Idealised 3D simulations of diabatically forced Ledoux convection

Abstract

Aims. We investigate the impact of dimensionality, resolution, and long timescales on convective numerical simulations forced by thermo-compositional diabatic processes. We focus our study on simulations that are stable to the Schwarzschild criterion but unstable to the Ledoux one (i.e. simulations with a stabilising temperature gradient and a destabilising mean-molecular-weight gradient). We aim to establish the possibility of a reduced temperature gradient in such setups. Methods. A suite of 3D simulations incorporating both time series and convergence studies were conducted using a high-performance numerical hydrodynamic code. We used, as a simplified and idealised test case, a sample region of the secondary atmosphere of a hot rocky exoplanet, of the order of the scale height of the system, within which the chemical transition CO + O ↔ CO2 could occur. Newtonian cooling was employed to force an equilibrium temperature, and a chemical source term was used to maintain a negative mean-molecular-weight gradient in the vertical direction. Results. Our results demonstrate that a mean-molecular-weight gradient and a chemical source term can reduce the atmosphere temperature gradient, a result that does not converge away with resolution and is stable when exploring long timescales. Simulations in two dimensions are prone to the development of shear modes, as already seen in the literature for double-diffusive convection. The 3D convective steady state is not impacted by these shear modes, suggesting that this phenomenon is linked to the dimensionality of the problem. We also show that the presence of the reduced temperature gradient is a function of the forcing timescales, disappearing if the chemical forcing is too slow. We find that the above transition leads to a bifurcation of the atmosphere’s temperature profile when the chemical forcing is fast. Such a bifurcation is reminiscent of the bifurcation seen in the boiling crisis for steam or liquid convection. Conclusions. With the reduced temperature gradient in these idealised setups, there exists the possibility of an analogy of the reddening (currently observed in the spectra of brown dwarfs) in the spectra of rocky exoplanet atmospheres. This possibility needs, however, to be checked with detailed 1D models in order to precisely characterise the equilibrium thermal and compositional gradients, the thermal and compositional forcing timescales, and the impact of a realistic equation of state to, in turn, assess if the regime identified here will develop in realistic situations. However, the possibility of this reddening cannot be excluded a priori. This prediction is new for terrestrial atmospheres and represents strong motivation for the use of diabatic models when analysing the atmospheric spectra of rocky exoplanets that will be observed with, for example, the James Webb Space Telescope.