/[MITgcm]/manual/s_phys_pkgs/text/gmredi.tex
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revision 1.2 by adcroft, Fri Sep 28 14:09:56 2001 UTC revision 1.3 by cnh, Thu Oct 25 18:36:56 2001 UTC
# Line 167  In the instance that $\kappa_{GM} = \kap Line 167  In the instance that $\kappa_{GM} = \kap
167  \end{array}  \end{array}
168  \right)  \right)
169  \end{equation}  \end{equation}
170  which differs from the variable laplacian diffusion tensor by only  which differs from the variable Laplacian diffusion tensor by only
171  two non-zero elements in the $z$-row.  two non-zero elements in the $z$-row.
172    
173  \fbox{ \begin{minipage}{4.75in}  \fbox{ \begin{minipage}{4.75in}
# Line 218  Substituting into the formula for $\kapp Line 218  Substituting into the formula for $\kapp
218  Experience with the GFDL model showed that the GM scheme has to be  Experience with the GFDL model showed that the GM scheme has to be
219  matched to the convective parameterization. This was originally  matched to the convective parameterization. This was originally
220  expressed in connection with the introduction of the KPP boundary  expressed in connection with the introduction of the KPP boundary
221  layer scheme (Large et al., 97) but infact, as subsequent experience  layer scheme (Large et al., 97) but in fact, as subsequent experience
222  with the MIT model has found, is necessary for any convective  with the MIT model has found, is necessary for any convective
223  parameterization.  parameterization.
224    
# Line 261  homogenized, unstable or nearly unstable Line 261  homogenized, unstable or nearly unstable
261  such regions can be either infinite, very large with a sign reversal  such regions can be either infinite, very large with a sign reversal
262  or simply very large. From a numerical point of view, large slopes  or simply very large. From a numerical point of view, large slopes
263  lead to large variations in the tensor elements (implying large bolus  lead to large variations in the tensor elements (implying large bolus
264  flow) and can be numerically unstable. This was first reognized by  flow) and can be numerically unstable. This was first recognized by
265  Cox, 1987, who implemented ``slope clipping'' in the isopycnal mixing  Cox, 1987, who implemented ``slope clipping'' in the isopycnal mixing
266  tensor. Here, the slope magnitude is simply restricted by an upper  tensor. Here, the slope magnitude is simply restricted by an upper
267  limit:  limit:
# Line 296  a) using the GM scheme with clipping and Line 296  a) using the GM scheme with clipping and
296  diffusion). The classic result of dramatically reduced mixed layers is  diffusion). The classic result of dramatically reduced mixed layers is
297  evident. Indeed, the deep convection sites to just one or two points  evident. Indeed, the deep convection sites to just one or two points
298  each and are much shallower than we might prefer. This, it turns out,  each and are much shallower than we might prefer. This, it turns out,
299  is due to the over zealous restratification due to the bolus transport  is due to the over zealous re-stratification due to the bolus transport
300  parameterization. Limiting the slopes also breaks the adiabatic nature  parameterization. Limiting the slopes also breaks the adiabatic nature
301  of the GM/Redi parameterization, re-introducing diabatic fluxes in  of the GM/Redi parameterization, re-introducing diabatic fluxes in
302  regions where the limiting is in effect.  regions where the limiting is in effect.
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