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1 heimbach 1.1 \subsection{OBCS: Open boundary conditions for regional modeling}
2    
3     \label{sec:pkg:obcs}
4     \begin{rawhtml}
5     <!-- CMIREDIR:package_obcs: -->
6     \end{rawhtml}
7    
8 heimbach 1.2 Authors:
9     Alistair Adcroft, Patrick Heimbach, Samar Katiwala, Martin Losch
10 heimbach 1.1
11     \subsubsection{Introduction
12     \label{sec:pkg:obcs:intro}}
13    
14 mlosch 1.7 The OBCS-package is fundamental to regional ocean modelling with the
15 mlosch 1.9 MITgcm, but there are so many details to be considered in
16 mlosch 1.7 regional ocean modelling that this package cannot accomodate all
17     imaginable and possible options. Therefore, for a regional simulation
18     with very particular details, it is recommended to familiarize oneself
19     not only with the compile- and runtime-options of this package, but
20     also with the code itself. In many cases it will be necessary to adapt
21     the obcs-code (in particular \code{S/R OBCS\_CALC}) to the application
22     in question; in these cases the obcs-package (together with the
23     rbcs-package, section \ref{sec:pkg:rbcs}) is a very
24     useful infrastructure for implementing special regional models.
25 heimbach 1.1
26     %----------------------------------------------------------------------
27    
28     \subsubsection{OBCS configuration and compiling
29 jmc 1.4 \label{sec:pkg:obcs:comp}}
30 heimbach 1.1
31     As with all MITgcm packages, OBCS can be turned on or off
32     at compile time
33     %
34     \begin{itemize}
35     %
36     \item
37 mlosch 1.6 using the \code{packages.conf} file by adding \code{obcs} to it,
38 heimbach 1.1 %
39     \item
40 mlosch 1.6 or using \code{genmake2} adding
41     \code{-enable=obcs} or \code{-disable=obcs} switches
42 heimbach 1.1 %
43     \item
44     \textit{Required packages and CPP options:} \\
45     %
46     To alternatives are available for prescribing open boundary values,
47     which differ in the way how OB's are treated in time:
48     A simple time-management (e.g. constant in time, or cyclic with
49     fixed fequency) is provided through
50 mlosch 1.6 S/R \code{obcs\_external\_fields\_load}.
51 heimbach 1.1 More sophisticated ``real-time'' (i.e. calendar time) management is
52 mlosch 1.6 available through \code{obcs\_prescribe\_read}.
53 heimbach 1.1 The latter case requires
54 mlosch 1.6 packages \code{cal} and \code{exf} to be enabled.
55 heimbach 1.1 %
56     \end{itemize}
57 jmc 1.5 (see also Section \ref{sec:buildingCode}).
58 heimbach 1.1
59     Parts of the OBCS code can be enabled or disabled at compile time
60     via CPP preprocessor flags. These options are set in
61 mlosch 1.6 \code{OBCS\_OPTIONS.h}. Table \ref{tab:pkg:obcs:cpp} summarizes them.
62 heimbach 1.1
63 jmc 1.5 \begin{table}[!ht]
64 heimbach 1.1 \centering
65     \label{tab:pkg:obcs:cpp}
66     {\footnotesize
67     \begin{tabular}{|l|l|}
68     \hline
69     \textbf{CPP option} & \textbf{Description} \\
70     \hline \hline
71 mlosch 1.6 \code{ALLOW\_OBCS\_NORTH} &
72 heimbach 1.1 enable Northern OB \\
73 mlosch 1.6 \code{ALLOW\_OBCS\_SOUTH} &
74 heimbach 1.1 enable Southern OB \\
75 mlosch 1.6 \code{ALLOW\_OBCS\_EAST} &
76 heimbach 1.1 enable Eastern OB \\
77 mlosch 1.6 \code{ALLOW\_OBCS\_WEST} &
78 heimbach 1.1 enable Western OB \\
79     \hline
80 mlosch 1.6 \code{ALLOW\_OBCS\_PRESCRIBE} &
81 heimbach 1.1 enable code for prescribing OB's \\
82 mlosch 1.6 \code{ALLOW\_OBCS\_SPONGE} &
83 heimbach 1.1 enable sponge layer code \\
84 mlosch 1.6 \code{ALLOW\_OBCS\_BALANCE} &
85 heimbach 1.1 enable code for balancing transports through OB's \\
86 mlosch 1.6 \code{ALLOW\_ORLANSKI} &
87 heimbach 1.1 enable Orlanski radiation conditions at OB's \\
88 mlosch 1.6 \code{ALLOW\_OBCS\_STEVENS} &
89     enable Stevens (1990) boundary conditions at OB's \\
90     & (currently only implemented for eastern and western \\
91     & boundaries and NOT for ptracers) \\
92 heimbach 1.1 \hline
93     \end{tabular}
94     }
95     \caption{~}
96     \end{table}
97    
98    
99     %----------------------------------------------------------------------
100    
101     \subsubsection{Run-time parameters
102     \label{sec:pkg:obcs:runtime}}
103    
104     Run-time parameters are set in files
105 mlosch 1.6 \code{data.pkg}, \code{data.obcs}, and \code{data.exf}
106 heimbach 1.1 if ``real-time'' prescription is requested
107 mlosch 1.6 (i.e. package \code{exf} enabled).
