Changeset 3294 for trunk/DOC/TexFiles/Chapters/Chap_DYN.tex

Timestamp:

2012-01-28T17:44:18+01:00 (13 years ago)

Author:

rblod

Message:

Merge of 3.4beta into the trunk

File:

• trunk/DOC/TexFiles/Chapters/Chap_DYN.tex (modified) (4 diffs, 1 prop)

trunk/DOC/TexFiles/Chapters/Chap_DYN.tex

@@ -189 +189 @@
 the relative vorticity term and horizontal kinetic energy for the planetary vorticity 
 term (MIX scheme) ; or conserving both the potential enstrophy of horizontally non-divergent 
-flow and horizontal kinetic energy (ENE scheme) (see  Appendix~\ref{Apdx_C_vor_zad}). 
+flow and horizontal kinetic energy (EEN scheme) (see  Appendix~\ref{Apdx_C_vor_zad}). In the 
+case of ENS, ENE or MIX schemes the land sea mask may be slightly modified to ensure the 
+consistency of vorticity term with analytical equations (\textit{ln\_dynvor\_con}=true).
 The vorticity terms are all computed in dedicated routines that can be found in 
 the \mdl{dynvor} module.
@@ -605 +607 @@
 Pressure gradient formulations in an $s$-coordinate have been the subject of a vast 
 number of papers ($e.g.$, \citet{Song1998, Shchepetkin_McWilliams_OM05}). 
-A number of different pressure gradient options are coded, but they are not yet fully 
-documented or tested. 
-
-$\bullet$ Traditional coding (see for example \citet{Madec_al_JPO96}: (\np{ln\_dynhpg\_sco}=true, 
-\np{ln\_dynhpg\_hel}=true)
+A number of different pressure gradient options are coded but the ROMS-like, density Jacobian with 
+cubic polynomial method is currently disabled whilst known bugs are under investigation.
+
+$\bullet$ Traditional coding (see for example \citet{Madec_al_JPO96}: (\np{ln\_dynhpg\_sco}=true)
 \begin{equation} \label{Eq_dynhpg_sco}
 \left\{ \begin{aligned}
@@ -622 +623 @@
 \eqref{Eq_dynhpg_zco_surf} - \eqref{Eq_dynhpg_zco}, and $z_T$ is the depth of 
 the $T$-point evaluated from the sum of the vertical scale factors at the $w$-point 
-($e_{3w}$). The version \np{ln\_dynhpg\_hel}=true has been added by Aike 
-Beckmann and involves a redefinition of the relative position of $T$-points relative 
-to $w$-points. 
-
-$\bullet$ Weighted density Jacobian (WDJ) \citep{Song1998} (\np{ln\_dynhpg\_wdj}=true)
+($e_{3w}$). 
+
+$\bullet$ Pressure Jacobian scheme (prj) (a research paper in preparation) (\np{ln\_dynhpg\_prj}=true)
 
 $\bullet$ Density Jacobian with cubic polynomial scheme (DJC) \citep{Shchepetkin_McWilliams_OM05} 
-(\np{ln\_dynhpg\_djc}=true)
-
-$\bullet$ Rotated axes scheme (rot) \citep{Thiem_Berntsen_OM06} (\np{ln\_dynhpg\_rot}=true)
-
-Note that expression \eqref{Eq_dynhpg_sco} is used when the variable volume 
-formulation is activated (\key{vvl}) because in that case, even with a flat bottom, 
-the coordinate surfaces are not horizontal but follow the free surface 
-\citep{Levier2007}. The other pressure gradient options are not yet available.
+(\np{ln\_dynhpg\_djc}=true) (currently disabled; under development)
+
+Note that expression \eqref{Eq_dynhpg_sco} is commonly used when the variable volume formulation is
+activated (\key{vvl}) because in that case, even with a flat bottom, the coordinate surfaces are not
+horizontal but follow the free surface \citep{Levier2007}. The pressure jacobian scheme
+(\np{ln\_dynhpg\_prj}=true) is available as an improved option to \np{ln\_dynhpg\_sco}=true when
+\key{vvl} is active.  The pressure Jacobian scheme uses a constrained cubic spline to reconstruct
+the density profile across the water column. This method maintains the monotonicity between the
+density nodes  The pressure can be calculated by analytical integration of the density profile and a
+pressure Jacobian method is used to solve the horizontal pressure gradient. This method can provide
+a more accurate calculation of the horizontal pressure gradient than the standard scheme.
 
