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\section{Flux-form momentum equations} |
\section{Flux-form momentum equations} |
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\label{sect:flux-form_momentum_equations} |
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The original finite volume model was based on the Eulerian flux form |
The original finite volume model was based on the Eulerian flux form |
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momentum equations. This is the default though the vector invariant |
momentum equations. This is the default though the vector invariant |
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vertical momentum to hydrostatic balance. |
vertical momentum to hydrostatic balance. |
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These terms are calculated in routines called from subroutine {\em |
These terms are calculated in routines called from subroutine {\em |
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CALC\_MOM\_RHS} a collected into the global arrays {\bf Gu}, {\bf Gv}, |
MOM\_FLUXFORM} a collected into the global arrays {\bf Gu}, {\bf Gv}, |
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and {\bf Gw}. |
and {\bf Gw}. |
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\fbox{ \begin{minipage}{4.75in} |
\fbox{ \begin{minipage}{4.75in} |
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{\em S/R CALC\_MOM\_RHS} ({\em pkg/mom\_fluxform/calc\_mom\_rhs.F}) |
{\em S/R MOM\_FLUXFORM} ({\em pkg/mom\_fluxform/mom\_fluxform.F}) |
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$G_u$: {\bf Gu} ({\em DYNVARS.h}) |
$G_u$: {\bf Gu} ({\em DYNVARS.h}) |
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{\em S/R MOM\_U\_ADV\_WV} ({\em mom\_u\_adv\_wv.F}) |
{\em S/R MOM\_U\_ADV\_WV} ({\em mom\_u\_adv\_wv.F}) |
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$uu$, $uv$, $vu$, $vv$: {\bf aF} (local to {\em calc\_mom\_rhs.F}) |
$uu$, $uv$, $vu$, $vv$: {\bf aF} (local to {\em mom\_fluxform.F}) |
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\end{minipage} } |
\end{minipage} } |
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\end{eqnarray} |
\end{eqnarray} |
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where the Coriolis parameters $f$ and $f'$ are defined: |
where the Coriolis parameters $f$ and $f'$ are defined: |
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\begin{eqnarray} |
\begin{eqnarray} |
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f & = & 2 \Omega \sin{\phi} \\ |
f & = & 2 \Omega \sin{\varphi} \\ |
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f' & = & 2 \Omega \cos{\phi} |
f' & = & 2 \Omega \cos{\varphi} |
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\end{eqnarray} |
\end{eqnarray} |
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where $\phi$ is geographic latitude when using spherical geometry, |
where $\varphi$ is geographic latitude when using spherical geometry, |
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otherwise the $\beta$-plane definition is used: |
otherwise the $\beta$-plane definition is used: |
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\begin{eqnarray} |
\begin{eqnarray} |
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f & = & f_o + \beta y \\ |
f & = & f_o + \beta y \\ |
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\marginpar{Need to change the default in code to match this} |
\marginpar{Need to change the default in code to match this} |
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where the subscripts on $f$ and $f'$ indicate evaluation of the |
