| 2 |
% $Name$ |
% $Name$ |
| 3 |
|
|
| 4 |
\section{Flux-form momentum equations} |
\section{Flux-form momentum equations} |
| 5 |
|
\label{sect:flux-form_momentum_equations} |
| 6 |
|
\begin{rawhtml} |
| 7 |
|
<!-- CMIREDIR:flux-form_momentum_eqautions: --> |
| 8 |
|
\end{rawhtml} |
| 9 |
|
|
| 10 |
The original finite volume model was based on the Eulerian flux form |
The original finite volume model was based on the Eulerian flux form |
| 11 |
momentum equations. This is the default though the vector invariant |
momentum equations. This is the default though the vector invariant |
| 110 |
\end{eqnarray} |
\end{eqnarray} |
| 111 |
where the Coriolis parameters $f$ and $f'$ are defined: |
where the Coriolis parameters $f$ and $f'$ are defined: |
| 112 |
\begin{eqnarray} |
\begin{eqnarray} |
| 113 |
f & = & 2 \Omega \sin{\phi} \\ |
f & = & 2 \Omega \sin{\varphi} \\ |
| 114 |
f' & = & 2 \Omega \cos{\phi} |
f' & = & 2 \Omega \cos{\varphi} |
| 115 |
\end{eqnarray} |
\end{eqnarray} |
| 116 |
where $\phi$ is geographic latitude when using spherical geometry, |
where $\varphi$ is geographic latitude when using spherical geometry, |
| 117 |
otherwise the $\beta$-plane definition is used: |
otherwise the $\beta$-plane definition is used: |
| 118 |
\begin{eqnarray} |
\begin{eqnarray} |
| 119 |
f & = & f_o + \beta y \\ |
f & = & f_o + \beta y \\ |
| 136 |
\marginpar{Need to change the default in code to match this} |
\marginpar{Need to change the default in code to match this} |
| 137 |
where the subscripts on $f$ and $f'$ indicate evaluation of the |
where the subscripts on $f$ and $f'$ indicate evaluation of the |
| 138 |
Coriolis parameters at the appropriate points in space. The above |
Coriolis parameters at the appropriate points in space. The above |
| 139 |
discretization does {\em not} conserve anything, especially energy. An |
discretization does {\em not} conserve anything, especially energy and |
| 140 |
option to recover this discretization has been retained for backward |
for historical reasons is the default for the code. A |
| 141 |
compatibility testing (set run-time logical {\bf |
flag controls this discretization: set run-time logical {\bf |
| 142 |
useNonconservingCoriolis} to {\em true} which otherwise defaults to |
useEnergyConservingCoriolis} to {\em true} which otherwise defaults to |
| 143 |
{\em false}). |
{\em false}. |
| 144 |
|
|
| 145 |
\fbox{ \begin{minipage}{4.75in} |
\fbox{ \begin{minipage}{4.75in} |
| 146 |
{\em S/R MOM\_CDSCHEME} ({\em mom\_cdscheme.F}) |
{\em S/R MOM\_CDSCHEME} ({\em mom\_cdscheme.F}) |
| 156 |
\subsection{Curvature metric terms} |
\subsection{Curvature metric terms} |
| 157 |
|
|
| 158 |
The most commonly used coordinate system on the sphere is the |
The most commonly used coordinate system on the sphere is the |
| 159 |
geographic system $(\lambda,\phi)$. The curvilinear nature of these |
geographic system $(\lambda,\varphi)$. The curvilinear nature of these |
| 160 |
coordinates on the sphere lead to some ``metric'' terms in the |
coordinates on the sphere lead to some ``metric'' terms in the |
