Question on the derivation of a prognostic equation for the mean concentration (Assume horizontal homogeneity in X)
In the question, T was not specifically mentioned to be a constant. So by also expanding $T = \overline{T} + t’$, we end up with the following answer. Where, the covariance term containing $\overline{c’t’}$ reflects that turbulence still plays a role in determining the mean quantity of C.