where the subscripts on $f$ and $f'$ indicate evaluation of the |
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Coriolis parameters at the appropriate points in space. The above |
Coriolis parameters at the appropriate points in space. The above |
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discretization does {\em not} conserve anything, especially energy. An |
discretization does {\em not} conserve anything, especially energy and |
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option to recover this discretization has been retained for backward |
for historical reasons is the default for the code. A |
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compatibility testing (set run-time logical {\bf |
flag controls this discretization: set run-time logical {\bf |
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useNonconservingCoriolis} to {\em true} which otherwise defaults to |
useEnergyConservingCoriolis} to {\em true} which otherwise defaults to |
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{\em false}). |
{\em false}. |
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\fbox{ \begin{minipage}{4.75in} |
\fbox{ \begin{minipage}{4.75in} |
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{\em S/R MOM\_CDSCHEME} ({\em mom\_cdscheme.F}) |
{\em S/R MOM\_CDSCHEME} ({\em mom\_cdscheme.F}) |
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{\em S/R MOM\_V\_CORIOLIS} ({\em mom\_v\_coriolis.F}) |
{\em S/R MOM\_V\_CORIOLIS} ({\em mom\_v\_coriolis.F}) |
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$G_u^{Cor}$, $G_v^{Cor}$: {\bf cF} (local to {\em calc\_mom\_rhs.F}) |
$G_u^{Cor}$, $G_v^{Cor}$: {\bf cF} (local to {\em mom\_fluxform.F}) |
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\end{minipage} } |
\end{minipage} } |
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\subsection{Curvature metric terms} |
\subsection{Curvature metric terms} |
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The most commonly used coordinate system on the sphere is the |
The most commonly used coordinate system on the sphere is the |
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geographic system $(\lambda,\phi)$. The curvilinear nature of these |
geographic system $(\lambda,\varphi)$. The curvilinear nature of these |
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coordinates on the sphere lead to some ``metric'' terms in the |
coordinates on the sphere lead to some ``metric'' terms in the |
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component momentum equations. Under the thin-atmosphere and |
component momentum equations. Under the thin-atmosphere and |
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hydrostatic approximations these terms are discretized: |
hydrostatic approximations these terms are discretized: |
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\begin{eqnarray} |
\begin{eqnarray} |
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{\cal A}_w \Delta r_f h_w G_u^{metric} & = & |
{\cal A}_w \Delta r_f h_w G_u^{metric} & = & |
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\overline{ \frac{ \overline{u}^i }{a} \tan{\phi} {\cal A}_c \Delta r_f h_c \overline{ v }^j }^i \\ |
\overline{ \frac{ \overline{u}^i }{a} \tan{\varphi} {\cal A}_c \Delta r_f h_c \overline{ v }^j }^i \\ |
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{\cal A}_s \Delta r_f h_s G_v^{metric} & = & |
{\cal A}_s \Delta r_f h_s G_v^{metric} & = & |
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- \overline{ \frac{ \overline{u}^i }{a} \tan{\phi} {\cal A}_c \Delta r_f h_c \overline{ u }^i }^j \\ |
