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branches/nemo_v3_3_beta/DOC/TexFiles/Chapters/Chap_TRA.tex
r2282 r2285 48 48 In the present chapter we also describe the diagnostic equations used to compute 49 49 the sea-water properties (density, Brunt-Vais\"{a}l\"{a} frequency, specific heat and 50 freezing point with associated modules \mdl{eosbn2} , \mdl{ocfzpt}and \mdl{phycst}).50 freezing point with associated modules \mdl{eosbn2} and \mdl{phycst}). 51 51 52 52 The different options available to the user are managed by namelist logicals or … … 79 79 \end{equation} 80 80 where $\tau$ is either T or S, and $b_t= e_{1t}\,e_{2t}\,e_{3t}$ is the volume of $T$-cells. 81 In pure $z$-coordinate (\key{zco} is defined), it reduces to : 82 \begin{equation} \label{Eq_tra_adv_zco} 83 ADV_\tau = - \frac{1}{e_{1t}\,e_{2t}} \left( \; \delta_i \left[ e_{2u} \;u \;\tau_u \right] 84 + \delta_j \left[ e_{1v} \;v \;\tau_v \right] \; \right) 85 - \frac{1}{e_{3t}} \delta_k \left[ w \;\tau_w \right] 86 \end{equation} 87 since the vertical scale factors are functions of $k$ only, and thus 88 $e_{3u} =e_{3v} =e_{3t} $. The flux form in \eqref{Eq_tra_adv} 81 The flux form in \eqref{Eq_tra_adv} 89 82 implicitly requires the use of the continuity equation. Indeed, it is obtained 90 83 by using the following equality : $\nabla \cdot \left( \vect{U}\,T \right)=\vect{U} \cdot \nabla T$ 91 84 which results from the use of the continuity equation, $\nabla \cdot \vect{U}=0$ or 92 $\partial _t e_3 + e_3\;\nabla \cdot \vect{U}=0$ in constant volume (default option) 93 or variable volume (\key{vvl} defined) case, respectively. 85 $ \partial _t e_3 + e_3\;\nabla \cdot \vect{U}=0$ in constant or variable volume case, respectively. 94 86 Therefore it is of paramount importance to design the discrete analogue of the 95 87 advection tendency so that it is consistent with the continuity equation in order to … … 481 473 It is therefore not recommended. 482 474 483 Note that 484 (a) In the pure $z$-coordinate (\key{zco} is defined), $e_{3u}$=$e_{3v}$=$e_{3t}$, 485 so that the vertical scale factors disappear from (\ref{Eq_tra_ldf_lap}) ; 486 (b) In the partial step $z$-coordinate (\np{ln\_zps}=true), tracers in horizontally 475 Note that in the partial step $z$-coordinate (\np{ln\_zps}=true), tracers in horizontally 487 476 adjacent cells are located at different depths in the vicinity of the bottom. 488 477 In this case, horizontal derivatives in (\ref{Eq_tra_ldf_lap}) at the bottom level … … 1096 1085 structure in equilibrium with its physics. 1097 1086 The choice of the shape of the Newtonian damping is controlled by two 1098 namelist parameters \np{ ??} and \np{nn\_zdmp}. The former allows us to specify: the1087 namelist parameters \np{nn\_hdmp} and \np{nn\_zdmp}. The former allows us to specify: the 1099 1088 width of the equatorial band in which no damping is applied; a decrease 1100 1089 in the vicinity of the coast; and a damping everywhere in the Red and Med Seas.
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