 %--------------------------------------------------------------------------------------------------------------
@@ -1162 +1164 @@
 
 % ================================================================
+% Neptune effect 
+% ================================================================
+\section  [Neptune effect (\textit{dynnept})]
+                {Neptune effect (\mdl{dynnept})}
+\label{DYN_nept}
+
+The "Neptune effect" (thus named in \citep{HollowayOM86}) is a
+parameterisation of the potentially large effect of topographic form stress
+(caused by eddies) in driving the ocean circulation. Originally developed for
+low-resolution models, in which it was applied via a Laplacian (second-order)
+diffusion-like term in the momentum equation, it can also be applied in eddy
+permitting or resolving models, in which a more scale-selective bilaplacian
+(fourth-order) implementation is preferred. This mechanism has a
+significant effect on boundary currents (including undercurrents), and the
+upwelling of deep water near continental shelves.
+
+The theoretical basis for the method can be found in 
+\citep{HollowayJPO92}, including the explanation of why form stress is not
+necessarily a drag force, but may actually drive the flow. 
+\citep{HollowayJPO94} demonstrate the effects of the parameterisation in
+the GFDL-MOM model, at a horizontal resolution of about 1.8 degrees. 
+\citep{HollowayOM08} demonstrate the biharmonic version of the
+parameterisation in a global run of the POP model, with an average horizontal
+grid spacing of about 32km.
+
+The NEMO implementation is a simplified form of that supplied by
+Greg Holloway, the testing of which was described in \citep{HollowayJGR09}.
+The major simplification is that a time invariant Neptune velocity
+field is assumed.  This is computed only once, during start-up, and
+made available to the rest of the code via a module.  Vertical
+diffusive terms are also ignored, and the model topography itself
+is used, rather than a separate topographic dataset as in
+\citep{HollowayOM08}.  This implementation is only in the iso-level
+formulation, as is the case anyway for the bilaplacian operator.
+
+The velocity field is derived from a transport stream function given by:
+
+\begin{equation} \label{Eq_dynnept_sf}
+\psi = -fL^2H
+\end{equation}
+
+where $L$ is a latitude-dependant length scale given by:
+
+\begin{equation} \label{Eq_dynnept_ls}
+L = l_1 + (l_2 -l_1)\left ( {1 + \cos 2\phi \over 2 } \right )
+\end{equation}
+
+where $\phi$ is latitude and $l_1$ and $l_2$ are polar and equatorial length scales respectively.
+Neptune velocity components, $u^*$, $v^*$ are derived from the stremfunction as:
+
+\begin{equation} \label{Eq_dynnept_vel}
+u^* = -{1\over H} {\partial \psi \over \partial y}\ \ \  ,\ \ \ v^* = {1\over H} {\partial \psi \over \partial x}
+\end{equation}
+
+\smallskip
+%----------------------------------------------namdom----------------------------------------------------
+\namdisplay{namdyn_nept}
+%--------------------------------------------------------------------------------------------------------
+\smallskip
+
+The Neptune effect is enabled when \np{ln\_neptsimp}=true (default=false).
+\np{ln\_smooth\_neptvel} controls whether a scale-selective smoothing is applied
+to the Neptune effect flow field (default=false) (this smoothing method is as
+used by Holloway).  \np{rn\_tslse} and \np{rn\_tslsp} are the equatorial and
+polar values respectively of the length-scale parameter $L$ used in determining
+the Neptune stream function \eqref{Eq_dynnept_sf} and \eqref{Eq_dynnept_ls}.
+Values at intermediate latitudes are given by a cosine fit, mimicking the
+variation of the deformation radius with latitude.  The default values of 12km
+and 3km are those given in \citep{HollowayJPO94}, appropriate for a coarse
+resolution model. The finer resolution study of \citep{HollowayOM08} increased
+the values of L by a factor of $\sqrt 2$ to 17km and 4.2km, thus doubling the
+stream function for a given topography.
+
+The simple formulation for ($u^*$, $v^*$) can give unacceptably large velocities
+in shallow water, and \citep{HollowayOM08} add an offset to the depth in the
+denominator to control this problem. In this implementation we offer instead (at
+the suggestion of G. Madec) the option of ramping down the Neptune flow field to
+zero over a finite depth range. The switch \np{ln\_neptramp} activates this
+option (default=false), in which case velocities at depths greater than
+\np{rn\_htrmax} are unaltered, but ramp down linearly with depth to zero at a
+depth of \np{rn\_htrmin} (and shallower).
+
+% ================================================================