Changeset 10442 for NEMO/trunk/doc/latex/NEMO/subfiles/annex_A.tex
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- 2018-12-21T15:18:38+01:00 (5 years ago)
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NEMO/trunk/doc/latex/NEMO/subfiles/annex_A.tex
r10414 r10442 20 20 21 21 In order to establish the set of Primitive Equation in curvilinear $s$-coordinates 22 ( $i.e.$an orthogonal curvilinear coordinate in the horizontal and22 (\ie an orthogonal curvilinear coordinate in the horizontal and 23 23 an Arbitrary Lagrangian Eulerian (ALE) coordinate in the vertical), 24 24 we start from the set of equations established in \autoref{subsec:PE_zco_Eq} for … … 273 273 \] 274 274 leads to the $s-$coordinate formulation of the total $z-$coordinate time derivative, 275 $i.e.$the total $s-$coordinate time derivative :275 \ie the total $s-$coordinate time derivative : 276 276 \begin{align} 277 277 \label{apdx:A_sco_Dt_vect} … … 312 312 % 313 313 Introducing the vertical scale factor inside the horizontal derivative of the first two terms 314 ( $i.e.$the horizontal divergence), it becomes :314 (\ie the horizontal divergence), it becomes : 315 315 \begin{align*} 316 316 { … … 355 355 \end{align*} 356 356 which leads to the $s-$coordinate flux formulation of the total $s-$coordinate time derivative, 357 $i.e.$the total $s-$coordinate time derivative in flux form:357 \ie the total $s-$coordinate time derivative in flux form: 358 358 \begin{flalign} 359 359 \label{apdx:A_sco_Dt_flux} … … 513 513 in particular the pressure gradient. 514 514 By contrast, $\omega$ is not $w$, the third component of the velocity, but the dia-surface velocity component, 515 $i.e.$the volume flux across the moving $s$-surfaces per unit horizontal area.515 \ie the volume flux across the moving $s$-surfaces per unit horizontal area. 516 516 517 517 … … 540 540 \biblio 541 541 542 \pindex 543 542 544 \end{document}
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