108 mlosch 1.8 vThese parameter files are read in S/R
109 mlosch 1.6 \code{packages\_readparms.F}, \code{obcs\_readparms.F}, and
110     \code{exf\_readparms.F}, respectively.
111 heimbach 1.1 Run-time parameters may be broken into 3 categories:
112     (i) switching on/off the package at runtime,
113     (ii) OBCS package flags and parameters,
114 mlosch 1.6 (iii) additional timing flags in \code{data.exf}, if selected.
115 heimbach 1.1
116     \paragraph{Enabling the package}
117     ~ \\
118     %
119     The OBCS package is switched on at runtime by setting
120 mlosch 1.6 \code{useOBCS = .TRUE.} in \code{data.pkg}.
121 heimbach 1.1
122     \paragraph{Package flags and parameters}
123     ~ \\
124     %
125     Table \ref{tab:pkg:obcs:runtime_flags} summarizes the
126 mlosch 1.6 runtime flags that are set in \code{data.obcs}, and
127 heimbach 1.1 their default values.
128    
129 jmc 1.5 \begin{table}[!ht]
130 heimbach 1.1 \centering
131     {\footnotesize
132     \begin{tabular}{|l|c|l|}
133     \hline
134     \textbf{Flag/parameter} & \textbf{default} & \textbf{Description} \\
135     \hline \hline
136 mlosch 1.6 \multicolumn{3}{|c|}{\textit{basic flags \& parameters} (OBCS\_PARM01) } \\
137 heimbach 1.1 \hline
138     OB\_Jnorth & 0 &
139     Nx-vector of J-indices (w.r.t. Ny) of Northern OB
140     at each I-position (w.r.t. Nx) \\
141     OB\_Jsouth & 0 &
142     Nx-vector of J-indices (w.r.t. Ny) of Southern OB
143     at each I-position (w.r.t. Nx) \\
144     OB\_Ieast & 0 &
145     Ny-vector of I-indices (w.r.t. Nx) of Eastern OB
146     at each J-position (w.r.t. Ny) \\
147     OB\_Iwest & 0 &
148     Ny-vector of I-indices (w.r.t. Nx) of Western OB
149     at each J-position (w.r.t. Ny) \\
150 mlosch 1.6 useOBCSprescribe & \code{.FALSE.} &
151 heimbach 1.1 ~ \\
152 mlosch 1.6 useOBCSsponge & \code{.FALSE.} &
153 heimbach 1.1 ~ \\
154 mlosch 1.6 useOBCSbalance & \code{.FALSE.} &
155 heimbach 1.1 ~ \\
156 mlosch 1.8 OBCS\_balanceFacN/S/E/W & 0 & factor(s) determining the details
157     of the balaning code \\
158 mlosch 1.6 useOrlanskiNorth/South/EastWest & \code{.FALSE.} &
159     turn on Orlanski boundary conditions for individual boundary\\
160     useStevensNorth/South/EastWest & \code{.FALSE.} &
161     turn on Stevens boundary conditions for individual boundary\\
162 heimbach 1.1 OB\textbf{X}\textbf{y}File & ~ &
163     file name of OB field \\
164     ~ & ~ &
165     \textbf{X}: \textbf{N}(orth), \textbf{S}(outh),
166     \textbf{E}(ast), \textbf{W}(est) \\
167     ~ & ~ &
168     \textbf{y}: \textbf{t}(emperature), \textbf{s}(salinity),
169 mlosch 1.6 \textbf{u}(-velocity), \textbf{v}(-velocity), \\
170     ~ & ~ &
171     \textbf{w}(-velocity), \textbf{eta}(sea surface height)\\
172     ~ & ~ &
173     \textbf{a}(sea ice area), \textbf{h}(sea ice thickness),
174     \textbf{sn}(snow thickness), \textbf{sl}(sea ice salinity)\\
175 heimbach 1.1 \hline
176 mlosch 1.6 \multicolumn{3}{|c|}{\textit{Orlanski parameters} (OBCS\_PARM02) } \\