| 161 |
component momentum equations. Under the thin-atmosphere and |
component momentum equations. Under the thin-atmosphere and |
| 162 |
hydrostatic approximations these terms are discretized: |
hydrostatic approximations these terms are discretized: |
| 163 |
\begin{eqnarray} |
\begin{eqnarray} |
| 164 |
{\cal A}_w \Delta r_f h_w G_u^{metric} & = & |
{\cal A}_w \Delta r_f h_w G_u^{metric} & = & |
| 165 |
\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 \\ |
| 166 |
{\cal A}_s \Delta r_f h_s G_v^{metric} & = & |
{\cal A}_s \Delta r_f h_s G_v^{metric} & = & |
| 167 |
- \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 \\ |
| 168 |
G_w^{metric} & = & 0 |
G_w^{metric} & = & 0 |
| 169 |
\end{eqnarray} |
\end{eqnarray} |
| 170 |
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 |
| 171 |
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 |
| 172 |
easy to see that this discretization satisfies all the properties of |
easy to see that this discretization satisfies all the properties of |
| 173 |
the discrete Coriolis terms since the metric factor $\frac{u}{a} |
the discrete Coriolis terms since the metric factor $\frac{u}{a} |
| 174 |
\tan{\phi}$ can be viewed as a modification of the vertical Coriolis |
\tan{\varphi}$ can be viewed as a modification of the vertical Coriolis |
| 175 |
parameter: $f \rightarrow f+\frac{u}{a} \tan{\phi}$. |
parameter: $f \rightarrow f+\frac{u}{a} \tan{\varphi}$. |
| 176 |
|
|
| 177 |
However, as for the Coriolis terms, a non-energy conserving form has |
However, as for the Coriolis terms, a non-energy conserving form has |
| 178 |
exclusively been used to date: |
exclusively been used to date: |
| 179 |
\begin{eqnarray} |
\begin{eqnarray} |
| 180 |
G_u^{metric} & = & \frac{u \overline{v}^{ij} }{a} \tan{\phi} \\ |
G_u^{metric} & = & \frac{u \overline{v}^{ij} }{a} \tan{\varphi} \\ |
| 181 |
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} |
| 182 |
\end{eqnarray} |
\end{eqnarray} |
| 183 |
where $\tan{\phi}$ is evaluated at the $u$ and $v$ points |
where $\tan{\varphi}$ is evaluated at the $u$ and $v$ points |
| 184 |
respectively. |
respectively. |
| 185 |
|
|
| 186 |
\fbox{ \begin{minipage}{4.75in} |
\fbox{ \begin{minipage}{4.75in} |
| 197 |
|
|
| 198 |
For the non-hydrostatic equations, dropping the thin-atmosphere |
For the non-hydrostatic equations, dropping the thin-atmosphere |
| 199 |
approximation re-introduces metric terms involving $w$ and are |
approximation re-introduces metric terms involving $w$ and are |
| 200 |
required to conserve anglular momentum: |
required to conserve angular momentum: |
| 201 |
\begin{eqnarray} |
\begin{eqnarray} |
| 202 |
{\cal A}_w \Delta r_f h_w G_u^{metric} & = & |
{\cal A}_w \Delta r_f h_w G_u^{metric} & = & |
| 203 |
- \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 \\ |
| 244 |
|
|
| 245 |
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 \\ |
| 249 |
\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 |
| 250 |
-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 \\ |
| 251 |
