Changeset 11693 for NEMO/trunk/doc/latex/NEMO/subfiles/chap_DYN.tex

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Timestamp:
2019-10-14T14:53:52+02:00 (13 months ago)
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Macros renaming

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 r11690 Furthermore, the tendency terms associated with the 2D barotropic vorticity balance (when \texttt{trdvor?} is defined) can be derived from the 3D terms. \gmcomment{STEVEN: not quite sure I've got the sense of the last sentence. does MISC correspond to "extracting tendency terms" or "vorticity balance"?} \cmtgm{STEVEN: not quite sure I've got the sense of the last sentence. Does MISC correspond to "extracting tendency terms" or "vorticity balance"?} %% ================================================================================================= as changes in the divergence of the barotropic transport are absorbed into the change of the level thicknesses, re-orientated downward. \gmcomment{not sure of this...  to be modified with the change in emp setting} \cmtgm{not sure of this...  to be modified with the change in emp setting} In the case of a linear free surface, the time derivative in \autoref{eq:DYN_wzv} disappears. The upper boundary condition applies at a fixed level $z=0$. $u$ and $v$ are located at different grid points, a price worth paying to avoid a double averaging in the pressure gradient term as in the $B$-grid. \gmcomment{ To circumvent this, Adcroft (ADD REF HERE) \cmtgm{ To circumvent this, Adcroft (ADD REF HERE) Nevertheless, this technique strongly distort the phase and group velocity of Rossby waves....} In the vertical, the centred $2^{nd}$ order evaluation of the advection is preferred, \ie\ $u_{uw}^{ubs}$ and $u_{vw}^{ubs}$ in \autoref{eq:DYN_adv_cen2} are used. UBS is diffusive and is associated with vertical mixing of momentum. \gmcomment{ gm  pursue the UBS is diffusive and is associated with vertical mixing of momentum. \cmtgm{ gm  pursue the sentence:Since vertical mixing of momentum is a source term of the TKE equation...  } there is also the possibility of using a $4^{th}$ order evaluation of the advective velocity as in ROMS. This is an error and should be suppressed soon. \gmcomment{action :  this have to be done} \cmtgm{action :  this have to be done} %% ================================================================================================= it is still significant as shown by \citet{levier.treguier.ea_rpt07} in the case of an analytical barotropic Kelvin wave. \gmcomment{               %%% copy from griffies Book \cmtgm{               %%% copy from griffies Book \textbf{title: Time stepping the barotropic system } %% gm %%======>>>>   given here the discrete eqs provided to the solver \gmcomment{               %%% copy from chap-model basics \cmtgm{               %%% copy from chap-model basics \[ % \label{eq:DYN_spg_flt} and $\mathrm {\mathbf M}$ represents the collected contributions of the Coriolis, hydrostatic pressure gradient, non-linear and viscous terms in \autoref{eq:MB_dyn}. }   %end gmcomment }   %end cmtgm Note that in the linear free surface formulation (\texttt{vvl?} not defined), no slip or partial slip boundary conditions are applied according to the user's choice (see \autoref{chap:LBC}). \gmcomment{ \cmtgm{ Hyperviscous operators are frequently used in the simulation of turbulent flows to control the dissipation of unresolved small scale features. the first derivative term normal to the coast depends on the free or no-slip lateral boundary conditions chosen, while the third derivative terms normal to the coast are set to zero (see \autoref{chap:LBC}). \gmcomment{add a remark on the the change in the position of the coefficient} \cmtgm{add a remark on the the change in the position of the coefficient} %% ================================================================================================= the snow-ice mass is taken into account when computing the surface pressure gradient. \gmcomment{ missing : the lateral boundary condition !!!   another external forcing \cmtgm{ missing : the lateral boundary condition !!!   another external forcing } and only array swapping and Asselin filtering is done in \mdl{dynnxt}. \onlyinsubfile{\input{../../global/epilogue}} \subinc{\input{../../global/epilogue}} \end{document}