/[MITgcm]/manual/s_phys_pkgs/text/obcs.tex

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-revision 1.9 by mlosch,
Thu Mar  3 07:46:09 2011 UTC
+revision 1.10 by mlosch,
Mon Mar 14 15:01:28 2011 UTC
 Line 153 
 their default values.
             ~ \\
          useOBCSbalance & \code{.FALSE.} &
             ~ \\
-            OBCS\_balanceFacN/S/E/W & 0 & factor(s) determining the details
+            OBCS\_balanceFacN/S/E/W & 1 & factor(s) determining the details
             of the balaning code \\
          useOrlanskiNorth/South/EastWest & \code{.FALSE.} &
             turn on Orlanski boundary conditions for individual boundary\\
 Line 386 
 example, we use the notation for an east
    \texttt{useStevensPhaseVel} and \texttt{useStevensAdvection} to
    \texttt{.FALSE.}.\end{itemize} See \citet{stevens:90} for details.
- \paragraph{OBCS\_BALANCE:} ~ \\
+ \paragraph{OBCS\_BALANCE\_FLOW:} ~ \\
  %
- This is not (yet) a separate routine in the code, but it may become
+ When turned on (\code{ALLOW\_OBCS\_BALANCE}
- one to make this code more transparent. The code is part of
- \code{S/R~OBCS\_CALC}. When turned on (\code{ALLOW\_OBCS\_BALANCE}
  defined in \code{OBCS\_OPTIONS.h} and \code{useOBCSbalance=.true.} in
- \code{data.obcs/OBCS\_PARM01}), the normal velocities across each of
+ \code{data.obcs/OBCS\_PARM01}), this routine balances the net flow
- the four boundaries are modified separately, so that the net volume
+ across the open boundaries. By default the net flow across the
- transport across \emph{each} boundary is zero. For example, for the
+ boundaries is computed and all normal velocities on boundaries are
- western boundary at $i=i_{b}$, the modified velocity is:
+ adjusted to obtain zero net inflow.
+ This behavior can be controlled with the runtime flags
+ \code{OBCS\_balanceFacN/S/E/W}. The values of these flags determine
+ how the net inflow is redistributed as small correction velocities
+ between the individual sections. A value ``\code{-1}'' balances an
+ individual boundary, values $>0$ determine the relative size of the
+ correction. For example, with the values
+ \begin{tabbing}
+  \code{OBCS\_balanceFac\_E}\=\code{ = 1.,} \\
+  \code{OBCS\_balanceFac\_W}\>\code{ = -1.,} \\
+  \code{OBCS\_balanceFac\_N}\>\code{ = 2.,} \\
+  \code{OBCS\_balanceFac\_S}\>\code{ = 0.,}
+ \end{tabbing}
+ will make the model
+ \begin{itemize}
+ \item correct Western \code{OBWu} by substracting a uniform velocity to
+ ensure zero net transport through Western OB
+ \item correct Eastern and Northern normal flow, with the Northern
+   velocity correction two times larger than Eastern correction, but
+   not the Southern normal flow to ensure that the total inflow through
+   East, Northern, and Southern OB is balanced
+ \end{itemize}
+ The old method of balancing the net flow for all sections individually
+ can be recovered by setting all flags to -1. Then the normal
+ velocities across each of the four boundaries are modified separately,
+ so that the net volume transport across \emph{each} boundary is
+ zero. For example, for the western boundary at $i=i_{b}$, the modified
+ velocity is:
  \[
  u(y,z) - \int_{\mbox{western boundary}}u\,dy\,dz \approx OBNu(j,k) - \sum_{j,k}
  OBNu(j,k) h_{w}(i_{b},j,k)\Delta{y_G(i_{b},j)}\Delta{z(k)}.
  \]
  This also ensures a net total inflow of zero through all boundaries to
- make it a useful flag to prevent infinite sea-level change within the
+ make it a useful flag for preventing infinite sea-level change within
- domain, but the flag is \emph{not} useful if you want to simulate,
+ the domain, but this combination of flags is \emph{not} useful if you
- say, a sector of the Southern Ocean with a strong ACC entering through
+ want to simulate, say, a sector of the Southern Ocean with a strong
- the western and leaving through the eastern boundary, because this
+ ACC entering through the western and leaving through the eastern
- flag will make sure that the strong inflow is removed. It is
+ boundary, because the value of ``\code{-1}'' for these flags will make
- recommended that this part of the code is adapted to the particular
+ sure that the strong inflow is removed.
- needs of the simulation in question.
  \paragraph{OBCS\_APPLY\_*:} ~ \\
  ~
- \paragraph{OBCS\_SPONGE} Setting sponge layer characteristics \\
+ \paragraph{OBCS\_SPONGE:} ~ \\
  %
- ~
+ The sponge layer code (turned on with \code{ALLOW\_OBCS\_SPONGE} and
+ \code{useOBCSsponge}) adds a relaxation term to the right-hand-side of
+ the momentum and tracer equations. The variables are relaxed towards
+ the boundary values with a relaxation time scale that increases
+ linearly with distance from the boundary
+ \[
+ G_{\chi}^{\mbox{(sponge)}} =
+ - \frac{\chi - [( L - \delta{L} ) \chi_{BC} + \delta{L}\chi]/L}
+ {[(L-\delta{L})\tau_{b}+\delta{L}\tau_{i}]/L}
+ = - \frac{\chi - [( 1 - l ) \chi_{BC} + l\chi]}
+ {[(1-l)\tau_{b}+l\tau_{i}]}
+ \]
+ where $\chi$ is the model variable (U/V/T/S) in the interior,
+ $\chi_{BC}$ the boundary value, $L$ the thickness of the sponge layer
+ (runtime parameter \code{spongeThickness} in number of grid points),
+ $\delta{L}\in[0,L]$ ($l\in[0,1]$) the distance from the boundary (also in grid points), and
+ $\tau_{b}$ (runtime parameters \code{Urelaxobcsbound} and
+ \code{Vrelaxobcsbound}) and $\tau_{i}$ (runtime parameters
+ \code{Urelaxobcsinner} and \code{Vrelaxobcsinner}) the relaxation time
+ scales on the boundary and at the interior termination of the sponge
+ layer. The parameters \code{Urelaxobcsbound/inner} set the relaxation
+ time scales for the Eastern and Western boundaries,
+ \code{Vrelaxobcsbound/inner} for the Northern and Southern boundaries.
  \paragraph{OB's with nonlinear free surface} ~ \\
  %

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