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|  | c1572375fa | 
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							|  | @ -22,8 +22,8 @@ | ||||||
| *.xdv | *.xdv | ||||||
| *-converted-to.* | *-converted-to.* | ||||||
| # these rules might exclude image files for figures etc. | # these rules might exclude image files for figures etc. | ||||||
| # *.ps | main*.ps | ||||||
| # *.eps | main*.eps | ||||||
| *.pdf | *.pdf | ||||||
| 
 | 
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| ## Generated if empty string is given at "Please type another file name for output:" | ## Generated if empty string is given at "Please type another file name for output:" | ||||||
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							|  | @ -145,14 +145,41 @@ | ||||||
| \end{center} | \end{center} | ||||||
| 
 | 
 | ||||||
| \section{Equations} | \section{Equations} | ||||||
| \subsection{Navier-Stokes} | \subsection{Fundamental equations} | ||||||
|  | \subsubsection{Navier-Stokes} | ||||||
| \begin{equation} | \begin{equation} | ||||||
|     \frac{D}{Dt} |     \frac{Du}{Dt} = \underbrace{-\frac{1}{\rho}\nabla p}_\mathrm{Pressure} - \underbrace{(2\Omega \times u)}_\mathrm{Coriolis} - \underbrace{g'K}_\mathrm{Gravity} + \underbrace{F^{**}}_\mathrm{Viscous} | ||||||
|  | \end{equation} | ||||||
|  | 
 | ||||||
|  | \subsubsection{Conservation of mass} | ||||||
|  | \begin{equation} | ||||||
|  |     \frac{D \rho}{Dt} + \rho(\nabla u) = 0  | ||||||
|  | \end{equation} | ||||||
|  | 
 | ||||||
|  | \subsubsection{First law of thermodynamics} | ||||||
|  | \begin{equation} | ||||||
|  |     \frac{D\theta}{Dt} = \bigg(\frac{\theta}{c_p T} \bigg) \mathcal{H} | ||||||
|  | \end{equation} | ||||||
|  | if $\mathcal{H} = 0$, the process is \textit{adiabatic} | ||||||
|  | 
 | ||||||
|  | \subsubsection{Equation of state} | ||||||
|  | \begin{equation} | ||||||
|  |     p = \rho RT | ||||||
| \end{equation} | \end{equation} | ||||||
| 
 | 
 | ||||||
| \subsection{Circulation} | \subsection{Circulation} | ||||||
| \begin{equation} | \begin{equation} | ||||||
|     C = \oint_c u \, dc = \oint (u \, dx + v \, dy + w \, dz) |     C = \oint_c \vec{v} \, dc = \oint (u \, dx + v \, dy + w \, dz) = \oint_0^{2\pi} \vec{v} \, r \, d\phi | ||||||
|  | \end{equation} | ||||||
|  | 
 | ||||||
|  | \subsection{Quasi geostrophic system of equations} | ||||||
|  | \begin{equation} | ||||||
|  |     \zeta = \frac{\partial v}{\partial x} - \frac{\partial u}{\partial y} | ||||||
|  | \end{equation} | ||||||
|  | 
 | ||||||
|  | \subsubsection*{Vorticity equation} | ||||||
|  | \begin{equation} | ||||||
|  |     \frac{D_h}{Dt} \zeta + \beta v = -f_0(\nabla_h \vec{v}) | ||||||
| \end{equation} | \end{equation} | ||||||
| 
 | 
 | ||||||
| \section{Concepts} | \section{Concepts} | ||||||
|  | @ -162,6 +189,20 @@ | ||||||
|     \frac{\partial}{\partial z} v_G = \bigg(\frac{1}{f}\frac{g}{\theta_0}\bigg)(k \times \nabla_h \theta^*) |     \frac{\partial}{\partial z} v_G = \bigg(\frac{1}{f}\frac{g}{\theta_0}\bigg)(k \times \nabla_h \theta^*) | ||||||
| \end{equation} | \end{equation} | ||||||
| 
 | 
 | ||||||
|  | \subsection{$Q$-Vector} | ||||||
|  | The $Q$-Vector indicates if there is cyclogenesis ($\mathcal{F} < 0$, $\mathcal{F} \sim \nabla_h Q$) | ||||||
|  | \vspace{2mm} \\ | ||||||
|  | How to determine the $Q$-Vector on weather charts: | ||||||
|  | \begin{enumerate} | ||||||
|  |     \item Locate regions with: | ||||||
|  |     \begin{itemize} | ||||||
|  |         \item Large temperature gradient | ||||||
|  |         \item Strong wind change | ||||||
|  |     \end{itemize} | ||||||
|  |     \item Determine wind-change vector | ||||||
|  |     \item Rotate that vector by $+90^\circ$ | ||||||
|  | \end{enumerate} | ||||||
|  | 
 | ||||||
| \scriptsize | \scriptsize | ||||||
| 
 | 
 | ||||||
| \section*{Copyleft} | \section*{Copyleft} | ||||||
|  |  | ||||||
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