- \overline{ \frac{ \overline{u}^i }{a} \tan{\varphi} {\cal A}_c \Delta r_f h_c \overline{ u }^i }^j \\ |
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G_w^{metric} & = & 0 |
G_w^{metric} & = & 0 |
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\end{eqnarray} |
\end{eqnarray} |
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where $a$ is the radius of the planet (sphericity is assumed) or the |
where $a$ is the radius of the planet (sphericity is assumed) or the |
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radial distance of the particle (i.e. a function of height). It is |
radial distance of the particle (i.e. a function of height). It is |
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easy to see that this discretization satisfies all the properties of |
easy to see that this discretization satisfies all the properties of |
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the discrete Coriolis terms since the metric factor $\frac{u}{a} |
the discrete Coriolis terms since the metric factor $\frac{u}{a} |
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\tan{\phi}$ can be viewed as a modification of the vertical Coriolis |
\tan{\varphi}$ can be viewed as a modification of the vertical Coriolis |
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parameter: $f \rightarrow f+\frac{u}{a} \tan{\phi}$. |
parameter: $f \rightarrow f+\frac{u}{a} \tan{\varphi}$. |
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However, as for the Coriolis terms, a non-energy conserving form has |
However, as for the Coriolis terms, a non-energy conserving form has |
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exclusively been used to date: |
exclusively been used to date: |
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\begin{eqnarray} |
\begin{eqnarray} |
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G_u^{metric} & = & \frac{u \overline{v}^{ij} }{a} \tan{\phi} \\ |
G_u^{metric} & = & \frac{u \overline{v}^{ij} }{a} \tan{\varphi} \\ |
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G_v^{metric} & = & \frac{ \overline{u}^{ij} \overline{u}^{ij}}{a} \tan{\phi} |
G_v^{metric} & = & \frac{ \overline{u}^{ij} \overline{u}^{ij}}{a} \tan{\varphi} |
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\end{eqnarray} |
\end{eqnarray} |
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where $\tan{\phi}$ is evaluated at the $u$ and $v$ points |
where $\tan{\varphi}$ is evaluated at the $u$ and $v$ points |
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respectively. |
respectively. |
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\fbox{ \begin{minipage}{4.75in} |
\fbox{ \begin{minipage}{4.75in} |
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{\em S/R MOM\_V\_METRIC\_SPHERE} ({\em mom\_v\_metric\_sphere.F}) |
{\em S/R MOM\_V\_METRIC\_SPHERE} ({\em mom\_v\_metric\_sphere.F}) |
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$G_u^{metric}$, $G_v^{metric}$: {\bf mT} (local to {\em calc\_mom\_rhs.F}) |
$G_u^{metric}$, $G_v^{metric}$: {\bf mT} (local to {\em mom\_fluxform.F}) |
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\end{minipage} } |
\end{minipage} } |
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For the non-hydrostatic equations, dropping the thin-atmosphere |
For the non-hydrostatic equations, dropping the thin-atmosphere |
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approximation re-introduces metric terms involving $w$ and are |
approximation re-introduces metric terms involving $w$ and are |
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required to conserve anglular momentum: |
