<p><b>mpetersen@lanl.gov</b> 2013-03-12 16:44:17 -0600 (Tue, 12 Mar 2013)</p><p>ocean user's guide: add namelist section descriptions.<br>
</p><hr noshade><pre><font color="gray">Modified: trunk/documents/users_guide/ocn/core_intro.tex
===================================================================
--- trunk/documents/users_guide/ocn/core_intro.tex 2013-03-12 21:48:33 UTC (rev 2594)
+++ trunk/documents/users_guide/ocn/core_intro.tex 2013-03-12 22:44:17 UTC (rev 2595)
@@ -1,7 +1,7 @@
\chapter{Governing Equations}
\label{chap:ocean-intro}
-({\bf To Be Addressed (TBA) 5.2, 5.3 are not in continuous form as stated in text}.) The governing equations for MPAS-Ocean, in continuous form, are\\ \\
+The governing equations for MPAS-Ocean are\\ \\
{\it momentum equation:}
\begin{equation}
\label{ocn:momentum continuous 1}
@@ -40,9 +40,8 @@
\rho = f_{eos}(\Theta,S,p)
\end{equation}
-Equations \ref{ocn:momentum continuous 1} through \ref{ocn:eos continuous 1} are a normal expression of the primitive equations; i.e. the incompressible Boussinesq equations in hydrostatic balance. Variable definitions are in Tables \ref{ocnTable:variables} and \ref{ocnTable:variables_Greek}. The momentum advection and Coriolis terms in (\ref{ocn:momentum continuous 1}) are presented in vorticity-kinetic energy form \citep[eqn 5]{Ringler_ea10jcp}.
+Equations \ref{ocn:momentum continuous 1} through \ref{ocn:eos continuous 1} are a normal expression of the primitive equations; i.e. the incompressible Boussinesq equations in hydrostatic balance. Variable definitions are in Tables \ref{ocnTable:variables} and \ref{ocnTable:variables_Greek}. The momentum advection and Coriolis terms in (\ref{ocn:momentum continuous 1}) are presented in vorticity-kinetic energy form \citep[eqn 5]{Ringler_ea10jcp}. The thickness and tracer equations describe a single layer in the vertical, where the operator $\overline{\left(\cdot\right)}^z$ is a vertical average over that layer (see derivation in Appedix A.2 of \citet{Ringler_ea13om}). Otherwise, \ref{ocn:momentum continuous 1}--\ref{ocn:eos continuous 1} are the model equations in continuous form. Details of the conversion to fully discretized equations are given in the appendices of \citet{Ringler_ea13om}.
-
\begin{table}[ht]
\caption{Latin variables used in prognostic equation set. Column 3 shows the native horizontal grid location. {\bf TBA. All variables are not at layer center as text states} All variables are located at the center of the layer in the vertical.}
\vspace{0.5cm} \centering
Modified: trunk/documents/users_guide/ocn/mpas_ocean.bib
===================================================================
--- trunk/documents/users_guide/ocn/mpas_ocean.bib 2013-03-12 21:48:33 UTC (rev 2594)
+++ trunk/documents/users_guide/ocn/mpas_ocean.bib 2013-03-12 22:44:17 UTC (rev 2595)
@@ -3,6 +3,17 @@
These references are specifically for the mpas-ocean core.
See the mpas_shared.bib file for references pertaining to all cores.
+%%%%%%%% mpas-ocean papers %%%%%%%%%
+
+@unpublished{Ringler_ea13om,
+author = {Ringler, TD and Petersen, MR and Higdon, R and Jacobsen, D and Jones, PW and Maltrud, M},
+title = {{A Muliti-resolution Approach to Global Ocean Modeling}},
+journal = {Ocean Modelling},
+year = {2013},
+note = "in press"
+}
+
+
%%%%%%%% grid and numerics %%%%%%%%%
@unpublished{Ringler06unpub,
Modified: trunk/documents/users_guide/ocn/namelist_table_documentation.tex
===================================================================
--- trunk/documents/users_guide/ocn/namelist_table_documentation.tex 2013-03-12 21:48:33 UTC (rev 2594)
+++ trunk/documents/users_guide/ocn/namelist_table_documentation.tex 2013-03-12 22:44:17 UTC (rev 2595)
@@ -60,6 +60,7 @@
}
\section[time\_integration]{\hyperref[sec:nm_sec_time_integration]{time\_integration}}
\label{sec:nm_tab_time_integration}
+\input{ocn/section_descriptions/time_integration.tex}
{\small
\begin{center}
\begin{longtable}{| p{2.0in} || p{4.0in} |}
Modified: trunk/documents/users_guide/ocn/section_descriptions/Rayleigh_damping.tex
===================================================================
--- trunk/documents/users_guide/ocn/section_descriptions/Rayleigh_damping.tex 2013-03-12 21:48:33 UTC (rev 2594)
+++ trunk/documents/users_guide/ocn/section_descriptions/Rayleigh_damping.tex 2013-03-12 22:44:17 UTC (rev 2595)
@@ -1 +1,2 @@
-A linear damping toward a state of rest is available with this namelist option.
+A linear damping toward a state of rest is available with this namelist option. It is implemented with a term on the RHS of the momentum equation of the form $-c_R {\bf u}$.