\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 \\ |
| 253 |
\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} |
| 256 |
where the non-dimensional factors $c_{lm\Delta^n}(\phi), \{l,m,n\} \in |
where the non-dimensional factors $c_{lm\Delta^n}(\varphi), \{l,m,n\} \in |
| 257 |
\{1,2\}$ define the ``cosine'' scaling with latitude which can be |
\{1,2\}$ define the ``cosine'' scaling with latitude which can be |
| 258 |
applied in various ad-hoc ways. For instance, $c_{11\Delta} = |
applied in various ad-hoc ways. For instance, $c_{11\Delta} = |
| 259 |
c_{21\Delta} = (\cos{\phi})^{3/2}$, $c_{12\Delta}=c_{22\Delta}=0$ would |
c_{21\Delta} = (\cos{\varphi})^{3/2}$, $c_{12\Delta}=c_{22\Delta}=0$ would |
| 260 |
represent the an-isotropic cosine scaling typically used on the |
represent the an-isotropic cosine scaling typically used on the |
| 261 |
``lat-lon'' grid for Laplacian viscosity. |
``lat-lon'' grid for Laplacian viscosity. |
| 262 |
\marginpar{Need to tidy up method for controlling this in code} |
\marginpar{Need to tidy up method for controlling this in code} |
| 263 |
|
|
| 264 |
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 |
| 265 |
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 |
| 266 |
make it very unlikely that a stable viscosity parameter exists across |
make it very unlikely that a stable viscosity parameter exists across |
| 267 |
the entire model domain. |
the entire model domain. |
| 294 |
The no-slip condition defines the normal gradient of a tangential flow |
The no-slip condition defines the normal gradient of a tangential flow |
| 295 |
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 |
| 296 |
stresses by using complicated functions of the masks and ``ghost'' |
stresses by using complicated functions of the masks and ``ghost'' |
| 297 |
points (see \cite{Adcroft+Marshall98}) we add the boundary stresses as |
points (see \cite{adcroft:98}) we add the boundary stresses as |
| 298 |
an additional source term in cells next to solid boundaries. This has |
an additional source term in cells next to solid boundaries. This has |
| 299 |
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 |
| 300 |
the interior stress calculation (code) independent of the boundary |
the interior stress calculation (code) independent of the boundary |
| 302 |
\begin{eqnarray} |
\begin{eqnarray} |
| 303 |
G_u^{side-drag} & = & |
G_u^{side-drag} & = & |
| 304 |
\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 |
| 305 |
\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) |
| 306 |
\\ |
\\ |
| 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 |
| 309 |
\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) |
| 310 |
\end{eqnarray} |
\end{eqnarray} |
| 311 |
|
|
| 312 |
In fact, the above discretization is not quite complete because it |
In fact, the above discretization is not quite complete because it |
| 313 |
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. $1-h_w < 1-h_\zeta$ |
| 315 |
|
|
| 316 |
\fbox{ \begin{minipage}{4.75in} |
\fbox{ \begin{minipage}{4.75in} |
| 317 |
{\em S/R MOM\_U\_SIDEDRAG} ({\em mom\_u\_sidedrag.F}) |
