/[MITgcm]/manual/s_algorithm/text/mom_fluxform.tex
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revision 1.9 by jmc, Tue Aug 2 20:54:44 2005 UTC revision 1.13 by jmc, Thu Feb 18 21:26:26 2010 UTC
# Line 29  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 90  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 149  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 188  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 223  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 256  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 279  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 318  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 355  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 393  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 405  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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