A New Model for Mixing by Double-Diffusive Convection (Semi-Convection). Iii. Thermal and Compositional Transport Through Non-Layered Oddc

Abstract

Oscillatory double-diffusive convection (ODDC; also known as semi-convection) refers to a type of doublediffusive instability that occurs in regions of planetary and stellar interiors that have a destabilizing thermal stratification and a stabilizing mean molecular weight stratification. In this series of papers, we use an extensive suite of three-dimensional (3D) numerical simulations to quantify the transport of heat and chemical species by ODDC. Rosenblum et al. first showed that ODDC can either spontaneously form layers that significantly enhance the transport of heat and chemical species compared to microscopic transport or remain in a state dominated by large-scale gravity waves, in which there is a more modest enhancement of the turbulent transport rates. Subsequent studies in this series focused on identifying under what conditions layers form and quantifying transport through layered systems. Here we proceed to characterize transport through systems that are unstable to ODDC, but do not undergo spontaneous layer formation. We measure the thermal and compositional fluxes in nonlayered ODDC from both two-dimensional (2D) and 3D numerical simulations, and show that 3D simulations are well approximated by similar simulations in a 2D domain. We find that the turbulent mixing rate in this regime is weak and can, to a first-level approximation, be neglected. We conclude by summarizing the findings of papers I through III into a single prescription for transport systems unstable to ODDC.

The Effect of Rotation on Oscillatory Double-Diffusive Convection (Semiconvection)

“…Importantly, as with the non-rotating simulation, layers never form at any point (when R −1 0 = 4.25). Consequently, fluxes through non-layered (high R −1 0 ) systems are effectively diffusive, and the conclusion from Moll et al (2016), namely that turbulent fluxes are negligible for non-layered systems, remains valid for all the simulations presented here.…”

Modelling of stellar convection

“…For instance, following comparisons between 2D and 3D direct numerical simulations of convection with a composition gradient of an active scalar (i.e., a gradient of helium in a mixture of hydrogen and helium in the case of a star), it was found that while layered semi-convection may well be investigated and quantitatively be described by 2D simulations (Moll et al. 2016 ), this is not the case in the fingering regime (Garaud and Brummell 2015 ). The latter can appear when the composition gradient drives the convective instability and is counteracted by the temperature gradient, which is just the other way round for layered semi-convection.…”

Computer simulations of Jupiter’s deep internal dynamics help interpret what Juno sees

“…That is, in this region, helium becomes insoluble in hydrogen and gravitationally falls through the fluid, which produces a stable layer with heavy fluid below light fluid. There may also be double-diffusive instabilities occurring below this layer due to very different molecular diffusion rates of temperature and heavy element composition in a region with a destabilizing (superadiabatic) thermal stratification and a stabilizing mean molecular weight stratification ( 31 ).…”