{\em S/R MOM\_U\_SIDEDRAG} ({\em mom\_u\_sidedrag.F}) |
| 328 |
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 |
| 330 |
first order but only next to boundaries; exactly where other terms |
first order but only next to boundaries; exactly where other terms |
| 331 |
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} \\ |
| 346 |
\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 |
|
|
| 353 |
\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}) |
| 405 |
\epsilon_{nh} \overline{ w^2 }^k \right) |
\epsilon_{nh} \overline{ w^2 }^k \right) |
| 406 |
\end{equation} |
\end{equation} |
| 407 |
|
|
| 408 |
|
\subsection{Mom Diagnostics} |
| 409 |
|
\label{sec:pkg:mom_common:diagnostics} |
| 410 |
|
|
| 411 |
|
\begin{verbatim} |
| 412 |
|
|
| 413 |
|
------------------------------------------------------------------------ |
| 414 |
|
<-Name->|Levs|<-parsing code->|<-- Units -->|<- Tile (max=80c) |
| 415 |
|
------------------------------------------------------------------------ |
| 416 |
|
VISCAHZ | 15 |SZ MR |m^2/s |Harmonic Visc Coefficient (m2/s) (Zeta Pt) |
| 417 |
|
VISCA4Z | 15 |SZ MR |m^4/s |Biharmonic Visc Coefficient (m4/s) (Zeta Pt) |
| 418 |
|
VISCAHD | 15 |SM MR |m^2/s |Harmonic Viscosity Coefficient (m2/s) (Div Pt) |
| 419 |
|
VISCA4D | 15 |SM MR |m^4/s |Biharmonic Viscosity Coefficient (m4/s) (Div Pt) |
| 420 |
|
VAHZMAX | 15 |SZ MR |m^2/s |CFL-MAX Harm Visc Coefficient (m2/s) (Zeta Pt) |
| 421 |
|
VA4ZMAX | 15 |SZ MR |m^4/s |CFL-MAX Biharm Visc Coefficient (m4/s) (Zeta Pt) |
| 422 |
|
VAHDMAX | 15 |SM MR |m^2/s |CFL-MAX Harm Visc Coefficient (m2/s) (Div Pt) |
| 423 |
|
VA4DMAX | 15 |SM MR |m^4/s |CFL-MAX Biharm Visc Coefficient (m4/s) (Div Pt) |
| 424 |
|
VAHZMIN | 15 |SZ MR |m^2/s |RE-MIN Harm Visc Coefficient (m2/s) (Zeta Pt) |
| 425 |
|
VA4ZMIN | 15 |SZ MR |m^4/s |RE-MIN Biharm Visc Coefficient (m4/s) (Zeta Pt) |
| 426 |
|
VAHDMIN | 15 |SM MR |m^2/s |RE-MIN Harm Visc Coefficient (m2/s) (Div Pt) |
| 427 |
|
VA4DMIN | 15 |SM MR |m^4/s |RE-MIN Biharm Visc Coefficient (m4/s) (Div Pt) |
| 428 |
|
VAHZLTH | 15 |SZ MR |m^2/s |Leith Harm Visc Coefficient (m2/s) (Zeta Pt) |
| 429 |
|
VA4ZLTH | 15 |SZ MR |m^4/s |Leith Biharm Visc Coefficient (m4/s) (Zeta Pt) |
| 430 |
|
VAHDLTH | 15 |SM MR |m^2/s |Leith Harm Visc Coefficient (m2/s) (Div Pt) |
| 431 |
|
VA4DLTH | 15 |SM MR |m^4/s |Leith Biharm Visc Coefficient (m4/s) (Div Pt) |
| 432 |
|
VAHZLTHD| 15 |SZ MR |m^2/s |LeithD Harm Visc Coefficient (m2/s) (Zeta Pt) |
| 433 |
|
VA4ZLTHD| 15 |SZ MR |m^4/s |LeithD Biharm Visc Coefficient (m4/s) (Zeta Pt) |
| 434 |
|
VAHDLTHD| 15 |SM MR |m^2/s |LeithD Harm Visc Coefficient (m2/s) (Div Pt) |
| 435 |
|
VA4DLTHD| 15 |SM MR |m^4/s |LeithD Biharm Visc Coefficient (m4/s) (Div Pt) |
| 436 |
|
VAHZSMAG| 15 |SZ MR |m^2/s |Smagorinsky Harm Visc Coefficient (m2/s) (Zeta Pt) |
| 437 |
|
VA4ZSMAG| 15 |SZ MR |m^4/s |Smagorinsky Biharm Visc Coeff. (m4/s) (Zeta Pt) |
| 438 |
|
VAHDSMAG| 15 |SM MR |m^2/s |Smagorinsky Harm Visc Coefficient (m2/s) (Div Pt) |
| 439 |
|
VA4DSMAG| 15 |SM MR |m^4/s |Smagorinsky Biharm Visc Coeff. (m4/s) (Div Pt) |