required to conserve angular momentum: |
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\begin{eqnarray} |
\begin{eqnarray} |
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{\cal A}_w \Delta r_f h_w G_u^{metric} & = & |
{\cal A}_w \Delta r_f h_w G_u^{metric} & = & |
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- \overline{ \frac{ \overline{u}^i \overline{w}^k }{a} {\cal A}_c \Delta r_f h_c }^i \\ |
- \overline{ \frac{ \overline{u}^i \overline{w}^k }{a} {\cal A}_c \Delta r_f h_c }^i \\ |
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{\em S/R MOM\_V\_METRIC\_NH} ({\em mom\_v\_metric\_nh.F}) |
{\em S/R MOM\_V\_METRIC\_NH} ({\em mom\_v\_metric\_nh.F}) |
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$G_u^{metric}$, $G_v^{metric}$: {\bf mT} (local to {\em calc\_mom\_rhs.F}) |
$G_u^{metric}$, $G_v^{metric}$: {\bf mT} (local to {\em mom\_fluxform.F}) |
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\end{minipage} } |
\end{minipage} } |
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The lateral viscous stresses are discretized: |
The lateral viscous stresses are discretized: |
246 |
\begin{eqnarray} |
\begin{eqnarray} |
247 |
\tau_{11} & = & A_h c_{11\Delta}(\phi) \frac{1}{\Delta x_f} \delta_i u |
\tau_{11} & = & A_h c_{11\Delta}(\varphi) \frac{1}{\Delta x_f} \delta_i u |
248 |
-A_4 c_{11\Delta^2}(\phi) \frac{1}{\Delta x_f} \delta_i \nabla^2 u \\ |
-A_4 c_{11\Delta^2}(\varphi) \frac{1}{\Delta x_f} \delta_i \nabla^2 u \\ |
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\tau_{12} & = & A_h c_{12\Delta}(\phi) \frac{1}{\Delta y_u} \delta_j u |
\tau_{12} & = & A_h c_{12\Delta}(\varphi) \frac{1}{\Delta y_u} \delta_j u |
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-A_4 c_{12\Delta^2}(\phi)\frac{1}{\Delta y_u} \delta_j \nabla^2 u \\ |
-A_4 c_{12\Delta^2}(\varphi)\frac{1}{\Delta y_u} \delta_j \nabla^2 u \\ |
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\tau_{21} & = & A_h c_{21\Delta}(\phi) \frac{1}{\Delta x_v} \delta_i v |
\tau_{21} & = & A_h c_{21\Delta}(\varphi) \frac{1}{\Delta x_v} \delta_i v |
252 |
-A_4 c_{21\Delta^2}(\phi) \frac{1}{\Delta x_v} \delta_i \nabla^2 v \\ |
-A_4 c_{21\Delta^2}(\varphi) \frac{1}{\Delta x_v} \delta_i \nabla^2 v \\ |
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\tau_{22} & = & A_h c_{22\Delta}(\phi) \frac{1}{\Delta y_f} \delta_j v |
\tau_{22} & = & A_h c_{22\Delta}(\varphi) \frac{1}{\Delta y_f} \delta_j v |
254 |
-A_4 c_{22\Delta^2}(\phi) \frac{1}{\Delta y_f} \delta_j \nabla^2 v |
-A_4 c_{22\Delta^2}(\varphi) \frac{1}{\Delta y_f} \delta_j \nabla^2 v |
255 |
\end{eqnarray} |
\end{eqnarray} |
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where the non-dimensional factors $c_{lm\Delta^n}(\phi), \{l,m,n\} \in |
where the non-dimensional factors $c_{lm\Delta^n}(\varphi), \{l,m,n\} \in |
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\{1,2\}$ define the ``cosine'' scaling with latitude which can be |
\{1,2\}$ define the ``cosine'' scaling with latitude which can be |
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applied in various ad-hoc ways. For instance, $c_{11\Delta} = |
applied in various ad-hoc ways. For instance, $c_{11\Delta} = |
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c_{21\Delta} = (\cos{\phi})^{3/2}$, $c_{12\Delta}=c_{22\Delta}=0$ would |
c_{21\Delta} = (\cos{\varphi})^{3/2}$, $c_{12\Delta}=c_{22\Delta}=1$ would |
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represent the an-isotropic cosine scaling typically used on the |
represent the an-isotropic cosine scaling typically used on the |
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``lat-lon'' grid for Laplacian viscosity. |
