Changeset 6289 for trunk/DOC/TexFiles/Chapters/Chap_LDF.tex

Timestamp:

2016-02-05T00:47:05+01:00 (8 years ago)

Author:

gm

Message:

#1673 DOC of the trunk - Update, see associated wiki page for description

File:

• trunk/DOC/TexFiles/Chapters/Chap_LDF.tex (modified) (2 diffs)

trunk/DOC/TexFiles/Chapters/Chap_LDF.tex

@@ -69 +69 @@
  r_{1u} &= \frac{e_{3u}}{ \left( e_{1u}\;\overline{\overline{e_{3w}}}^{\,i+1/2,\,k} \right)}
            \;\delta_{i+1/2}[z_t] 
-      &\approx \frac{1}{e_{1u}}\; \delta_{i+1/2}[z_t] 
+      &\approx \frac{1}{e_{1u}}\; \delta_{i+1/2}[z_t] \ \ \
 \\
  r_{2v} &= \frac{e_{3v}}{\left( e_{2v}\;\overline{\overline{e_{3w}}}^{\,j+1/2,\,k} \right)} 
            \;\delta_{j+1/2} [z_t] 
-      &\approx \frac{1}{e_{2v}}\; \delta_{j+1/2}[z_t] 
+      &\approx \frac{1}{e_{2v}}\; \delta_{j+1/2}[z_t] \ \ \
 \\
  r_{1w} &= \frac{1}{e_{1w}}\;\overline{\overline{\delta_{i+1/2}[z_t]}}^{\,i,\,k+1/2}
@@ -448 +448 @@
 \label{LDF_eiv}
 
+%%gm  from Triad appendix  : to be incorporated....
+\gmcomment{
+Values of iso-neutral diffusivity and GM coefficient are set as
+described in \S\ref{LDF_coef}. If none of the keys \key{traldf\_cNd},
+N=1,2,3 is set (the default), spatially constant iso-neutral $A_l$ and
+GM diffusivity $A_e$ are directly set by \np{rn\_aeih\_0} and
+\np{rn\_aeiv\_0}. If 2D-varying coefficients are set with
+\key{traldf\_c2d} then $A_l$ is reduced in proportion with horizontal
+scale factor according to \eqref{Eq_title} \footnote{Except in global ORCA
+  $0.5^{\circ}$ runs with \key{traldf\_eiv}, where
+  $A_l$ is set like $A_e$ but with a minimum vale of
+  $100\;\mathrm{m}^2\;\mathrm{s}^{-1}$}. In idealised setups with
+\key{traldf\_c2d}, $A_e$ is reduced similarly, but if \key{traldf\_eiv}
+is set in the global configurations with \key{traldf\_c2d}, a horizontally varying $A_e$ is
+instead set from the Held-Larichev parameterisation\footnote{In this
+  case, $A_e$ at low latitudes $|\theta|<20^{\circ}$ is further
+  reduced by a factor $|f/f_{20}|$, where $f_{20}$ is the value of $f$
+  at $20^{\circ}$~N} (\mdl{ldfeiv}) and \np{rn\_aeiv\_0} is ignored
+unless it is zero.
+}
+
 When Gent and McWilliams [1990] diffusion is used (\key{traldf\_eiv} defined), 
 an eddy induced tracer advection term is added, the formulation of which