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Changeset 11015 for NEMO/trunk/doc/latex/SI3/subfiles/chap_model_basics.tex – NEMO

Ignore:
Timestamp:
2019-05-20T20:57:09+02:00 (5 years ago)
Author:
nicolasmartin
Message:

Modification of the content to be in line with the NEMO manual
SI3 manual can now be build like the NEMO manual with ./manual_build.sh SI3

  • Mimick the directory organisation with main and subfiles folders.
  • Regarding the particular case of namelists
    • Remove the duplicates already contained in the global namelists folder at 1st level of ./doc
    • Keep the namelists sub-folder only for namdyn_adv & namsbc which already exist in ocean namelists
  • Rewriting of SI3_manual.tex with NEMO_manual.tex as template to easily highlight differences
  • Updating of several paths for figures/namelists inclusion or LaTeX files referencing
  • LaTeX source:
    • Replacement of \forfile command for namelists with pre-configured \nlst alias
    • " "" \bm with \mathbf (save installation of an extra package)
Location:
NEMO/trunk/doc/latex/SI3/subfiles
Files:
1 edited
1 moved

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  • NEMO/trunk/doc/latex/SI3/subfiles/chap_model_basics.tex

    r9974 r11015  
    11 
    2 \documentclass[../../tex_main/NEMO_manual]{subfiles} 
     2\documentclass[../main/SI3_manual]{subfiles} 
    33 
    44\begin{document} 
    … …  
    4141\begin{center} 
    4242\vspace{0cm} 
    43 \includegraphics[height=10cm,angle=-00]{../Figures/ice_scheme.png} 
    44 \caption{Representation of the ice pack, using multiple categories with specific ice concentration ($a_l, l=1, 2, ..., L$), thickness ($h^i_l$), snow depth ($h^s_l$), vertical temperature and salinity profiles ($T^i_{kl}$, $S^{*}_{kl}$) and a single ice velocity vector ($\bm{u}$).} 
     43\includegraphics[height=10cm,angle=-00]{ice_scheme} 
     44\caption{Representation of the ice pack, using multiple categories with specific ice concentration ($a_l, l=1, 2, ..., L$), thickness ($h^i_l$), snow depth ($h^s_l$), vertical temperature and salinity profiles ($T^i_{kl}$, $S^{*}_{kl}$) and a single ice velocity vector ($\mathbf{u}$).} 
    4545\label{ice_scheme} 
    4646\end{center} 
    … …  
    162162%------------------------------------------------------------------------------------------------------------------------- 
    163163 
    164 We first present the essentials of the thickness distribution framework \citep{Thorndikeetal75}. Consider a given region of area $R$ centered at spatial coordinates $(\bm{x})$ at a given time $t$. $R$ could be e.g. a model grid cell. The ice thickness distribution $g(\mathbf{x},t, h)$ is introduced as follows: 
     164We first present the essentials of the thickness distribution framework \citep{Thorndikeetal75}. Consider a given region of area $R$ centered at spatial coordinates $(\mathbf{x})$ at a given time $t$. $R$ could be e.g. a model grid cell. The ice thickness distribution $g(\mathbf{x},t, h)$ is introduced as follows: 
    165165\begin{linenomath} 
    166166\begin{align} 
    … …  
    184184\begin{center} 
    185185\vspace{0cm} 
    186 \includegraphics[height=6cm,angle=-00]{../Figures/g_h.png} 
     186\includegraphics[height=6cm,angle=-00]{g_h} 
    187187\caption{Representation of the relation between real thickness profiles and the ice thickness distribution function $g(h)$} 
    188188\label{fig_g_h} 
    … …  
    202202\begin{linenomath} 
    203203\begin{align} 
    204 \frac{\partial a_l}{\partial t} = - \bm{\nabla} \cdot (a_l \mathbf{u}) + \Theta^a_l + \int_{H^*_{l-1}}^{H^*_l} dh \psi. 
     204\frac{\partial a_l}{\partial t} = - \mathbf{\nabla} \cdot (a_l \mathbf{u}) + \Theta^a_l + \int_{H^*_{l-1}}^{H^*_l} dh \psi. 
    205205\label{eq:gt} 
    206206\end{align} 
    … …  
    211211\begin{linenomath} 
    212212\begin{align} 
    213  A(\bm{x},t) &=\int_{0^+}^{\infty} dh \cdot g(h,\bm{x},t) \sim A_{ij} = \sum_{l=1}^L a_{ijl}, & \\ 
