/[MITgcm]/manual/s_phys_pkgs/text/obcs.tex
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revision 1.10 by mlosch, Mon Mar 14 15:01:28 2011 UTC revision 1.11 by mlosch, Wed Mar 16 10:39:25 2011 UTC
# Line 400  This behavior can be controlled with the Line 400  This behavior can be controlled with the
400  how the net inflow is redistributed as small correction velocities  how the net inflow is redistributed as small correction velocities
401  between the individual sections. A value ``\code{-1}'' balances an  between the individual sections. A value ``\code{-1}'' balances an
402  individual boundary, values $>0$ determine the relative size of the  individual boundary, values $>0$ determine the relative size of the
403  correction. For example, with the values  correction. For example, the values
404  \begin{tabbing}  \begin{tabbing}
405   \code{OBCS\_balanceFac\_E}\=\code{ = 1.,} \\   \code{OBCS\_balanceFacE}\code{ = 1.,} \\
406   \code{OBCS\_balanceFac\_W}\>\code{ = -1.,} \\   \code{OBCS\_balanceFacW}\code{ = -1.,} \\
407   \code{OBCS\_balanceFac\_N}\>\code{ = 2.,} \\   \code{OBCS\_balanceFacN}\code{ = 2.,} \\
408   \code{OBCS\_balanceFac\_S}\>\code{ = 0.,}   \code{OBCS\_balanceFacS}\code{ = 0.,}
409  \end{tabbing}  \end{tabbing}
410  will make the model  make the model
411  \begin{itemize}  \begin{itemize}
412  \item correct Western \code{OBWu} by substracting a uniform velocity to  \item correct Western \code{OBWu} by substracting a uniform velocity to
413  ensure zero net transport through Western OB  ensure zero net transport through the Western open boundary;
414  \item correct Eastern and Northern normal flow, with the Northern  \item correct Eastern and Northern normal flow, with the Northern
415    velocity correction two times larger than Eastern correction, but    velocity correction two times larger than the Eastern correction, but
416    not the Southern normal flow to ensure that the total inflow through    \emph{not} the Southern normal flow, to ensure that the total inflow through
417    East, Northern, and Southern OB is balanced    East, Northern, and Southern open boundary is balanced.
418  \end{itemize}  \end{itemize}
419    
420  The old method of balancing the net flow for all sections individually  The old method of balancing the net flow for all sections individually
# Line 427  velocity is: Line 427  velocity is:
427  u(y,z) - \int_{\mbox{western boundary}}u\,dy\,dz \approx OBNu(j,k) - \sum_{j,k}  u(y,z) - \int_{\mbox{western boundary}}u\,dy\,dz \approx OBNu(j,k) - \sum_{j,k}
428  OBNu(j,k) h_{w}(i_{b},j,k)\Delta{y_G(i_{b},j)}\Delta{z(k)}.  OBNu(j,k) h_{w}(i_{b},j,k)\Delta{y_G(i_{b},j)}\Delta{z(k)}.
429  \]  \]
430  This also ensures a net total inflow of zero through all boundaries to  This also ensures a net total inflow of zero through all boundaries,
431  make it a useful flag for preventing infinite sea-level change within  but this combination of flags is \emph{not} useful if you want to
432  the domain, but this combination of flags is \emph{not} useful if you  simulate, say, a sector of the Southern Ocean with a strong ACC
433  want to simulate, say, a sector of the Southern Ocean with a strong  entering through the western and leaving through the eastern boundary,
434  ACC entering through the western and leaving through the eastern  because the value of ``\code{-1}'' for these flags will make sure that
435  boundary, because the value of ``\code{-1}'' for these flags will make  the strong inflow is removed. Clearly, gobal balancing with
436  sure that the strong inflow is removed.  \code{OBCS\_balanceFacE/W/N/S} $\ge0$ is the preferred method.
437    
438  \paragraph{OBCS\_APPLY\_*:} ~ \\  \paragraph{OBCS\_APPLY\_*:} ~ \\
439  ~  ~
# Line 455  G_{\chi}^{\mbox{(sponge)}} = Line 455  G_{\chi}^{\mbox{(sponge)}} =
455  where $\chi$ is the model variable (U/V/T/S) in the interior,  where $\chi$ is the model variable (U/V/T/S) in the interior,
456  $\chi_{BC}$ the boundary value, $L$ the thickness of the sponge layer  $\chi_{BC}$ the boundary value, $L$ the thickness of the sponge layer
457  (runtime parameter \code{spongeThickness} in number of grid points),  (runtime parameter \code{spongeThickness} in number of grid points),
458  $\delta{L}\in[0,L]$ ($l\in[0,1]$) the distance from the boundary (also in grid points), and  $\delta{L}\in[0,L]$ ($\frac{\delta{L}}{L}=l\in[0,1]$) the distance from the boundary (also in grid points), and
459  $\tau_{b}$ (runtime parameters \code{Urelaxobcsbound} and  $\tau_{b}$ (runtime parameters \code{Urelaxobcsbound} and
460  \code{Vrelaxobcsbound}) and $\tau_{i}$ (runtime parameters  \code{Vrelaxobcsbound}) and $\tau_{i}$ (runtime parameters
461  \code{Urelaxobcsinner} and \code{Vrelaxobcsinner}) the relaxation time  \code{Urelaxobcsinner} and \code{Vrelaxobcsinner}) the relaxation time
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