Scalar transport equations

Transport equations for generic scalar variables \(\phi_i\) are of the form

\begin{equation} \DD{\rhobar \phi_i}{t} = \parfrac{}{x_j} \left[ \left( \frac{\mu}{Sc} + \frac{\mu_T}{Sc_T} \right) \parfrac{\phi_i}{x_j} \right] \end{equation}

with the Schmidt number \(Sc\) and the turbulent Schmidt number \(Sc_T\).