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2 changed files with 46 additions and 5 deletions
4
.gitignore
vendored
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.gitignore
vendored
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@ -22,8 +22,8 @@
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*.xdv
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*.xdv
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*-converted-to.*
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*-converted-to.*
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# these rules might exclude image files for figures etc.
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# these rules might exclude image files for figures etc.
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# *.ps
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main*.ps
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# *.eps
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main*.eps
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*.pdf
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*.pdf
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## Generated if empty string is given at "Please type another file name for output:"
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## Generated if empty string is given at "Please type another file name for output:"
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47
main.tex
47
main.tex
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@ -145,14 +145,41 @@
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\end{center}
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\end{center}
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\section{Equations}
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\section{Equations}
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\subsection{Navier-Stokes}
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\subsection{Fundamental equations}
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\subsubsection{Navier-Stokes}
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\begin{equation}
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\begin{equation}
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\frac{D}{Dt}
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\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}
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\end{equation}
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\subsubsection{Conservation of mass}
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\begin{equation}
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\frac{D \rho}{Dt} + \rho(\nabla u) = 0
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\end{equation}
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\subsubsection{First law of thermodynamics}
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\begin{equation}
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\frac{D\theta}{Dt} = \bigg(\frac{\theta}{c_p T} \bigg) \mathcal{H}
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\end{equation}
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if $\mathcal{H} = 0$, the process is \textit{adiabatic}
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\subsubsection{Equation of state}
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\begin{equation}
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p = \rho RT
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\end{equation}
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\end{equation}
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\subsection{Circulation}
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\subsection{Circulation}
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\begin{equation}
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\begin{equation}
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C = \oint_c u \, dc = \oint (u \, dx + v \, dy + w \, dz)
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C = \oint_c \vec{v} \, dc = \oint (u \, dx + v \, dy + w \, dz) = \oint_0^{2\pi} \vec{v} \, r \, d\phi
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\end{equation}
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\subsection{Quasi geostrophic system of equations}
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\begin{equation}
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\zeta = \frac{\partial v}{\partial x} - \frac{\partial u}{\partial y}
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\end{equation}
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\subsubsection*{Vorticity equation}
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\begin{equation}
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\frac{D_h}{Dt} \zeta + \beta v = -f_0(\nabla_h \vec{v})
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\end{equation}
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\end{equation}
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\section{Concepts}
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\section{Concepts}
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@ -162,6 +189,20 @@
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\frac{\partial}{\partial z} v_G = \bigg(\frac{1}{f}\frac{g}{\theta_0}\bigg)(k \times \nabla_h \theta^*)
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\frac{\partial}{\partial z} v_G = \bigg(\frac{1}{f}\frac{g}{\theta_0}\bigg)(k \times \nabla_h \theta^*)
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\end{equation}
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\end{equation}
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\subsection{$Q$-Vector}
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The $Q$-Vector indicates if there is cyclogenesis ($\mathcal{F} < 0$, $\mathcal{F} \sim \nabla_h Q$)
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\vspace{2mm} \\
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How to determine the $Q$-Vector on weather charts:
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\begin{enumerate}
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\item Locate regions with:
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\begin{itemize}
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\item Large temperature gradient
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\item Strong wind change
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\end{itemize}
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\item Determine wind-change vector
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\item Rotate that vector by $+90^\circ$
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\end{enumerate}
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\scriptsize
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\scriptsize
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\section*{Copyleft}
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\section*{Copyleft}
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