    214  V_i(\bm{x},t)&=\int_{0}^{\infty} dh \cdot g(h,\bm{x},t) \cdot h \sim V^i_{ij} = \sum_{l=1}^L v^i_{ijl}. & \\ 
     213 A(\mathbf{x},t) &=\int_{0^+}^{\infty} dh \cdot g(h,\mathbf{x},t) \sim A_{ij} = \sum_{l=1}^L a_{ijl}, & \\ 
     214 V_i(\mathbf{x},t)&=\int_{0}^{\infty} dh \cdot g(h,\mathbf{x},t) \cdot h \sim V^i_{ij} = \sum_{l=1}^L v^i_{ijl}. & \\ 
    215215\end{align} 
    216216\end{linenomath} 
    … …  
    228228\begin{linenomath} 
    229229\begin{align} 
    230 m \frac{\partial \bm{u}} {\partial t} & = \bm{\nabla}\cdot\bm{\sigma} +A \left(\bm{\tau}_{a}+\bm{\tau}_{w}\right) - m f \bm{k} \times \bm{u} - m g \bm{\nabla}{\eta}, 
     230m \frac{\partial \mathbf{u}} {\partial t} & = \mathbf{\nabla}\cdot\mathbf{\sigma} +A \left(\mathbf{\tau}_{a}+\mathbf{\tau}_{w}\right) - m f \mathbf{k} \times \mathbf{u} - m g \mathbf{\nabla}{\eta}, 
    231231\label{a} 
    232232\end{align} 
    233233\end{linenomath} 
    234 where $m=\rho_i V_i + \rho_s V_s $ is the ice and snow mass per unit area, $\bm{u}$ is the ice velocity, $\bm{\sigma}$ is the internal stress tensor, $\bm{\tau}_a$ and $\bm{\tau}_w$ are the air and ocean stresses, respectively, $f$ is the Coriolis parameter, $\bm{k}$ is a unit vector pointing upwards, $g$ is the gravity acceleration and $\eta$ is the ocean surface elevation. The EVP approach used in LIM \citep{Bouillonetal13} gives the stress tensor as a function of the strain rate tensor $\dot{\bm{\epsilon}}$ and some of the sea ice state variables: 
    235 \begin{linenomath} 
    236 \begin{align} 
    237 \bm{\sigma} & = \bm{\sigma} (\dot{ \bm{\epsilon}}, \text{ice state}). 
     234where $m=\rho_i V_i + \rho_s V_s $ is the ice and snow mass per unit area, $\mathbf{u}$ is the ice velocity, $\mathbf{\sigma}$ is the internal stress tensor, $\mathbf{\tau}_a$ and $\mathbf{\tau}_w$ are the air and ocean stresses, respectively, $f$ is the Coriolis parameter, $\mathbf{k}$ is a unit vector pointing upwards, $g$ is the gravity acceleration and $\eta$ is the ocean surface elevation. The EVP approach used in LIM \citep{Bouillonetal13} gives the stress tensor as a function of the strain rate tensor $\dot{\mathbf{\epsilon}}$ and some of the sea ice state variables: 
     235\begin{linenomath} 
     236\begin{align} 
     237\mathbf{\sigma} & = \mathbf{\sigma} (\dot{ \mathbf{\epsilon}}, \text{ice state}). 
    238238\end{align} 
    239239\end{linenomath} 
    … …  
    245245\end{align} 
    246246\end{linenomath} 
    247 including the effets of transport, thermodynamics ($\Theta^X$) and mechanical redistribution ($\Psi^X$). Solving these $jpl.(4+2.jpk)$ equations gives the temporal evolution of $\bm{u}$, $\bm{\sigma}$ and the rest of the global (extensive) variables listed in Table \ref{GVariables_table}. 
     247including the effets of transport, thermodynamics ($\Theta^X$) and mechanical redistribution ($\Psi^X$). Solving these $jpl.(4+2.jpk)$ equations gives the temporal evolution of $\mathbf{u}$, $\mathbf{\sigma}$ and the rest of the global (extensive) variables listed in Table \ref{GVariables_table}. 
    248248 
    249249\section{Ice Dynamics} 
    … …  
    272272\begin{center} 
    273273\vspace{0cm} 
    274 \includegraphics[height=6cm,angle=-00]{../Figures/yield_curve.png} 
     274\includegraphics[height=6cm,angle=-00]{yield_curve} 
    275275\caption{Elliptical yield curve used in the VP rheologies, drawn in the space of the principal components of the stress tensor ($\sigma_1$ and $\sigma_2$).} 
    276276\label{fig_yield} 
    … …  
    383383\begin{center} 
    384384\vspace{0cm} 
    385 \includegraphics[height=8cm,angle=-00]{../Figures/Thermal_properties.png} 
     385\includegraphics[height=8cm,angle=-00]{Thermal_properties} 
    386386\caption{Thermal properties of sea ice vs temperature for different bulk salinities: brine fraction, specific enthalpy, thermal conductivity, and effective specific heat.} 
    387387\label{fig_thermal_properties} 
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