diff --git a/.gitignore b/.gitignore index f7f6043..d6fcb13 100644 --- a/.gitignore +++ b/.gitignore @@ -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:" diff --git a/main.tex b/main.tex index 7922f38..f2ebbef 100644 --- a/main.tex +++ b/main.tex @@ -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}