| 153 |
~ \\ |
~ \\ |
| 154 |
useOBCSbalance & \code{.FALSE.} & |
useOBCSbalance & \code{.FALSE.} & |
| 155 |
~ \\ |
~ \\ |
| 156 |
OBCS\_balanceFacN/S/E/W & 0 & factor(s) determining the details |
OBCS\_balanceFacN/S/E/W & 1 & factor(s) determining the details |
| 157 |
of the balaning code \\ |
of the balaning code \\ |
| 158 |
useOrlanskiNorth/South/EastWest & \code{.FALSE.} & |
useOrlanskiNorth/South/EastWest & \code{.FALSE.} & |
| 159 |
turn on Orlanski boundary conditions for individual boundary\\ |
turn on Orlanski boundary conditions for individual boundary\\ |
| 364 |
$\chi_{ob}$ (note: passive tracers are currently not implemented and |
$\chi_{ob}$ (note: passive tracers are currently not implemented and |
| 365 |
the code stops when package \code{ptracers} is used together with this |
the code stops when package \code{ptracers} is used together with this |
| 366 |
option). Currently, the code vertically averages the normal velocity |
option). Currently, the code vertically averages the normal velocity |
| 367 |
as specified. From these prescribed values the code computes the |
as specified in \code{OB[E,W]u} or \code{OB[N,S]v}. From these |
| 368 |
boundary values for the next timestep $n+1$ as follows (as an |
prescribed values the code computes the boundary values for the next |
| 369 |
example, we use the notation for an eastern or western boundary): |
timestep $n+1$ as follows (as an example, we use the notation for an |
| 370 |
|
eastern or western boundary): |
| 371 |
\begin{itemize} |
\begin{itemize} |
| 372 |
\item $u^{n+1}(y,z) = \bar{u}_{ob}(y) + u'(y,z)$, where $u_{n}'$ is the |
\item $u^{n+1}(y,z) = \bar{u}_{ob}(y) + (u')^{n}(y,z)$, where $(u')^{n}$ |
| 373 |
deviation from the vertically averaged velocity one grid point |
is the deviation from the vertically averaged velocity at timestep |
| 374 |
inward from the boundary. |
$n$ one grid point inward from the boundary. |
| 375 |
\item If $u^{n+1}$ is directed into the model domain, the boudary |
\item If $u^{n+1}$ is directed into the model domain, the boudary |
| 376 |
value for tracer $\chi$ is restored to the prescribed values: |
value for tracer $\chi$ is restored to the prescribed values: |
| 377 |
\[\chi^{n+1} = \chi^{n} + \frac{\Delta{t}}{\tau_\chi} (\chi_{ob} - |
\[\chi^{n+1} = \chi^{n} + \frac{\Delta{t}}{\tau_\chi} (\chi_{ob} - |
| 378 |
\chi^{n}),\] where $\tau_\chi$ is the relaxation time |
\chi^{n}),\] where $\tau_\chi$ is the relaxation time |
| 379 |
scale \texttt{T/SrelaxStevens}. |
scale \texttt{T/SrelaxStevens}. The new $\chi^{n+1}$ is then subject |
| 380 |
\item If $u^{n+1}$ is directed out of the model domain, the tracer is |
to the advection by $u^{n+1}$. |
| 381 |
advected out of the domain with $u^{n+1}+c$, where $c$ is a phase |
\item If $u^{n+1}$ is directed out of the model domain, the tracer |
| 382 |
velocity estimated as |
$\chi^{n+1}$ on the boundary at timestep $n+1$ is estimated from |
| 383 |
$\frac{1}{2}\frac{\partial\chi}{\partial{t}}/\frac{\partial\chi}{\partial{x}}$. |
advection advected out of the domain with $u^{n+1}+c$, where $c$ is |
| 384 |
|
a phase velocity estimated as |
| 385 |
|
$\frac{1}{2}\frac{\partial\chi}{\partial{t}}/\frac{\partial\chi}{\partial{x}}$. The |
| 386 |
|
numerical scheme is (as an example for an eastern boundary): |
| 387 |
|
\[\chi_{i,j,k}^{n+1} = \chi_{i,j,k}^{n} + \Delta{t} |
