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							|  | @ -22,8 +22,8 @@ | |||
| *.xdv | ||||
| *-converted-to.* | ||||
| # these rules might exclude image files for figures etc. | ||||
| main*.ps | ||||
| main*.eps | ||||
| # *.ps | ||||
| # *.eps | ||||
| *.pdf | ||||
| 
 | ||||
| ## Generated if empty string is given at "Please type another file name for output:" | ||||
|  |  | |||
							
								
								
									
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							|  | @ -145,41 +145,14 @@ | |||
| \end{center} | ||||
| 
 | ||||
| \section{Equations} | ||||
| \subsection{Fundamental equations} | ||||
| \subsubsection{Navier-Stokes} | ||||
| \subsection{Navier-Stokes} | ||||
| \begin{equation} | ||||
|     \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 | ||||
|     \frac{D}{Dt} | ||||
| \end{equation} | ||||
| 
 | ||||
| \subsection{Circulation} | ||||
| \begin{equation} | ||||
|     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}) | ||||
|     C = \oint_c u \, dc = \oint (u \, dx + v \, dy + w \, dz) | ||||
| \end{equation} | ||||
| 
 | ||||
| \section{Concepts} | ||||
|  | @ -189,20 +162,6 @@ if $\mathcal{H} = 0$, the process is \textit{adiabatic} | |||
|     \frac{\partial}{\partial z} v_G = \bigg(\frac{1}{f}\frac{g}{\theta_0}\bigg)(k \times \nabla_h \theta^*) | ||||
| \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 | ||||
| 
 | ||||
| \section*{Copyleft} | ||||
|  |  | |||
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