with dimensionless variables $ui$ is the fluid velocity, $p\u0302$ is the piezometric pressure, $\rho \u0303$ and $\rho *$ are the excess densities with respect to the reference density $\rho 0$ or the undisturbed background stratification $\rho H(z)$, respectively. Other parameters defined are: $Reeff$ is the effective Reynolds number, $Fr$ is the Froude number, $Pr$ is the Prandtl number, $Prturb$ is the turbulent Prandtl number, and $Rib$ is the bulk Richardson number. The effective viscosity is such that $1/\nu eff=1/\nu +1/\nu turb$, with $\nu $ is the fluid kinematic viscosity, and $\nu turb$ is the modeled turbulent viscosity; $g$ is the gravity acceleration. High Reynolds number conditions are assumed and $Pr\u2248Prturb\u22481$ for simplicity, but those assumptions are not necessarily valid for all stratified conditions, and these quantities will vary depending on the source of density difference and turbulence field. The turbulent viscosity, $\nu turb=k/\omega $, is obtained from a blended $k\u2212\epsilon /k\u2212\omega $ model, modified to include stratification effects. The turbulent kinetic energy $k$ and the specific dissipation rate $\omega $ are obtained from
Display Formula

(4)$\u2202k\u2202t+(uj\u2212\sigma k\u2202\nu turb\u2202xj)\u2202k\u2202xj\u22121Pek\u22022k\u2202xj2+Sk,0\u2212Rib\nu turb\sigma \rho \u2202\rho \u0303\u2202z=0$

Display Formula(5)$\u2202\omega \u2202t+(uj\u2212\sigma \omega \u2202\nu turb\u2202xj)\u2202\omega \u2202xj\u22121Pe\omega \u22022\omega \u2202xj2+S\omega ,0\u2212\alpha bRib\nu turb\sigma \rho \omega k\u2202\rho \u0303\u2202z=0$