| 388 |
|
(u^{n+1}+c)_{i_{b},j,k}\frac{\chi_{i_{b},j,k}^{n} |
| 389 |
|
- \chi_{i_{b}-1,j,k}^{n}}{\Delta{x}_{i_{b},j}^{C}}\mbox{, if }u_{i_{b},j,k}^{n+1}>0, |
| 390 |
|
\] where $i_{b}$ is the boundary index. |
| 391 |
|
|
| 392 |
For test purposes, the phase velocity contribution or the entire |
For test purposes, the phase velocity contribution or the entire |
| 393 |
advection can |
advection can be turned off by setting the corresponding parameters |
|
be turned off by setting the corresponding parameters |
|
| 394 |
\texttt{useStevensPhaseVel} and \texttt{useStevensAdvection} to |
\texttt{useStevensPhaseVel} and \texttt{useStevensAdvection} to |
| 395 |
\texttt{.FALSE.}.\end{itemize} See \citet{stevens:90} for details. |
\texttt{.FALSE.}.\end{itemize} See \citet{stevens:90} for details. |
| 396 |
|
|
| 397 |
\paragraph{OBCS\_BALANCE:} ~ \\ |
\paragraph{OBCS\_BALANCE\_FLOW:} ~ \\ |
| 398 |
% |
% |
| 399 |
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} |
|
| 400 |
defined in \code{OBCS\_OPTIONS.h} and \code{useOBCSbalance=.true.} in |
defined in \code{OBCS\_OPTIONS.h} and \code{useOBCSbalance=.true.} in |
| 401 |
\code{data.obcs/OBCS\_PARM01}), the normal velocities across each of |
\code{data.obcs/OBCS\_PARM01}), this routine balances the net flow |
| 402 |
the four boundaries are modified separately, so that the net volume |
across the open boundaries. By default the net flow across the |
| 403 |
transport across \emph{each} boundary is zero. For example, for the |
boundaries is computed and all normal velocities on boundaries are |
| 404 |
western boundary at $i=i_{b}$, the modified velocity is: |
adjusted to obtain zero net inflow. |
| 405 |
|
|
| 406 |
|
This behavior can be controlled with the runtime flags |
| 407 |
|
\code{OBCS\_balanceFacN/S/E/W}. The values of these flags determine |
| 408 |
|
how the net inflow is redistributed as small correction velocities |
| 409 |
|
between the individual sections. A value ``\code{-1}'' balances an |
| 410 |
|
individual boundary, values $>0$ determine the relative size of the |
| 411 |
|
correction. For example, the values |
| 412 |
|
\begin{tabbing} |
| 413 |
|
\code{OBCS\_balanceFacE}\code{ = 1.,} \\ |
| 414 |
|
\code{OBCS\_balanceFacW}\code{ = -1.,} \\ |
| 415 |
|
\code{OBCS\_balanceFacN}\code{ = 2.,} \\ |
| 416 |
|
\code{OBCS\_balanceFacS}\code{ = 0.,} |
| 417 |
|
\end{tabbing} |
| 418 |
|
make the model |
| 419 |
|
\begin{itemize} |
| 420 |
|
\item correct Western \code{OBWu} by substracting a uniform velocity to |
| 421 |
|
ensure zero net transport through the Western open boundary; |
| 422 |
|
\item correct Eastern and Northern normal flow, with the Northern |
| 423 |
|
velocity correction two times larger than the Eastern correction, but |
| 424 |
|
\emph{not} the Southern normal flow, to ensure that the total inflow through |
| 425 |
|
East, Northern, and Southern open boundary is balanced. |
| 426 |
|
\end{itemize} |
| 427 |
|
|
| 428 |
|
The old method of balancing the net flow for all sections individually |
| 429 |
|
can be recovered by setting all flags to -1. Then the normal |
| 430 |
|
velocities across each of the four boundaries are modified separately, |
| 431 |
|
so that the net volume transport across \emph{each} boundary is |
| 432 |
|
zero. For example, for the western boundary at $i=i_{b}$, the modified |
