$$ \frac{\partial \overline{u_i u_j}}{\partial t}+C_{ij} = P_{ij}+\Phi_{ij}+d^{\nu}_{ij}+d^{t}_{ij}+d^{p}_{ij}-\varepsilon_{ij} $$

Convection term $$ C_{ij}=U_k\,\frac{\partial \overline{u_i u_j}}{\partial x_k} $$

Production term $$ P_{ij}=-\Big(\,\overline{u_i u_k}\,\frac{\partial U_j}{\partial x_k} +\overline{u_j u_k}\,\frac{\partial U_i}{\partial x_k}\Big) $$

Pressure-strain-rate correlation $$ \Phi_{ij}= \overline{\frac{p}{\rho}\Big(\frac{\partial u_i}{\partial x_j} +\frac{\partial u_j}{\partial x_i}\Big)} $$

Molecular diffusion $$ d^{\nu}_{ij}=\frac{\partial}{\partial x_k} \Big(\nu\,\frac{\partial \overline{u_i u_j}}{\partial x_k}\Big) $$

Velocity-fluctuation diffusion $$ d^{t}_{ij}=-\,\frac{\partial}{\partial x_k}\overline{u_i u_j u_k} $$

Pressure-fluctuation diffusion $$ d^{p}_{ij}=-\,\frac{\partial}{\partial x_k} \!\left(\frac{\overline{p\,u_j}}{\rho}\,\delta_{ik} +\frac{\overline{p\,u_i}}{\rho}\,\delta_{jk}\right) $$

Viscous dissipation $$ \varepsilon_{ij}=2\nu\,\overline{\frac{\partial u_i}{\partial x_k} \frac{\partial u_j}{\partial x_k}} $$