``lat-lon'' grid for Laplacian viscosity. |
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\marginpar{Need to tidy up method for controlling this in code} |
\marginpar{Need to tidy up method for controlling this in code} |
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It should be noted that dispite the ad-hoc nature of the scaling, some |
It should be noted that despite the ad-hoc nature of the scaling, some |
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scaling must be done since on a lat-lon grid the converging meridians |
scaling must be done since on a lat-lon grid the converging meridians |
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make it very unlikely that a stable viscosity parameter exists across |
make it very unlikely that a stable viscosity parameter exists across |
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the entire model domain. |
the entire model domain. |
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{\em S/R MOM\_V\_YVISCFLUX} ({\em mom\_v\_yviscflux.F}) |
{\em S/R MOM\_V\_YVISCFLUX} ({\em mom\_v\_yviscflux.F}) |
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$\tau_{11}$, $\tau_{12}$, $\tau_{22}$, $\tau_{22}$: {\bf vF}, {\bf |
$\tau_{11}$, $\tau_{12}$, $\tau_{21}$, $\tau_{22}$: {\bf vF}, {\bf |
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v4F} (local to {\em calc\_mom\_rhs.F}) |
v4F} (local to {\em mom\_fluxform.F}) |
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\end{minipage} } |
\end{minipage} } |
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Two types of lateral boundary condition exist for the lateral viscous |
Two types of lateral boundary condition exist for the lateral viscous |
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The no-slip condition defines the normal gradient of a tangential flow |
The no-slip condition defines the normal gradient of a tangential flow |
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such that the flow is zero on the boundary. Rather than modify the |
such that the flow is zero on the boundary. Rather than modify the |
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stresses by using complicated functions of the masks and ``ghost'' |
stresses by using complicated functions of the masks and ``ghost'' |
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points (see \cite{Adcroft+Marshall98}) we add the boundary stresses as |
points (see \cite{adcroft:98}) we add the boundary stresses as |
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an additional source term in cells next to solid boundaries. This has |
an additional source term in cells next to solid boundaries. This has |
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the advantage of being able to cope with ``thin walls'' and also makes |
the advantage of being able to cope with ``thin walls'' and also makes |
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the interior stress calculation (code) independent of the boundary |
the interior stress calculation (code) independent of the boundary |
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\begin{eqnarray} |
\begin{eqnarray} |
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G_u^{side-drag} & = & |
G_u^{side-drag} & = & |
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\frac{4}{\Delta z_f} \overline{ (1-h_\zeta) \frac{\Delta x_v}{\Delta y_u} }^j |
\frac{4}{\Delta z_f} \overline{ (1-h_\zeta) \frac{\Delta x_v}{\Delta y_u} }^j |
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\left( A_h c_{12\Delta}(\phi) u - A_4 c_{12\Delta^2}(\phi) \nabla^2 u \right) |
