  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.
