Tracer Equation

The tracer equation is obtained using the same calculation as for the continuity equation and then regrouping the time derivative terms in the left hand side :

$$\begin{multline} \frac{1}{e_3} \frac{\partial \left( e_3 T \right)}{\partial t}... ...} \frac{\partial }{\partial k} \left( Tw \right) + D^{T} +F^{T} \end{multline}$$

The expression for the advection term is a straight consequence of (A.4), the expression of the 3D divergence in the $s-$coordinates established above.