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revision 1.7 by adcroft, Tue Nov 13 18:15:26 2001 UTC revision 1.11 by jmc, Mon Jun 26 01:03:47 2006 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 277  viscA4}), has units of $m^4 s^{-1}$. Line 280  viscA4}), has units of $m^4 s^{-1}$.
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  $\tau_{11}$, $\tau_{12}$, $\tau_{22}$, $\tau_{22}$: {\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})  $\tau_{13}^{bottom-drag}$, $\tau_{23}^{bottom-drag}$: {\bf vf} (local to {\em mom\_fluxform.F})
397  \end{minipage} }  \end{minipage} }
398    
399  \subsection{Derivation of discrete energy conservation}  \subsection{Derivation of discrete energy conservation}
# Line 402  KE = \frac{1}{2} \left( \overline{ u^2 } Line 405  KE = \frac{1}{2} \left( \overline{ u^2 }
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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