--- manual/s_phys_pkgs/text/obcs.tex 2011/02/28 08:28:47 1.7 +++ manual/s_phys_pkgs/text/obcs.tex 2011/03/16 10:39:25 1.11 @@ -12,7 +12,7 @@ \label{sec:pkg:obcs:intro}} The OBCS-package is fundamental to regional ocean modelling with the -MITgcm, but because there are so many details to be considered in +MITgcm, but there are so many details to be considered in regional ocean modelling that this package cannot accomodate all imaginable and possible options. Therefore, for a regional simulation with very particular details, it is recommended to familiarize oneself @@ -105,7 +105,7 @@ \code{data.pkg}, \code{data.obcs}, and \code{data.exf} if ``real-time'' prescription is requested (i.e. package \code{exf} enabled). -These parameter files are read in S/R +vThese parameter files are read in S/R \code{packages\_readparms.F}, \code{obcs\_readparms.F}, and \code{exf\_readparms.F}, respectively. Run-time parameters may be broken into 3 categories: @@ -153,6 +153,8 @@ ~ \\ useOBCSbalance & \code{.FALSE.} & ~ \\ + 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\\ useStevensNorth/South/EastWest & \code{.FALSE.} & @@ -242,21 +244,26 @@ means there is no corresponding OB in that column/row. For a Northern/Southern OB, the OB V point is to the South/North. For an Eastern/Western OB, the OB U point is to the West/East. - -\begin{verbatim} - For example - OB_Jnorth(3)=34 means that: - T( 3 ,34) is a an OB point - U(3:4,34) is a an OB point - V( 4 ,34) is a an OB point - while - OB_Jsouth(3)=1 means that: - T( 3 ,1) is a an OB point - U(3:4,1) is a an OB point - V( 4 ,2) is a an OB point -\end{verbatim} - -For convenience, negative values for Jnorth/Ieast refer to +For example, +\begin{tabbing} + \code{OB\_Jnorth(3)=34} \= means that: \= \\ + \> \code{T(3,34)} \> is a an OB point \\ + \> \code{U(3,34)} \> is a an OB point \\ + \> \code{V(3,34)} \> is a an OB point \\ + \code{OB\_Jsouth(3)=1} \> means that: \\ + \> \code{T(3,1)} \> is a an OB point \\ + \> \code{U(3,1)} \> is a an OB point \\ + \> \code{V(3,2)} \> is a an OB point \\ + \code{OB\_Ieast(10)=69} \> means that: \> \\ + \> \code{T(69,10)} \> is a an OB point \\ + \> \code{U(69,10)} \> is a an OB point \\ + \> \code{V(69,10)} \> is a an OB point \\ + \code{OB\_Iwest(10)=1} \> means that: \> \\ + \> \code{T(1,10)} \> is a an OB point \\ + \> \code{U(2,10)} \> is a an OB point \\ + \> \code{V(1,10)} \> is a an OB point +\end{tabbing} +For convenience, negative values for \code{Jnorth}/\code{Ieast} refer to points relative to the Northern/Eastern edges of the model eg. $\tt OB\_Jnorth(3)=-1$ means that the point $\tt (3,Ny)$ is a northern OB. @@ -379,35 +386,83 @@ \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 -one to make this code more transparent. The code is part of -\code{S/R~OBCS\_CALC}. When turned on (\code{ALLOW\_OBCS\_BALANCE} +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 -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: +\code{data.obcs/OBCS\_PARM01}), this routine balances the net flow +across the open boundaries. By default the net flow across the +boundaries is computed and all normal velocities on boundaries are +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, the values +\begin{tabbing} + \code{OBCS\_balanceFacE}\code{ = 1.,} \\ + \code{OBCS\_balanceFacW}\code{ = -1.,} \\ + \code{OBCS\_balanceFacN}\code{ = 2.,} \\ + \code{OBCS\_balanceFacS}\code{ = 0.,} +\end{tabbing} +make the model +\begin{itemize} +\item correct Western \code{OBWu} by substracting a uniform velocity to +ensure zero net transport through the Western open boundary; +\item correct Eastern and Northern normal flow, with the Northern + velocity correction two times larger than the Eastern correction, but + \emph{not} the Southern normal flow, to ensure that the total inflow through + East, Northern, and Southern open boundary 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 -domain, but the flag is \emph{not} useful if you want to simulate, -say, a sector of the Southern Ocean with a strong ACC entering through -the western and leaving through the eastern boundary, because this -flag will make sure that the strong inflow is removed. It is -recommended that this part of the code is adapted to the particular -needs of the simulation in question. +This also ensures a net total inflow of zero through all boundaries, +but this combination of flags is \emph{not} useful if you want to +simulate, say, a sector of the Southern Ocean with a strong ACC +entering through the western and leaving through the eastern boundary, +because the value of ``\code{-1}'' for these flags will make sure that +the strong inflow is removed. Clearly, gobal balancing with +\code{OBCS\_balanceFacE/W/N/S} $\ge0$ is the preferred method. \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), +$\delta{L}\in[0,L]$ ($\frac{\delta{L}}{L}=l\in[0,1]$) 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} ~ \\ % @@ -462,8 +517,10 @@ \item \code{exp4}: box with 4 open boundaries, simulating flow over a Gaussian bump based on \citet{adcroft:97}, also tests Stevens-boundary conditions; -\item \code{dome}: based on ``Denmark Strait Overflow Model - Experiment'', use Orlanski-BCs; +\item \code{dome}: based on the project ``Dynamics of Overflow Mixing + and Entrainment'' + (\url{http://www.rsmas.miami.edu/personal/tamay/DOME/dome.html}), uses + Orlanski-BCs; \item \code{internal\_wave}: uses a heavily modified \code{S/R~OBCS\_CALC} \item \code{seaice\_obcs}: simple example who to use the sea-ice related code, based on \code{lab\_sea};