Note on the conditional moment closure in turbulent shear flows

The general equation for the conditional expectation of a reactive scalar can be simplified for turbulent shear flows. The weak dependence of the conditional expectation on a coordinate across the shear flow, which was assumed earlier, is proved by asymptotic analysis. This analysis is an analog of the traditional boundary layer methods for the conventional (unconditional) expectations in turbulent flows, but it is carried out for the conditional expectation and the conserved scalar probability density function.