| 433 |
|
velocity is: |
| 434 |
\[ |
\[ |
| 435 |
u(y,z) - \int_{\mbox{western boundary}}u\,dy\,dz \approx OBNu(j,k) - \sum_{j,k} |
u(y,z) - \int_{\mbox{western boundary}}u\,dy\,dz \approx OBNu(j,k) - \sum_{j,k} |
| 436 |
OBNu(j,k) h_{w}(i_{b},j,k)\Delta{y_G(i_{b},j)}\Delta{z(k)}. |
OBNu(j,k) h_{w}(i_{b},j,k)\Delta{y_G(i_{b},j)}\Delta{z(k)}. |
| 437 |
\] |
\] |
| 438 |
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, |
| 439 |
make it a useful flag to prevent infinite sea-level change within the |
but this combination of flags is \emph{not} useful if you want to |
| 440 |
domain, but the flag is \emph{not} useful if you want to simulate, |
simulate, say, a sector of the Southern Ocean with a strong ACC |
| 441 |
say, a sector of the Southern Ocean with a strong ACC entering through |
entering through the western and leaving through the eastern boundary, |
| 442 |
the western and leaving through the eastern boundary, because this |
because the value of ``\code{-1}'' for these flags will make sure that |
| 443 |
flag will make sure that the strong inflow is removed. It is |
the strong inflow is removed. Clearly, gobal balancing with |
| 444 |
recommended that this part of the code is adapted to the particular |
\code{OBCS\_balanceFacE/W/N/S} $\ge0$ is the preferred method. |
|
needs of the simulation in question. |
|
| 445 |
|
|
| 446 |
\paragraph{OBCS\_APPLY\_*:} ~ \\ |
\paragraph{OBCS\_APPLY\_*:} ~ \\ |
| 447 |
~ |
~ |
| 448 |
|
|
| 449 |
\paragraph{OBCS\_SPONGE} Setting sponge layer characteristics \\ |
\paragraph{OBCS\_SPONGE:} ~ \\ |
| 450 |
% |
% |
| 451 |
~ |
The sponge layer code (turned on with \code{ALLOW\_OBCS\_SPONGE} and |
| 452 |
|
\code{useOBCSsponge}) adds a relaxation term to the right-hand-side of |
| 453 |
|
the momentum and tracer equations. The variables are relaxed towards |
| 454 |
|
the boundary values with a relaxation time scale that increases |
| 455 |
|
linearly with distance from the boundary |
| 456 |
|
\[ |
| 457 |
|
G_{\chi}^{\mbox{(sponge)}} = |
| 458 |
|
- \frac{\chi - [( L - \delta{L} ) \chi_{BC} + \delta{L}\chi]/L} |
| 459 |
|
{[(L-\delta{L})\tau_{b}+\delta{L}\tau_{i}]/L} |
| 460 |
|
= - \frac{\chi - [( 1 - l ) \chi_{BC} + l\chi]} |
| 461 |
|
{[(1-l)\tau_{b}+l\tau_{i}]} |
| 462 |
|
\] |
| 463 |
|
where $\chi$ is the model variable (U/V/T/S) in the interior, |
| 464 |
|
$\chi_{BC}$ the boundary value, $L$ the thickness of the sponge layer |
| 465 |
|
(runtime parameter \code{spongeThickness} in number of grid points), |
| 466 |
|
$\delta{L}\in[0,L]$ ($\frac{\delta{L}}{L}=l\in[0,1]$) the distance from the boundary (also in grid points), and |
| 467 |
|
$\tau_{b}$ (runtime parameters \code{Urelaxobcsbound} and |
| 468 |
|
\code{Vrelaxobcsbound}) and $\tau_{i}$ (runtime parameters |
| 469 |
|
\code{Urelaxobcsinner} and \code{Vrelaxobcsinner}) the relaxation time |
| 470 |
|
scales on the boundary and at the interior termination of the sponge |
| 471 |
|
layer. The parameters \code{Urelaxobcsbound/inner} set the relaxation |
| 472 |
|
time scales for the Eastern and Western boundaries, |
| 473 |
|
\code{Vrelaxobcsbound/inner} for the Northern and Southern boundaries. |
| 474 |
|
|
| 475 |
\paragraph{OB's with nonlinear free surface} ~ \\ |
\paragraph{OB's with nonlinear free surface} ~ \\ |
| 476 |
% |
% |
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