A New Model for Mixing By Double-Diffusive Convection (Semi-Convection). III. Thermal and Compositional Transport Through Non-Layered ODDC

TL;DR

This paper investigates heat and chemical transport in non-layered oscillatory double-diffusive convection (ODDC) through 3D simulations, revealing weak turbulent mixing and providing a unified transport prescription.

Contribution

It characterizes transport in non-layered ODDC systems, showing 2D simulations suffice and turbulent mixing is minimal, extending previous layered system studies.

Findings

3D simulations are well approximated by 2D simulations.

Turbulent mixing in non-layered ODDC is weak and often negligible.

Provides a unified transport prescription for ODDC based on multiple studies.

Abstract

Oscillatory double-diffusive convection (ODDC) (also known as semi- convection) refers to a type of double diffusive instability that occurs in regions of planetary and stellar interiors which 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. (2011) first showed that ODDC can either spontaneously form layers, which significantly enhance the transport of heat and chemical species compared to mi- croscopic 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 have focused on identifying under what condi- tions layers form (Mirouh et al. 2012), and quantifying transport through layered systems (Wood et al. 2013). Here we proceed to characterize transport through systems that are unstable to the ODDC instability, but do not undergo spon- taneous layer formation. We measure the thermal and compositional fluxes in non-layered ODDC from both 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 by ODDC.