Compare commits

...

2 commits

Author SHA1 Message Date
Jannis Portmann
cb5f84a7eb Add output ps to ignores 2023-02-03 18:07:52 +01:00
Jannis Portmann
c1572375fa Some additions 2023-02-03 18:06:51 +01:00
2 changed files with 46 additions and 5 deletions

4
.gitignore vendored
View file

@ -22,8 +22,8 @@
*.xdv
*-converted-to.*
# these rules might exclude image files for figures etc.
# *.ps
# *.eps
main*.ps
main*.eps
*.pdf
## Generated if empty string is given at "Please type another file name for output:"

View file

@ -145,14 +145,41 @@
\end{center}
\section{Equations}
\subsection{Navier-Stokes}
\subsection{Fundamental equations}
\subsubsection{Navier-Stokes}
\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}
\subsection{Circulation}
\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}
\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^*)
\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}