boundaries

Elliptical instability of compressible flow in ellipsoids

Elliptical instability is due to a parametric resonance of two inertial modes in a fluid velocity field with elliptical streamlines. This flow is a simple model of the motion in a tidally deformed, rotating body. Elliptical instability typically leads to three-dimensional turbulence. The associated turbulent dissipation together with the dissipation of the large scale mode may be important for the synchronization process in stellar and planetary binary systems. In order to determine the influence of the compressibility on the stability limits of tidal flows in stars or planets, we calculate the growth rates of perturbations in flows with elliptical streamlines within ellipsoidal boundaries of small ellipticity. In addition, the influence of the orbiting frequency of the tidal perturber $\Omega_P$ and the viscosity of the fluid are taken into account

Transition to finger convection in double-diffusive convection

Finger convection is observed experimentally in an electrodeposition cell in which a destabilizing gradient of copper ions is maintained against a stabilizing temperature gradient. This double-diffusive system shows finger convection even if the total density stratification is unstable. Finger convection is replaced by an ordinary convection roll if convection is fast enough to prevent sufficient heat diffusion between neighboring fingers, or if the thermal buoyancy force is less than 1/30 of the compositional buoyancy force. At the transition, the ion transport is larger than without an opposing temperature gradient

Transitions in turbulent rotating Rayleigh-B\'enard convection

Numerical simulations of rotating Rayleigh-B\'enard convection are presented for both no slip and free slip boundaries. The goal is to find a criterion distinguishing convective flows dominated by the Coriolis force from those nearly unaffected by rotation. If one uses heat transport as an indicator of which regime the flow is in, one finds that the transition between the flow regimes always occurs at the same value of a certain combination of Reynolds, Prandtl and Ekman numbers for both boundary conditions. If on the other hand one uses the helicity of the velocity field to identify flows nearly independent of rotation, one finds the transition at a different location in parameter space

High Rayleigh number convection with double diffusive fingers

An electrodeposition cell is used to sustain a destabilizing concentration difference of copper ions in aqueous solution between the top and bottom boundaries of the cell. The resulting convecting motion is analogous to Rayleigh-B\'enard convection at high Prandtl numbers. In addition, a stabilizing temperature gradient is imposed across the cell. Even for thermal buoyancy two orders of magnitude smaller than chemical buoyancy, the presence of the weak stabilizing gradient has a profound effect on the convection pattern. Double diffusive fingers appear in all cases. The size of these fingers and the flow velocities are independent of the height of the cell, but they depend on the ion concentration difference between top and bottom boundaries as well as on the imposed temperature gradient. The scaling of the mass transport is compatible with previous results on double diffusive convection

Treatment of non-ideality in the SPACCIM multiphase model – Part 1: Model development

Ambient tropospheric deliquesced particles generally comprise a complex mixture of electrolytes, organic compounds, and water. Dynamic modeling of physical and chemical processes in this complex matrix is challenging. Thus, up-to-date multiphase chemistry models generally do not consider non-ideal solution effects. Therefore, the present study was aimed at presenting further development of the SPACCIM (Spectral Aerosol Cloud Chemistry Interaction Model) through treatment of solution non-ideality, which has not been considered before. The present paper firstly describes the model developments including (i) the implementation of solution non-ideality in aqueous-phase reaction kinetics in the SPACCIM framework, (ii) the advancements in the coupling scheme of microphysics and multiphase chemistry and (iii) the required adjustments of the numerical schemes, especially in the sparse linear solver and the calculation of the Jacobian. Secondly, results of sensitivity investigations are outlined, aiming at the evaluation of different activity coefficient modules and the examination of the contributions of different intermolecular forces to the overall activity coefficients. Finally, first results obtained with the new model framework are presented. The SPACCIM parcel model was developed and, so far, applied for the description of aerosol–cloud interactions. To advance SPACCIM also for modeling physical and chemical processes in deliquesced particles, the solution non-ideality has to be taken into account by utilizing activities in reaction terms instead of aqueous concentrations. The main goal of the extended approach was to provide appropriate activity coefficients for solved species. Therefore, an activity coefficient module was incorporated into the kinetic model framework of SPACCIM. Based on an intercomparison of different activity coefficient models and the comparison with experimental data, the AIOMFAC approach was implemented and extended by additional interaction parameters from the literature for mixed organic–inorganic systems. Moreover, the performance and the capability of the applied activity coefficient module were evaluated by means of water activity measurements, literature data and results of other activity coefficient models. Comprehensive comparison studies showed that the SpactMod (SPACCIM activity coefficient module) is valuable for predicting the thermodynamic behavior of complex mixtures of multicomponent atmospheric aerosol particles. First simulations with a detailed chemical mechanism have demonstrated the applicability of SPACCIM-SpactMod. The simulations indicate that the treatment of solution non-ideality might be needed for modeling multiphase chemistry processes in deliquesced particles. The modeled activity coefficients imply that chemical reaction fluxes of chemical processes in deliquesced particles can be both decreased and increased depending on the particular species involved in the reactions. For key ions, activity coefficients on the order of 0.1–0.8 and a strong dependency on the charge state as well as the RH conditions are modeled, implying a lowered chemical processing of ions in concentrated solutions. In contrast, modeled activity coefficients of organic compounds are in some cases larger than 1 under deliquesced particle conditions and suggest the possibility of an increased chemical processing of organic compounds. Moreover, the model runs have shown noticeable differences in the pH values calculated with and without consideration of solution non-ideality. On average, the predicted pH values of the simulations considering solution non-ideality are -0.27 and -0.44 pH units lower under 90 and 70%RH con- ditions, respectively. More comprehensive results of detailed SPACCIM-SpactMod studies on the multiphase processing in organic–inorganic mixtures of deliquesced particles are described in a companion paper