/[MITgcm]/manual/s_algorithm/text/mom_fluxform.tex
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revision 1.6 by cnh, Thu Oct 25 18:36:53 2001 UTC revision 1.10 by molod, Thu Apr 6 00:38:17 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 291  handled using the lopped cells. Line 294  handled using the lopped cells.
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
# Line 343  In the interior the vertical stresses ar Line 346  In the interior the vertical stresses ar
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})
# 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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