From 6ea1665ffb9db4210e45a9664c602d261326ea9b Mon Sep 17 00:00:00 2001 From: lumlauf <lars.umlauf@io-warnemuende.de> Date: Wed, 29 May 2024 18:26:09 +0200 Subject: [PATCH] added description for omega equation --- src/turbulence/omegaeq.F90 | 49 ++++++++++++++++++++++++++++++++++++-- 1 file changed, 47 insertions(+), 2 deletions(-) diff --git a/src/turbulence/omegaeq.F90 b/src/turbulence/omegaeq.F90 index 5c654e12..0be3fb6e 100644 --- a/src/turbulence/omegaeq.F90 +++ b/src/turbulence/omegaeq.F90 @@ -8,8 +8,53 @@ subroutine omegaeq(nlev,dt,u_taus,u_taub,z0s,z0b,h,NN,SS) ! !DESCRIPTION: -! Under construction. Please refer to Umlauf et al. (2003) and Umlauf and Burchard (2003) -! for the basic documentation of the $k$-$\omega$ model and its boundary conditions. +! The $k$-$\omega$ model described by \cite{UmlaufEtAl3003} solves +! a transport equation for the inverse turbulence time scale, +! $ \omega = (c_\mu^0)^4 \varepsilon /k$, of the following form: +! \begin{equation} +! \label{omega} +! \dot{\omega} +! = +! {\cal D}_\omega +! + \frac{\omega}{k} ( c_{\omega 1} P + c_{\omega 3} G +! - c_{\omega 2} \varepsilon ) +! \comma +! \end{equation} +! where $\dot{\omega}$ denotes the material derivative of $\omega$. +! The production terms $P$ and $G$ follow from \eq{PandG} and +! ${\cal D}_\omega$ represents the sum of the viscous and turbulent +! transport terms. +! +! For horizontally homogeneous flows, the transport term ${\cal D}_\omega$ +! appearing in \eq{dissipation} is presently expressed by a simple +! gradient formulation, +! \begin{equation} +! \label{diffusionOmega} +! {\cal D}_\omega = \frstder{z} +! \left( \dfrac{\nu_t}{\sigma_\omega} \partder{\omega}{z} \right) +! \comma +! \end{equation} +! where $\sigma_\omega$ is the constant Schmidt-number for $\omega$. +! +! Model constants are summarized in \tab{tab:KW_constants}. Similar +! to the two-equations models, the model parameter $c_{omega 3}$ +! determines the value of the stationory Richardson number. It is +! computed numerically by solving \eq{Ri_st}. +! \begin{table}[ht] +! \begin{center} +! \begin{tabular}{cccccc} +! & $c_\mu^0$ & $\sigma_k$ & $\sigma_\omega$ +! & $c_{\omega 1}$ & $c_{\omega 2}$ \\[1mm] \hline +! \cite{Rodi87} & $0.55$ & $2.0$ & $2.0$ & $0.56$ & $0.83$ \\ +! \end{tabular} +! \caption{\label{tab:KW_constants} Constants appearing in +! \eq{omega} and \eq{diffusionOmega}.} +! \end{center} +! \end{table} +! +! At the end of this routine the length-scale can be constrained according to a +! suggestion of \cite{Galperinetal88}. This feature is optional and can be activated +! by setting {\tt length\_lim = .true.} in {\tt gotm.yaml}. ! ! !USES: use turbulence, only: P,B,PSTK,num