177 heimbach 1.1 \hline
178     cvelTimeScale & 2000 sec &
179     averaging period for phase speed \\
180     CMAX & 0.45 m/s &
181     maximum allowable phase speed-CFL for AB-II \\
182     CFIX & 0.8 m/s &
183     fixed boundary phase speed \\
184 mlosch 1.6 useFixedCEast & \code{.FALSE.} &
185 heimbach 1.1 ~ \\
186 mlosch 1.6 useFixedCWest & \code{.FALSE.} &
187 heimbach 1.1 ~ \\
188     \hline
189 mlosch 1.6 \multicolumn{3}{|c|}{\textit{Sponge-layer parameters} (OBCS\_PARM03)} \\
190 heimbach 1.1 \hline
191     spongeThickness & 0 &
192     sponge layer thickness (in \# grid points) \\
193     Urelaxobcsinner & 0 sec &
194     relaxation time scale at the
195     innermost sponge layer point of a meridional OB \\
196     Vrelaxobcsinner & 0 sec &
197     relaxation time scale at the
198     innermost sponge layer point of a zonal OB \\
199     Urelaxobcsbound & 0 sec &
200     relaxation time scale at the
201     outermost sponge layer point of a meridional OB \\
202     Vrelaxobcsbound & 0 sec &
203     relaxation time scale at the
204     outermost sponge layer point of a zonal OB \\
205 mlosch 1.6 \hline
206     \multicolumn{3}{|c|}{\textit{Stevens parameters} (OBCS\_PARM04) } \\
207     \hline
208     T/SrelaxStevens & 0~sec & relaxation time scale for
209     temperature/salinity \\
210     useStevensPhaseVel & \code{.TRUE.} & \\
211     useStevensAdvection & \code{.TRUE.} & \\
212 heimbach 1.1 \hline
213     \hline
214     \end{tabular}
215     }
216 jmc 1.5 \caption{pkg OBCS run-time parameters}
217     \label{tab:pkg:obcs:runtime_flags}
218 heimbach 1.1 \end{table}
219    
220    
221    
222     %----------------------------------------------------------------------
223    
224 heimbach 1.2 \subsubsection{Defining open boundary positions
225     \label{sec:pkg:obcs:defining}}
226    
227     There are four open boundaries (OBs), a
228     Northern, Southern, Eastern, and Western.
229     All OB locations are specified by their absolute
230     meridional (Northern/Southern) or zonal (Eastern/Western) indices.
231 mlosch 1.6 Thus, for each zonal position $i=1,\ldots,N_x$ a meridional index
232 heimbach 1.2 $j$ specifies the Northern/Southern OB position,
233 mlosch 1.6 and for each meridional position $j=1,\ldots,N_y$, a zonal index
234 heimbach 1.2 $i$ specifies the Eastern/Western OB position.
235 mlosch 1.6 For Northern/Southern OB this defines an $N_x$-dimensional
236 heimbach 1.2 ``row'' array $\tt OB\_Jnorth(Ny)$ / $\tt OB\_Jsouth(Ny)$,
237 mlosch 1.6 and an $N_y$-dimenisonal
238     ``column'' array $\tt OB\_Ieast(Nx)$ / $\tt OB\_Iwest(Nx)$.
239 heimbach 1.2 Positions determined in this way allows Northern/Southern
240     OBs to be at variable $j$ (or $y$) positions, and Eastern/Western
241     OBs at variable $i$ (or $x$) positions.
242     Here, indices refer to tracer points on the C-grid.
243     A zero (0) element in $\tt OB\_I\ldots$, $\tt OB\_J\ldots$
244     means there is no corresponding OB in that column/row.
