Changeset 11558 for NEMO/trunk/doc/latex/NEMO/subfiles/apdx_s_coord.tex
- Timestamp:
- 2019-09-17T17:04:06+02:00 (5 years ago)
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NEMO/trunk/doc/latex/NEMO/subfiles/apdx_s_coord.tex
r11543 r11558 63 63 Using the first form and considering a change $\delta i$ with $j, z$ and $t$ held constant, shows that 64 64 \begin{equation} 65 \label{eq:SCOORD_s_chain_rule }65 \label{eq:SCOORD_s_chain_rule1} 66 66 \left. {\frac{\partial \bullet }{\partial i}} \right|_{j,z,t} = 67 67 \left. {\frac{\partial \bullet }{\partial i}} \right|_{j,s,t} … … 102 102 the model equations in the curvilinear $s-$coordinate system are: 103 103 \begin{equation} 104 \label{eq:SCOORD_s_chain_rule }104 \label{eq:SCOORD_s_chain_rule2} 105 105 \begin{aligned} 106 106 &\left. {\frac{\partial \bullet }{\partial t}} \right|_z = … … 128 128 \label{sec:SCOORD_continuity} 129 129 130 Using (\autoref{eq:SCOORD_s_chain_rule }) and130 Using (\autoref{eq:SCOORD_s_chain_rule1}) and 131 131 the fact that the horizontal scale factors $e_1$ and $e_2$ do not depend on the vertical coordinate, 132 132 the divergence of the velocity relative to the ($i$,$j$,$z$) coordinate system is transformed as follows in order to … … 272 272 + w \;\frac{\partial u}{\partial z} \\ 273 273 % 274 \intertext{introducing the chain rule (\autoref{eq:SCOORD_s_chain_rule }) }274 \intertext{introducing the chain rule (\autoref{eq:SCOORD_s_chain_rule1}) } 275 275 % 276 276 &= \left. {\frac{\partial u }{\partial t}} \right|_z … … 317 317 \end{subequations} 318 318 % 319 Applying the time derivative chain rule (first equation of (\autoref{eq:SCOORD_s_chain_rule })) to $u$ and319 Applying the time derivative chain rule (first equation of (\autoref{eq:SCOORD_s_chain_rule1})) to $u$ and 320 320 using (\autoref{eq:SCOORD_w_in_s}) provides the expression of the last term of the right hand side, 321 321 \[
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