\left( A_h c_{12\Delta}(\varphi) u - A_4 c_{12\Delta^2}(\varphi) \nabla^2 u \right) |
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\\ |
\\ |
307 |
G_v^{side-drag} & = & |
G_v^{side-drag} & = & |
308 |
\frac{4}{\Delta z_f} \overline{ (1-h_\zeta) \frac{\Delta y_u}{\Delta x_v} }^i |
\frac{4}{\Delta z_f} \overline{ (1-h_\zeta) \frac{\Delta y_u}{\Delta x_v} }^i |
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\left( A_h c_{21\Delta}(\phi) v - A_4 c_{21\Delta^2}(\phi) \nabla^2 v \right) |
\left( A_h c_{21\Delta}(\varphi) v - A_4 c_{21\Delta^2}(\varphi) \nabla^2 v \right) |
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\end{eqnarray} |
\end{eqnarray} |
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In fact, the above discretization is not quite complete because it |
In fact, the above discretization is not quite complete because it |
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assumes that the bathymetry at velocity points is deeper than at |
assumes that the bathymetry at velocity points is deeper than at |
314 |
neighbouring vorticity points, e.g. $1-h_w < 1-h_\zeta$ |
neighboring vorticity points, e.g. $1-h_w < 1-h_\zeta$ |
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\fbox{ \begin{minipage}{4.75in} |
\fbox{ \begin{minipage}{4.75in} |
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{\em S/R MOM\_U\_SIDEDRAG} ({\em mom\_u\_sidedrag.F}) |
{\em S/R MOM\_U\_SIDEDRAG} ({\em mom\_u\_sidedrag.F}) |
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{\em S/R MOM\_V\_SIDEDRAG} ({\em mom\_v\_sidedrag.F}) |
{\em S/R MOM\_V\_SIDEDRAG} ({\em mom\_v\_sidedrag.F}) |
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$G_u^{side-drag}$, $G_v^{side-drag}$: {\bf vF} (local to {\em calc\_mom\_rhs.F}) |
$G_u^{side-drag}$, $G_v^{side-drag}$: {\bf vF} (local to {\em mom\_fluxform.F}) |
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\end{minipage} } |
\end{minipage} } |
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to the variable grid lengths introduced by the finite volume |
to the variable grid lengths introduced by the finite volume |
329 |
formulation. This reduces the formal accuracy of these terms to just |
formulation. This reduces the formal accuracy of these terms to just |
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first order but only next to boundaries; exactly where other terms |
first order but only next to boundaries; exactly where other terms |
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appear such as linar and quadratic bottom drag. |
appear such as linear and quadratic bottom drag. |
332 |
\begin{eqnarray} |
\begin{eqnarray} |
333 |
G_u^{v-diss} & = & |
G_u^{v-diss} & = & |
334 |
\frac{1}{\Delta r_f h_w} \delta_k \tau_{13} \\ |
\frac{1}{\Delta r_f h_w} \delta_k \tau_{13} \\ |
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\tau_{33} & = & A_v \frac{1}{\Delta r_f} \delta_k w |
\tau_{33} & = & A_v \frac{1}{\Delta r_f} \delta_k w |
347 |
\end{eqnarray} |
\end{eqnarray} |
348 |
It should be noted that in the non-hydrostatic form, the stress tensor |
It should be noted that in the non-hydrostatic form, the stress tensor |
349 |
is even less consistent than for the hydrostatic (see Wazjowicz |
is even less consistent than for the hydrostatic (see |
350 |
\cite{Waojz}). It is well known how to do this properly (see Griffies |
\cite{wajsowicz:93}). It is well known how to do this properly (see |
351 |
\cite{Griffies}) and is on the list of to-do's. |
\cite{griffies:00}) and is on the list of to-do's. |
352 |
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\fbox{ \begin{minipage}{4.75in} |