+
Modified: trunk/documents/users_guide/ocn/section_descriptions/hmix_del2.tex
===================================================================
--- trunk/documents/users_guide/ocn/section_descriptions/hmix_del2.tex 2013-03-12 21:48:33 UTC (rev 2594)
+++ trunk/documents/users_guide/ocn/section_descriptions/hmix_del2.tex 2013-03-12 22:44:17 UTC (rev 2595)
@@ -1,4 +1,4 @@
-{\bf TBA: biharmonic refers to del4, laplacian refers to del2.}The biharmonic, or Laplacian, turbulence closure is simply
+The ``del2'', or Laplacian, turbulence closures are
\begin{eqnarray}
\label{h_mom_diff_cont}
& {\bf D}^u_h=</font>
<font color="black">u_h </font>
<font color="black">abla^2 {\bf u} = </font>
<font color="black">u_h(</font>
<font color="gray">abla \delta + {\bf
@@ -6,23 +6,13 @@
\label{h_tr_diff_cont}
& D^\varphi_h = </font>
<font color="black">abla\cdot\left(h \kappa_h </font>
<font color="red">abla\varphi \right)
\end{eqnarray}
-in continuous form and
-\begin{eqnarray}
-\label{h_mom_diff_discrete}
-& \left[{\bf D}^u_h\right]_{k,e}
- =</font>
<font color="black">u_h([</font>
<font color="black">abla \delta_{k,:}]_{e} +[ {\bf k}\times </font>
<font color="red">abla
-\widehat{\eta}_{k,:}]_{e}),\\
-\label{h_tr_diff_discrete}
-& \left[D^\varphi_h\right]_{k,i}
- = [</font>
<font color="black">abla\cdot(\widehat{h}_{k,:} \kappa_h </font>
<font color="red">abla\varphi_{k,:} )]_{i}
-\end{eqnarray}
-in discrete form. The biharmonic operator smooths the momentum and
+for momentum and tracers, respectively. Variable definitions appear in Tables \ref{ocnTable:variables} and \ref{ocnTable:variables_Greek}. The momentum diffusion is in divergence-vorticity form because it is a natural discretization of the vector Laplacian operator with a C-grid staggering.
+
+
+The Laplacian operator smooths the momentum and
tracer fields, and smooths more strongly at small scales than at large
scales. This operator is the two dimensional form of the heat equation,
$u_t=</font>
<font color="black">u u_{xx}$, described in introductory books on partial
differential equations. The strength of mixing is controlled by the
viscosity, $</font>
<font color="gray">u_h$, for the momentum equation, and the diffusion,
$\kappa_h$, for the tracer equation.
-
-{\color{red} \bf to do: describe scaling with mesh, visc vorticity term, and apvm scale
-factor.}
Modified: trunk/documents/users_guide/ocn/section_descriptions/hmix_del4.tex
===================================================================
--- trunk/documents/users_guide/ocn/section_descriptions/hmix_del4.tex 2013-03-12 21:48:33 UTC (rev 2594)
+++ trunk/documents/users_guide/ocn/section_descriptions/hmix_del4.tex 2013-03-12 22:44:17 UTC (rev 2595)
@@ -1 +1,20 @@
-add specific form of biharmonic (del4) operator.
+{\color{red} TBA: check negative sign}
+The ``del4'', or biharmonic, turbulence closures are
+\begin{eqnarray}
+\label{h_mom_del4_cont}
+& {\bf D}^u_h=-</font>
<font color="black">u_h </font>
<font color="blue">abla^4 {\bf u} \\
+\label{h_tr_del4_cont}
+& D^\varphi_h = -</font>
<font color="black">abla\cdot\left(h \kappa_h </font>
<font color="black">abla \left[</font>
<font color="black">abla\cdot\left(h </font>
<font color="blue">abla\varphi \right) \right] \right)
+\end{eqnarray}
+for momentum and tracers, respectively. These are both computed by applying the Laplacian operator twice. For momentum, this can be written in terms of divergence and vorticity as
+\begin{eqnarray}
+&\delta=</font>
<font color="blue">abla\cdot{\bf u}\\
+&\eta={\bf k} \cdot \left( </font>
<font color="blue">abla \times {\bf u} \right)+f\\
+&</font>
<font color="black">abla^2{\bf u}=(</font>
<font color="black">abla \delta + {\bf k}\times </font>
<font color="blue">abla \eta) \\
+&\delta_2=</font>
<font color="black">abla\cdot(</font>
<font color="blue">abla^2{\bf u})\\
+&\eta_2={\bf k} \cdot \left( </font>
<font color="black">abla \times (</font>
<font color="blue">abla^2{\bf u}) \right)+f\\
+& {\bf D}^u_h= </font>
<font color="black">u_h (</font>
<font color="black">abla \delta_2 + {\bf k}\times </font>
<font color="gray">abla \eta_2)
+\label{h_tr_del4_cont}
+\end{eqnarray}
+
+The biharmonic operator is similar to the Laplacian operator, but smooths more strongly at high wavenumbers.
Added: trunk/documents/users_guide/ocn/section_descriptions/time_integration.tex
===================================================================
--- trunk/documents/users_guide/ocn/section_descriptions/time_integration.tex (rev 0)
+++ trunk/documents/users_guide/ocn/section_descriptions/time_integration.tex 2013-03-12 22:44:17 UTC (rev 2595)
@@ -0,0 +1 @@
+The time integration namelist controls parameters that pertain to all time-stepping methods. Options that are specific to a particular time-stepping method are contained in a separate namelist for that method, below.
</font>
</pre>