245     For a Northern/Southern OB, the OB V point is to the South/North.
246     For an Eastern/Western OB, the OB U point is to the West/East.
247 mlosch 1.8 For example,
248     \begin{tabbing}
249     \code{OB\_Jnorth(3)=34} \= means that: \= \\
250     \> \code{T(3,34)} \> is a an OB point \\
251     \> \code{U(3,34)} \> is a an OB point \\
252     \> \code{V(3,34)} \> is a an OB point \\
253     \code{OB\_Jsouth(3)=1} \> means that: \\
254     \> \code{T(3,1)} \> is a an OB point \\
255     \> \code{U(3,1)} \> is a an OB point \\
256     \> \code{V(3,2)} \> is a an OB point \\
257     \code{OB\_Ieast(10)=69} \> means that: \> \\
258     \> \code{T(69,10)} \> is a an OB point \\
259     \> \code{U(69,10)} \> is a an OB point \\
260     \> \code{V(69,10)} \> is a an OB point \\
261     \code{OB\_Iwest(10)=1} \> means that: \> \\
262     \> \code{T(1,10)} \> is a an OB point \\
263     \> \code{U(2,10)} \> is a an OB point \\
264     \> \code{V(1,10)} \> is a an OB point
265     \end{tabbing}
266     For convenience, negative values for \code{Jnorth}/\code{Ieast} refer to
267 heimbach 1.2 points relative to the Northern/Eastern edges of the model
268     eg. $\tt OB\_Jnorth(3)=-1$ means that the point $\tt (3,Ny)$
269     is a northern OB.
270    
271     \noindent
272     \textsf{Add special comments for case \#define NONLIN\_FRSURF,
273     see obcs\_ini\_fixed.F}
274    
275     %----------------------------------------------------------------------
276    
277 heimbach 1.1 \subsubsection{Equations and key routines
278     \label{sec:pkg:obcs:equations}}
279    
280 heimbach 1.2 \paragraph{OBCS\_READPARMS:} ~ \\
281     Set OB positions through arrays
282     {\tt OB\_Jnorth(Ny), OB\_Jsouth(Ny), OB\_Ieast(Nx), OB\_Iwest(Nx)},
283 jmc 1.5 and runtime flags (see Table \ref{tab:pkg:obcs:runtime_flags}).
284 heimbach 1.1
285     \paragraph{OBCS\_CALC:} ~ \\
286 heimbach 1.2 %
287     Top-level routine for filling values to be applied at OB for
288     $T,S,U,V,\eta$ into corresponding
289     ``slice'' arrays $(x,z)$, $(y,z)$ for each OB:
290     $\tt OB[N/S/E/W][t/s/u/v]$; e.g. for salinity array at
291     Southern OB, array name is $\tt OBSt$.
292     Values filled are either
293     %
294     \begin{itemize}
295     %
296     \item
297     constant vertical $T,S$ profiles as specified in file
298     {\tt data} ({\tt tRef(Nr), sRef(Nr)}) with zero velocities $U,V$,
299     %
300     \item
301     $T,S,U,V$ values determined via Orlanski radiation conditions
302     (see below),
303     %
304     \item
305     prescribed time-constant or time-varying fields (see below).
306     %
307 mlosch 1.6 \item
308     use prescribed boundary fields to compute Stevens boundary conditions.
309 heimbach 1.2 \end{itemize}
310    
311 mlosch 1.6 \paragraph{ORLANSKI:} ~ \\
312 heimbach 1.2 %
313 mlosch 1.6 Orlanski radiation conditions \citep{orl:76}, examples can be found in
314     \code{verification/dome} and
315     \code{verification/tutorial\_plume\_on\_slope}
316     (\ref{sec:eg-gravityplume}).
317    
318     \paragraph{OBCS\_PRESCRIBE\_READ:} ~ \\
319     %
320     When \code{useOBCSprescribe = .TRUE.} the model tries to read
321     temperature, salinity, u- and v-velocities from files specified in the
322     runtime parameters \code{OB[N/S/E/W][t/s/u/v]File}. These files are
323     the usual IEEE, big-endian files with dimensions of a section along an
324     open boundary:
325     \begin{itemize}
326     \item For North/South boundary files the dimensions are
327     $(N_x\times N_r\times\mbox{time levels})$, for East/West boundary
328     files the dimensions are $(N_y\times N_r\times\mbox{time levels})$.
329     \item If a non-linear free surface is used
330     (\ref{sec:nonlinear-freesurface}), additional files
331     \code{OB[N/S/E/W]etaFile} for the sea surface height $\eta$ with
332     dimension $(N_{x/y}\times\mbox{time levels})$ may be specified.
