Changeset 3989 for branches/2013/dev_r3853_CNRS9_ConfSetting/DOC/TexFiles/Chapters/Chap_Model_Basics_zstar.tex
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- 2013-07-24T11:48:35+02:00 (11 years ago)
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branches/2013/dev_r3853_CNRS9_ConfSetting/DOC/TexFiles/Chapters/Chap_Model_Basics_zstar.tex
r3294 r3989 1 1 % ================================================================ 2 % Chapter 1 ÑModel Basics2 % Chapter 1 � Model Basics 3 3 % ================================================================ 4 4 % ================================================================ … … 53 53 Because $z^\star$ has a time independent range, all grid cells have static increments 54 54 ds, and the sum of the ver tical increments yields the time independent ocean 55 depth % ·k ds = H.55 depth %�k ds = H. 56 56 The $z^\star$ coordinate is therefore invisible to undulations of the 57 57 free surface, since it moves along with the free surface. This proper ty means that … … 78 78 \namdisplay{nam_dynspg} 79 79 %------------------------------------------------------------------------------------------------------------ 80 Options are defined through the \ngn{nam\_dynspg} namelist variables. 80 81 The surface pressure gradient term is related to the representation of the free surface (\S\ref{PE_hor_pg}). The main distinction is between the fixed volume case (linear free surface or rigid lid) and the variable volume case (nonlinear free surface, \key{vvl} is active). In the linear free surface case (\S\ref{PE_free_surface}) and rigid lid (\S\ref{PE_rigid_lid}), the vertical scale factors $e_{3}$ are fixed in time, while in the nonlinear case (\S\ref{PE_free_surface}) they are time-dependent. With both linear and nonlinear free surface, external gravity waves are allowed in the equations, which imposes a very small time step when an explicit time stepping is used. Two methods are proposed to allow a longer time step for the three-dimensional equations: the filtered free surface, which is a modification of the continuous equations (see \eqref{Eq_PE_flt}), and the split-explicit free surface described below. The extra term introduced in the filtered method is calculated implicitly, so that the update of the next velocities is done in module \mdl{dynspg\_flt} and not in \mdl{dynnxt}. 81 82 … … 114 115 \namdisplay{namdom} 115 116 %-------------------------------------------------------------------------------------------------------------- 116 The split-explicit free surface formulation used in OPA follows the one proposed by \citet{Griffies2004}. The general idea is to solve the free surface equation with a small time step, while the three dimensional prognostic variables are solved with a longer time step that is a multiple of \np{rdtbt} (Figure III.3). 117 The split-explicit free surface formulation used in OPA follows the one proposed by \citet{Griffies2004}. The general idea is to solve the free surface equation with a small time step, while the three dimensional prognostic variables are solved with a longer time step that is a multiple of \np{rdtbt} 118 in the \ngn{namdom} namelist. 119 (Figure III.3). 117 120 118 121 %> > > > > > > > > > > > > > > > > > > > > > > > > > > >
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