| 440 |
|
momKE | 15 |SM MR |m^2/s^2 |Kinetic Energy (in momentum Eq.) |
| 441 |
|
momHDiv | 15 |SM MR |s^-1 |Horizontal Divergence (in momentum Eq.) |
| 442 |
|
momVort3| 15 |SZ MR |s^-1 |3rd component (vertical) of Vorticity |
| 443 |
|
Strain | 15 |SZ MR |s^-1 |Horizontal Strain of Horizontal Velocities |
| 444 |
|
Tension | 15 |SM MR |s^-1 |Horizontal Tension of Horizontal Velocities |
| 445 |
|
UBotDrag| 15 |UU 129MR |m/s^2 |U momentum tendency from Bottom Drag |
| 446 |
|
VBotDrag| 15 |VV 128MR |m/s^2 |V momentum tendency from Bottom Drag |
| 447 |
|
USidDrag| 15 |UU 131MR |m/s^2 |U momentum tendency from Side Drag |
| 448 |
|
VSidDrag| 15 |VV 130MR |m/s^2 |V momentum tendency from Side Drag |
| 449 |
|
Um_Diss | 15 |UU 133MR |m/s^2 |U momentum tendency from Dissipation |
| 450 |
|
Vm_Diss | 15 |VV 132MR |m/s^2 |V momentum tendency from Dissipation |
| 451 |
|
Um_Advec| 15 |UU 135MR |m/s^2 |U momentum tendency from Advection terms |
| 452 |
|
Vm_Advec| 15 |VV 134MR |m/s^2 |V momentum tendency from Advection terms |
| 453 |
|
Um_Cori | 15 |UU 137MR |m/s^2 |U momentum tendency from Coriolis term |
| 454 |
|
Vm_Cori | 15 |VV 136MR |m/s^2 |V momentum tendency from Coriolis term |
| 455 |
|
Um_Ext | 15 |UU 137MR |m/s^2 |U momentum tendency from external forcing |
| 456 |
|
Vm_Ext | 15 |VV 138MR |m/s^2 |V momentum tendency from external forcing |
| 457 |
|
Um_AdvZ3| 15 |UU 141MR |m/s^2 |U momentum tendency from Vorticity Advection |
| 458 |
|
Vm_AdvZ3| 15 |VV 140MR |m/s^2 |V momentum tendency from Vorticity Advection |
| 459 |
|
Um_AdvRe| 15 |UU 143MR |m/s^2 |U momentum tendency from vertical Advection (Explicit part) |
| 460 |
|
Vm_AdvRe| 15 |VV 142MR |m/s^2 |V momentum tendency from vertical Advection (Explicit part) |
| 461 |
|
ADVx_Um | 15 |UM 145MR |m^4/s^2 |Zonal Advective Flux of U momentum |
| 462 |
|
ADVy_Um | 15 |VZ 144MR |m^4/s^2 |Meridional Advective Flux of U momentum |
| 463 |
|
ADVrE_Um| 15 |WU LR |m^4/s^2 |Vertical Advective Flux of U momentum (Explicit part) |
| 464 |
|
ADVx_Vm | 15 |UZ 148MR |m^4/s^2 |Zonal Advective Flux of V momentum |
| 465 |
|
ADVy_Vm | 15 |VM 147MR |m^4/s^2 |Meridional Advective Flux of V momentum |
| 466 |
|
ADVrE_Vm| 15 |WV LR |m^4/s^2 |Vertical Advective Flux of V momentum (Explicit part) |
| 467 |
|
VISCx_Um| 15 |UM 151MR |m^4/s^2 |Zonal Viscous Flux of U momentum |
| 468 |
|
VISCy_Um| 15 |VZ 150MR |m^4/s^2 |Meridional Viscous Flux of U momentum |
| 469 |
|
VISrE_Um| 15 |WU LR |m^4/s^2 |Vertical Viscous Flux of U momentum (Explicit part) |
| 470 |
|
VISrI_Um| 15 |WU LR |m^4/s^2 |Vertical Viscous Flux of U momentum (Implicit part) |
| 471 |
|
VISCx_Vm| 15 |UZ 155MR |m^4/s^2 |Zonal Viscous Flux of V momentum |
| 472 |
|
VISCy_Vm| 15 |VM 154MR |m^4/s^2 |Meridional Viscous Flux of V momentum |
| 473 |
|
VISrE_Vm| 15 |WV LR |m^4/s^2 |Vertical Viscous Flux of V momentum (Explicit part) |
| 474 |
|
VISrI_Vm| 15 |WV LR |m^4/s^2 |Vertical Viscous Flux of V momentum (Implicit part) |
| 475 |
|
\end{verbatim} |
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