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revision 1.7 by adcroft, Tue Nov 13 18:15:26 2001 UTC revision 1.13 by jmc, Thu Feb 18 21:26:26 2010 UTC
# Line 2  Line 2 
2  % $Name$  % $Name$
3    
4  \section{Flux-form momentum equations}  \section{Flux-form momentum equations}
5  \label{sec:flux-form_momentum_eqautions}  \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
# Line 26  In the hydrostatic limit, $G_w=0$ and $\ Line 29  In the hydrostatic limit, $G_w=0$ and $\
29  vertical momentum to hydrostatic balance.  vertical momentum to hydrostatic balance.
30    
31  These terms are calculated in routines called from subroutine {\em  These terms are calculated in routines called from subroutine {\em
32  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},
33  and {\bf Gw}.  and {\bf Gw}.
34    
35  \fbox{ \begin{minipage}{4.75in}  \fbox{ \begin{minipage}{4.75in}
36  {\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})
37    
38  $G_u$: {\bf Gu} ({\em DYNVARS.h})  $G_u$: {\bf Gu} ({\em DYNVARS.h})
39    
# Line 87  conserves kinetic energy. Line 90  conserves kinetic energy.
90    
91  {\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})
92    
93  $uu$, $uv$, $vu$, $vv$: {\bf aF} (local to {\em calc\_mom\_rhs.F})  $uu$, $uv$, $vu$, $vv$: {\bf aF} (local to {\em mom\_fluxform.F})
94  \end{minipage} }  \end{minipage} }
95    
96    
# Line 146  useEnergyConservingCoriolis} to {\em tru Line 149  useEnergyConservingCoriolis} to {\em tru
149    
150  {\em S/R MOM\_V\_CORIOLIS} ({\em mom\_v\_coriolis.F})  {\em S/R MOM\_V\_CORIOLIS} ({\em mom\_v\_coriolis.F})
151    
152  $G_u^{Cor}$, $G_v^{Cor}$: {\bf cF} (local to {\em calc\_mom\_rhs.F})  $G_u^{Cor}$, $G_v^{Cor}$: {\bf cF} (local to {\em mom\_fluxform.F})
153  \end{minipage} }  \end{minipage} }
154    
155    
# Line 185  respectively. Line 188  respectively.
188    
189  {\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})
190    
191  $G_u^{metric}$, $G_v^{metric}$: {\bf mT} (local to {\em calc\_mom\_rhs.F})  $G_u^{metric}$, $G_v^{metric}$: {\bf mT} (local to {\em mom\_fluxform.F})
192  \end{minipage} }  \end{minipage} }
193    
194    
# Line 220  G_w^{metric} & = & Line 223  G_w^{metric} & = &
223    
224  {\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})
225    
226  $G_u^{metric}$, $G_v^{metric}$: {\bf mT} (local to {\em calc\_mom\_rhs.F})  $G_u^{metric}$, $G_v^{metric}$: {\bf mT} (local to {\em mom\_fluxform.F})
227  \end{minipage} }  \end{minipage} }
228    
229    
# Line 253  The lateral viscous stresses are discret Line 256  The lateral viscous stresses are discret
256  where the non-dimensional factors $c_{lm\Delta^n}(\varphi), \{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, $c_{11\Delta} =
259  c_{21\Delta} = (\cos{\varphi})^{3/2}$, $c_{12\Delta}=c_{22\Delta}=0$ would  c_{21\Delta} = (\cos{\varphi})^{3/2}$, $c_{12\Delta}=c_{22\Delta}=1$ would
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}
# Line 276  viscA4}), has units of $m^4 s^{-1}$. Line 279  viscA4}), has units of $m^4 s^{-1}$.
279    
280  {\em S/R MOM\_V\_YVISCFLUX} ({\em mom\_v\_yviscflux.F})  {\em S/R MOM\_V\_YVISCFLUX} ({\em mom\_v\_yviscflux.F})
281    
282  $\tau_{11}$, $\tau_{12}$, $\tau_{22}$, $\tau_{22}$: {\bf vF}, {\bf  $\tau_{11}$, $\tau_{12}$, $\tau_{21}$, $\tau_{22}$: {\bf vF}, {\bf
283  v4F} (local to {\em calc\_mom\_rhs.F})  v4F} (local to {\em mom\_fluxform.F})
284  \end{minipage} }  \end{minipage} }
285    
286  Two types of lateral boundary condition exist for the lateral viscous  Two types of lateral boundary condition exist for the lateral viscous
# Line 315  neighboring vorticity points, e.g. $1-h_ Line 318  neighboring vorticity points, e.g. $1-h_
318    
319  {\em S/R MOM\_V\_SIDEDRAG} ({\em mom\_v\_sidedrag.F})  {\em S/R MOM\_V\_SIDEDRAG} ({\em mom\_v\_sidedrag.F})
320    
321  $G_u^{side-drag}$, $G_v^{side-drag}$: {\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})
322  \end{minipage} }  \end{minipage} }
323    
324    
# Line 352  is even less consistent than for the hyd Line 355  is even less consistent than for the hyd
355    
356  {\em S/R MOM\_V\_RVISCLFUX} ({\em mom\_v\_rviscflux.F})  {\em S/R MOM\_V\_RVISCLFUX} ({\em mom\_v\_rviscflux.F})
357    
358  $\tau_{13}$: {\bf urf} (local to {\em calc\_mom\_rhs.F})  $\tau_{13}$: {\bf urf} (local to {\em mom\_fluxform.F})
359    
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    
363    
# Line 390  dimensionless with typical values in the Line 393  dimensionless with typical values in the
393    
394  {\em S/R MOM\_V\_BOTTOMDRAG} ({\em mom\_v\_bottomdrag.F})  {\em S/R MOM\_V\_BOTTOMDRAG} ({\em mom\_v\_bottomdrag.F})
395    
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    
400  \subsection{Derivation of discrete energy conservation}  \subsection{Derivation of discrete energy conservation}
# Line 402  KE = \frac{1}{2} \left( \overline{ u^2 } Line 406  KE = \frac{1}{2} \left( \overline{ u^2 }
406  \epsilon_{nh} \overline{ w^2 }^k \right)  \epsilon_{nh} \overline{ w^2 }^k \right)
407  \end{equation}  \end{equation}
408    
409    \subsection{Mom Diagnostics}
410    \label{sec:pkg:mom_common:diagnostics}
411    
412    \begin{verbatim}
413    
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}
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