333     \item If non-hydrostatic dynamics are used
334     (\ref{sec:non-hydrostatic}), additional files
335     \code{OB[N/S/E/W]wFile} for the vertical velocity $w$ with
336 mlosch 1.7 dimensions $(N_{x/y}\times N_r\times\mbox{time levels})$ can be
337 mlosch 1.6 specified.
338     \item If \code{useSEAICE=.TRUE.} then additional files
339     \code{OB[N/S/E/W][a,h,sl,sn,uice,vice]} for sea ice area, thickness
340     (\code{HEFF}), seaice salinity, snow and ice velocities
341 mlosch 1.7 $(N_{x/y}\times\mbox{time levels})$ can be specified.
342 mlosch 1.6 \end{itemize}
343 mlosch 1.7 As in \code{S/R external\_fields\_load} or the \code{exf}-package, the
344     code reads two time levels for each variable, e.g.\ \code{OBNu0} and
345     \code{OBNu1}, and interpolates linearly between these time levels to
346     obtain the value \code{OBNu} at the current model time (step). When the
347     \code{exf}-package is used, the time levels are controlled for each
348     boundary separately in the same way as the \code{exf}-fields in
349     \code{data.exf}, namelist \code{EXF\_NML\_OBCS}. The runtime flags
350 mlosch 1.6 follow the above naming conventions, e.g. for the western boundary the
351     corresponding flags are \code{OBCWstartdate1/2} and
352     \code{OBCWperiod}. Sea-ice boundary values are controlled separately
353 mlosch 1.7 with \code{siobWstartdate1/2} and \code{siobWperiod}. When the
354     \code{exf}-package is not used, the time levels are controlled by the
355     runtime flags \code{externForcingPeriod} and \code{externForcingCycle}
356     in \code{data}, see \code{verification/exp4} for an example.
357 mlosch 1.6
358     \paragraph{OBCS\_CALC\_STEVENS:} ~ \\
359     (THE IMPLEMENTATION OF THESE BOUNDARY CONDITIONS IS NOT COMPLETE. SO
360     FAR ONLY EASTERN AND WESTERN BOUNDARIES ARE SUPPORTED.) \\
361     The boundary conditions following \citet{stevens:90} require the
362     vertically averaged normal velocity (originally specified as a stream
363     function along the open boundary) $\bar{u}_{ob}$ and the tracer fields
364     $\chi_{ob}$ (note: passive tracers are currently not implemented and
365     the code stops when package \code{ptracers} is used together with this
366     option). Currently, the code vertically averages the normal velocity
367     as specified. From these prescribed values the code computes the
368     boundary values for the next timestep $n+1$ as follows (as an
369     example, we use the notation for an eastern or western boundary):
370     \begin{itemize}
371     \item $u^{n+1}(y,z) = \bar{u}_{ob}(y) + u'(y,z)$, where $u_{n}'$ is the
372     deviation from the vertically averaged velocity one grid point
373     inward from the boundary.
374     \item If $u^{n+1}$ is directed into the model domain, the boudary
375     value for tracer $\chi$ is restored to the prescribed values:
376     \[\chi^{n+1} = \chi^{n} + \frac{\Delta{t}}{\tau_\chi} (\chi_{ob} -
377     \chi^{n}),\] where $\tau_\chi$ is the relaxation time
378     scale \texttt{T/SrelaxStevens}.
379     \item If $u^{n+1}$ is directed out of the model domain, the tracer is
380     advected out of the domain with $u^{n+1}+c$, where $c$ is a phase
381     velocity estimated as
382     $\frac{1}{2}\frac{\partial\chi}{\partial{t}}/\frac{\partial\chi}{\partial{x}}$.
383     For test purposes, the phase velocity contribution or the entire
384     advection can
385     be turned off by setting the corresponding parameters
386     \texttt{useStevensPhaseVel} and \texttt{useStevensAdvection} to
387     \texttt{.FALSE.}.\end{itemize} See \citet{stevens:90} for details.
