Abstract
The local equations of Xiong's theory of convection with one-point correlation functions contain the equations for an extended mixing length theory of convection with helium flux by Umezu & Nakakita. The equations also contain the equations for overstable convection of Kato. Similar equations can be derived from those of Grossman et al. and Canuto. The local convection and the overstable convection can be treated in a unified way with their localized equations.
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