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- 2011-10-13T17:25:00+02:00 (13 years ago)
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branches/2011/dev_r2787_NOCS_NEPTUNE/DOC/TexFiles/Chapters/Chap_DYN.tex
r2541 r2915 1162 1162 1163 1163 % ================================================================ 1164 % Neptune effect 1165 % ================================================================ 1166 \section [Neptune effect (\textit{dynnept})] 1167 {Neptune effect (\mdl{dynnept})} 1168 \label{DYN_nept} 1169 1170 The "Neptune effect" (thus named in \citep{HollowayOM86}) is a 1171 parameterisation of the potentially large effect of topographic form stress 1172 (caused by eddies) in driving the ocean circulation. Originally developed for 1173 low-resolution models, in which it was applied via a Laplacian (second-order) 1174 diffusion-like term in the momentum equation, it can also be applied in eddy 1175 permitting or resolving models, in which a more scale-selective bilaplacian 1176 (fourth-order) implementation is preferred. This mechanism has a 1177 significant effect on boundary currents (including undercurrents), and the 1178 upwelling of deep water near continental shelves. 1179 1180 The theoretical basis for the method can be found in 1181 \citep{HollowayJPO92}, including the explanation of why form stress is not 1182 necessarily a drag force, but may actually drive the flow. 1183 \citep{HollowayJPO94} demonstrate the effects of the parameterisation in 1184 the GFDL-MOM model, at a horizontal resolution of about 1.8 degrees. 1185 \citep{HollowayOM08} demonstrate the biharmonic version of the 1186 parameterisation in a global run of the POP model, with an average horizontal 1187 grid spacing of about 32km. 1188 1189 The NEMO implementation is a simplified form of that supplied by 1190 Greg Holloway, the testing of which was described in \citep{HollowayJGR09}. 1191 The major simplification is that a time invariant Neptune velocity 1192 field is assumed. This is computed only once, during start-up, and 1193 made available to the rest of the code via a module. Vertical 1194 diffusive terms are also ignored, and the model topography itself 1195 is used, rather than a separate topographic dataset as in 1196 \citep{HollowayOM08}. This implementation is only in the iso-level 1197 formulation, as is the case anyway for the bilaplacian operator. 1198 1199 The velocity field is derived from a transport stream function given by: 1200 1201 \begin{equation} \label{Eq_dynnept_sf} 1202 \psi = -fL^2H 1203 \end{equation} 1204 1205 where $L$ is a latitude-dependant length scale given by: 1206 1207 \begin{equation} \label{Eq_dynnept_ls} 1208 L = l_1 + (l_2 -l_1)\left ( {1 + \cos 2\phi \over 2 } \right ) 1209 \end{equation} 1210 1211 where $\phi$ is latitude and $l_1$ and $l_2$ are polar and equatorial length scales respectively. 1212 Neptune velocity components, $u^*$, $v^*$ are derived from the stremfunction as: 1213 1214 \begin{equation} \label{Eq_dynnept_vel} 1215 u^* = -{1\over H} {\partial \psi \over \partial y}\ \ \ ,\ \ \ v^* = {1\over H} {\partial \psi \over \partial x} 1216 \end{equation} 1217 1218 \smallskip 1219 %----------------------------------------------namdom---------------------------------------------------- 1220 \namdisplay{namdyn_nept} 1221 %-------------------------------------------------------------------------------------------------------- 1222 \smallskip 1223 1224 The Neptune effect is enabled when \np{ln\_neptsimp}=true (default=false). 1225 \np{ln\_smooth\_neptvel} controls whether a scale-selective smoothing is applied 1226 to the Neptune effect flow field (default=false) (this smoothing method is as 1227 used by Holloway). \np{rn\_tslse} and \np{rn\_tslsp} are the equatorial and 1228 polar values respectively of the length-scale parameter $L$ used in determining 1229 the Neptune stream function \eqref{Eq_dynnept_sf} and \eqref{Eq_dynnept_ls}. 1230 Values at intermediate latitudes are given by a cosine fit, mimicking the 1231 variation of the deformation radius with latitude. The default values of 12km 1232 and 3km are those given in \citep{HollowayJPO94}, appropriate for a coarse 1233 resolution model. The finer resolution study of \citep{HollowayOM08} increased 1234 the values of L by a factor of $\sqrt 2$ to 17km and 4.2km, thus doubling the 1235 stream function for a given topography. 1236 1237 The simple formulation for ($u^*$, $v^*$) can give unacceptably large velocities 1238 in shallow water, and \citep{HollowayOM08} add an offset to the depth in the 1239 denominator to control this problem. In this implementation we offer instead (at 1240 the suggestion of G. Madec) the option of ramping down the Neptune flow field to 1241 zero over a finite depth range. The switch \np{ln\_neptramp} activates this 1242 option (default=false), in which case velocities at depths greater than 1243 \np{rn\_htrmax} are unaltered, but ramp down linearly with depth to zero at a 1244 depth of \np{rn\_htrmin} (and shallower). 1245 1246 % ================================================================
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