\fbox{ \begin{minipage}{4.75in} |
354 |
{\em S/R MOM\_U\_RVISCLFUX} ({\em mom\_u\_rviscflux.F}) |
{\em S/R MOM\_U\_RVISCLFUX} ({\em mom\_u\_rviscflux.F}) |
355 |
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356 |
{\em S/R MOM\_V\_RVISCLFUX} ({\em mom\_v\_rviscflux.F}) |
{\em S/R MOM\_V\_RVISCLFUX} ({\em mom\_v\_rviscflux.F}) |
357 |
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|
358 |
$\tau_{13}$: {\bf urf} (local to {\em calc\_mom\_rhs.F}) |
$\tau_{13}$: {\bf urf} (local to {\em mom\_fluxform.F}) |
359 |
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|
360 |
$\tau_{23}$: {\bf vrf} (local to {\em calc\_mom\_rhs.F}) |
$\tau_{23}$: {\bf vrf} (local to {\em mom\_fluxform.F}) |
361 |
\end{minipage} } |
\end{minipage} } |
362 |
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363 |
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394 |
{\em S/R MOM\_V\_BOTTOMDRAG} ({\em mom\_v\_bottomdrag.F}) |
{\em S/R MOM\_V\_BOTTOMDRAG} ({\em mom\_v\_bottomdrag.F}) |
395 |
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396 |
$\tau_{13}^{bottom-drag}$, $\tau_{23}^{bottom-drag}$: {\bf vf} (local to {\em calc\_mom\_rhs.F}) |
$\tau_{13}^{bottom-drag}/\Delta r_f$, $\tau_{23}^{bottom-drag}/\Delta r_f$: |
397 |
|
{\bf vf} (local to {\em mom\_fluxform.F}) |
398 |
\end{minipage} } |
\end{minipage} } |
399 |
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\subsection{Derivation of discrete energy conservation} |
\subsection{Derivation of discrete energy conservation} |
406 |
\epsilon_{nh} \overline{ w^2 }^k \right) |
\epsilon_{nh} \overline{ w^2 }^k \right) |
407 |
\end{equation} |
\end{equation} |
408 |
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409 |
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\subsection{Mom Diagnostics} |
410 |
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\label{sec:pkg:mom_common:diagnostics} |
411 |
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412 |
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\begin{verbatim} |
413 |
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414 |
|
------------------------------------------------------------------------ |
415 |
|
<-Name->|Levs|<-parsing code->|<-- Units -->|<- Tile (max=80c) |
416 |
|
------------------------------------------------------------------------ |
417 |
|
VISCAHZ | 15 |SZ MR |m^2/s |Harmonic Visc Coefficient (m2/s) (Zeta Pt) |
418 |
|
VISCA4Z | 15 |SZ MR |m^4/s |Biharmonic Visc Coefficient (m4/s) (Zeta Pt) |
419 |
|
VISCAHD | 15 |SM MR |m^2/s |Harmonic Viscosity Coefficient (m2/s) (Div Pt) |
420 |
|
VISCA4D | 15 |SM MR |m^4/s |Biharmonic Viscosity Coefficient (m4/s) (Div Pt) |
421 |
|
VAHZMAX | 15 |SZ MR |m^2/s |CFL-MAX Harm Visc Coefficient (m2/s) (Zeta Pt) |
422 |
|
VA4ZMAX | 15 |SZ MR |m^4/s |CFL-MAX Biharm Visc Coefficient (m4/s) (Zeta Pt) |
423 |
|
VAHDMAX | 15 |SM MR |m^2/s |CFL-MAX Harm Visc Coefficient (m2/s) (Div Pt) |
424 |
|
VA4DMAX | 15 |SM MR |m^4/s |CFL-MAX Biharm Visc Coefficient (m4/s) (Div Pt) |
425 |
|
VAHZMIN | 15 |SZ MR |m^2/s |RE-MIN Harm Visc Coefficient (m2/s) (Zeta Pt) |
426 |
|
VA4ZMIN | 15 |SZ MR |m^4/s |RE-MIN Biharm Visc Coefficient (m4/s) (Zeta Pt) |
427 |
|
VAHDMIN | 15 |SM MR |m^2/s |RE-MIN Harm Visc Coefficient (m2/s) (Div Pt) |
428 |
|
VA4DMIN | 15 |SM MR |m^4/s |RE-MIN Biharm Visc Coefficient (m4/s) (Div Pt) |
429 |
|
VAHZLTH | 15 |SZ MR |m^2/s |Leith Harm Visc Coefficient (m2/s) (Zeta Pt) |
430 |
|
VA4ZLTH | 15 |SZ MR |m^4/s |Leith Biharm Visc Coefficient (m4/s) (Zeta Pt) |
431 |
|
VAHDLTH | 15 |SM MR |m^2/s |Leith Harm Visc Coefficient (m2/s) (Div Pt) |
432 |
|
VA4DLTH | 15 |SM MR |m^4/s |Leith Biharm Visc Coefficient (m4/s) (Div Pt) |
