# Changeset 3142 for branches/2011/dev_NEMO_MERGE_2011/DOC/TexFiles/Chapters/Chap_DYN.tex

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2011-11-17T15:54:45+01:00 (10 years ago)
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Branch dev_NEMO_MERGE_2011. Minor documentation changes and check in dynhpg.F90 to prevent use of buggy horizontal pressure gradient option

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 r3116 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. 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) ($e_{3w}$). $\bullet$ 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) $\bullet$ Pressure Jacobian scheme (prj) \citep{Thiem_Berntsen_OM06} (\np{ln\_dynhpg\_prj}=true) 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}. Only the pressure jacobian scheme (\np{ln\_dynhpg\_prj}=true) is available as an alternative to the default \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 and is of a higher order than the linear interpolation method. 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 should provide a more accurate calculation of the horizontal pressure gradient than the standard scheme. (\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. %--------------------------------------------------------------------------------------------------------------