388 heimbach 1.1
389 mlosch 1.7 \paragraph{OBCS\_BALANCE:} ~ \\
390 heimbach 1.1 %
391 mlosch 1.7 This is not (yet) a separate routine in the code, but it may become
392     one to make this code more transparent. The code is part of
393     \code{S/R~OBCS\_CALC}. When turned on (\code{ALLOW\_OBCS\_BALANCE}
394     defined in \code{OBCS\_OPTIONS.h} and \code{useOBCSbalance=.true.} in
395     \code{data.obcs/OBCS\_PARM01}), the normal velocities across each of
396     the four boundaries are modified separately, so that the net volume
397     transport across \emph{each} boundary is zero. For example, for the
398     western boundary at $i=i_{b}$, the modified velocity is:
399     \[
400     u(y,z) - \int_{\mbox{western boundary}}u\,dy\,dz \approx OBNu(j,k) - \sum_{j,k}
401     OBNu(j,k) h_{w}(i_{b},j,k)\Delta{y_G(i_{b},j)}\Delta{z(k)}.
402     \]
403     This also ensures a net total inflow of zero through all boundaries to
404     make it a useful flag to prevent infinite sea-level change within the
405     domain, but the flag is \emph{not} useful if you want to simulate,
406     say, a sector of the Southern Ocean with a strong ACC entering through
407     the western and leaving through the eastern boundary, because this
408     flag will make sure that the strong inflow is removed. It is
409     recommended that this part of the code is adapted to the particular
410     needs of the simulation in question.
411 heimbach 1.1
412 heimbach 1.2 \paragraph{OBCS\_APPLY\_*:} ~ \\
413 heimbach 1.1 ~
414    
415 heimbach 1.2 \paragraph{OBCS\_SPONGE} Setting sponge layer characteristics \\
416 heimbach 1.1 %
417     ~
418    
419     \paragraph{OB's with nonlinear free surface} ~ \\
420     %
421     ~
422    
423    
424     %----------------------------------------------------------------------
425    
426     \subsubsection{Flow chart
427     \label{sec:pkg:obcs:flowchart}}
428    
429    
430     {\footnotesize
431     \begin{verbatim}
432    
433     C !CALLING SEQUENCE:
434     c ...
435    
436     \end{verbatim}
437     }
438    
439     %----------------------------------------------------------------------
440    
441     \subsubsection{OBCS diagnostics
442     \label{sec:pkg:obcs:diagnostics}}
443    
444     Diagnostics output is available via the diagnostics package
445     (see Section \ref{sec:pkg:diagnostics}).
446     Available output fields are summarized in
447     Table \ref{tab:pkg:obcs:diagnostics}.
448    
449 jmc 1.5 \begin{table}[!ht]
450 heimbach 1.1 \centering
451     \label{tab:pkg:obcs:diagnostics}
452     {\footnotesize
453     \begin{verbatim}
454     ------------------------------------------------------
455     <-Name->|Levs|grid|<-- Units -->|<- Tile (max=80c)
456     ------------------------------------------------------
457    
458     \end{verbatim}
459     }
460     \caption{~}
461     \end{table}
462    
463     %----------------------------------------------------------------------
464    
465     \subsubsection{Reference experiments}
466 mlosch 1.7 In the directory \code{verifcation}, the following experiments use
467     \code{obcs}:
468     \begin{itemize}
469     \item \code{exp4}: box with 4 open boundaries, simulating flow over a
470     Gaussian bump based on \citet{adcroft:97}, also tests
471     Stevens-boundary conditions;
472 mlosch 1.8 \item \code{dome}: based on the project ``Dynamics of Overflow Mixing
473     and Entrainment''
474     (\url{http://www.rsmas.miami.edu/personal/tamay/DOME/dome.html}), uses
475     Orlanski-BCs;
476 mlosch 1.7 \item \code{internal\_wave}: uses a heavily modified \code{S/R~OBCS\_CALC}
477     \item \code{seaice\_obcs}: simple example who to use the sea-ice
478     related code, based on \code{lab\_sea};
479     \item \code{tutorial\_plume\_on\_slope}: uses Orlanski-BCs, see also
480     section~\ref{sec:eg-gravityplume}.
481     \end{itemize}
482 heimbach 1.1
483    
484    
485     %----------------------------------------------------------------------
486    
487     \subsubsection{References}
488    
489 molod 1.3 \subsubsection{Experiments and tutorials that use obcs}
490     \label{sec:pkg:obcs:experiments}
491    
492     \begin{itemize}
493 mlosch 1.7 \item \code{tutorial\_plume\_on\_slope} (section~\ref{sec:eg-gravityplume})
494 molod 1.3 \end{itemize}
495    
496 mlosch 1.6
497     %%% Local Variables:
498     %%% mode: latex
499     %%% TeX-master: "../../manual"
500     %%% End:

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