433 |
|
VAHZLTHD| 15 |SZ MR |m^2/s |LeithD Harm Visc Coefficient (m2/s) (Zeta Pt) |
434 |
|
VA4ZLTHD| 15 |SZ MR |m^4/s |LeithD Biharm Visc Coefficient (m4/s) (Zeta Pt) |
435 |
|
VAHDLTHD| 15 |SM MR |m^2/s |LeithD Harm Visc Coefficient (m2/s) (Div Pt) |
436 |
|
VA4DLTHD| 15 |SM MR |m^4/s |LeithD Biharm Visc Coefficient (m4/s) (Div Pt) |
437 |
|
VAHZSMAG| 15 |SZ MR |m^2/s |Smagorinsky Harm Visc Coefficient (m2/s) (Zeta Pt) |
438 |
|
VA4ZSMAG| 15 |SZ MR |m^4/s |Smagorinsky Biharm Visc Coeff. (m4/s) (Zeta Pt) |
439 |
|
VAHDSMAG| 15 |SM MR |m^2/s |Smagorinsky Harm Visc Coefficient (m2/s) (Div Pt) |
440 |
|
VA4DSMAG| 15 |SM MR |m^4/s |Smagorinsky Biharm Visc Coeff. (m4/s) (Div Pt) |
441 |
|
momKE | 15 |SM MR |m^2/s^2 |Kinetic Energy (in momentum Eq.) |
442 |
|
momHDiv | 15 |SM MR |s^-1 |Horizontal Divergence (in momentum Eq.) |
443 |
|
momVort3| 15 |SZ MR |s^-1 |3rd component (vertical) of Vorticity |
444 |
|
Strain | 15 |SZ MR |s^-1 |Horizontal Strain of Horizontal Velocities |
445 |
|
Tension | 15 |SM MR |s^-1 |Horizontal Tension of Horizontal Velocities |
446 |
|
UBotDrag| 15 |UU 129MR |m/s^2 |U momentum tendency from Bottom Drag |
447 |
|
VBotDrag| 15 |VV 128MR |m/s^2 |V momentum tendency from Bottom Drag |
448 |
|
USidDrag| 15 |UU 131MR |m/s^2 |U momentum tendency from Side Drag |
449 |
|
VSidDrag| 15 |VV 130MR |m/s^2 |V momentum tendency from Side Drag |
450 |
|
Um_Diss | 15 |UU 133MR |m/s^2 |U momentum tendency from Dissipation |
451 |
|
Vm_Diss | 15 |VV 132MR |m/s^2 |V momentum tendency from Dissipation |
452 |
|
Um_Advec| 15 |UU 135MR |m/s^2 |U momentum tendency from Advection terms |
453 |
|
Vm_Advec| 15 |VV 134MR |m/s^2 |V momentum tendency from Advection terms |
454 |
|
Um_Cori | 15 |UU 137MR |m/s^2 |U momentum tendency from Coriolis term |
455 |
|
Vm_Cori | 15 |VV 136MR |m/s^2 |V momentum tendency from Coriolis term |
456 |
|
Um_Ext | 15 |UU 137MR |m/s^2 |U momentum tendency from external forcing |
457 |
|
Vm_Ext | 15 |VV 138MR |m/s^2 |V momentum tendency from external forcing |
458 |
|
Um_AdvZ3| 15 |UU 141MR |m/s^2 |U momentum tendency from Vorticity Advection |
459 |
|
Vm_AdvZ3| 15 |VV 140MR |m/s^2 |V momentum tendency from Vorticity Advection |
460 |
|
Um_AdvRe| 15 |UU 143MR |m/s^2 |U momentum tendency from vertical Advection (Explicit part) |
461 |
|
Vm_AdvRe| 15 |VV 142MR |m/s^2 |V momentum tendency from vertical Advection (Explicit part) |
462 |
|
ADVx_Um | 15 |UM 145MR |m^4/s^2 |Zonal Advective Flux of U momentum |
463 |
|
ADVy_Um | 15 |VZ 144MR |m^4/s^2 |Meridional Advective Flux of U momentum |
464 |
|
ADVrE_Um| 15 |WU LR |m^4/s^2 |Vertical Advective Flux of U momentum (Explicit part) |
465 |
|
ADVx_Vm | 15 |UZ 148MR |m^4/s^2 |Zonal Advective Flux of V momentum |
466 |
|
ADVy_Vm | 15 |VM 147MR |m^4/s^2 |Meridional Advective Flux of V momentum |
467 |
|
ADVrE_Vm| 15 |WV LR |m^4/s^2 |Vertical Advective Flux of V momentum (Explicit part) |
468 |
|
VISCx_Um| 15 |UM 151MR |m^4/s^2 |Zonal Viscous Flux of U momentum |
469 |
|
VISCy_Um| 15 |VZ 150MR |m^4/s^2 |Meridional Viscous Flux of U momentum |
470 |
|
VISrE_Um| 15 |WU LR |m^4/s^2 |Vertical Viscous Flux of U momentum (Explicit part) |
471 |
|
VISrI_Um| 15 |WU LR |m^4/s^2 |Vertical Viscous Flux of U momentum (Implicit part) |
472 |
|
VISCx_Vm| 15 |UZ 155MR |m^4/s^2 |Zonal Viscous Flux of V momentum |
473 |
|
VISCy_Vm| 15 |VM 154MR |m^4/s^2 |Meridional Viscous Flux of V momentum |
474 |
|
VISrE_Vm| 15 |WV LR |m^4/s^2 |Vertical Viscous Flux of V momentum (Explicit part) |
475 |
|
VISrI_Vm| 15 |WV LR |m^4/s^2 |Vertical Viscous Flux of V momentum (Implicit part) |
476 |
|
\end{verbatim} |