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4 changed files with 56 additions and 13 deletions
2
Jenkinsfile
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Jenkinsfile
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@ -4,7 +4,7 @@ node {
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}
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stage('Build PDF') {
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sh 'latexmk -xelatex -jobname=lsd-zf main.tex'
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sh 'latexmk -xelatex -jobname=lsd-zf -f main.tex'
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}
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stage('Archive PDF') {
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BIN
img/eta.png
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img/eta.png
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After Width: | Height: | Size: 20 KiB |
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main.bib
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main.bib
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@ -0,0 +1,7 @@
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@misc{wernliLectureScript,
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title = {Lecture {{Script}}},
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author = {Wernli, Heini and Papritz, Lukas},
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url = {https://ethz.ch/content/dam/ethz/special-interest/usys/iac/iac-dam/documents/edu/courses/dynamics_of_large_scale_flow/LSD_2022.pdf},
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urldate = {2022-09-10},
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file = {/Users/thisfro/Zotero/storage/ERN2IM82/Lecture Script.pdf}
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}
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60
main.tex
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main.tex
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\documentclass[8pt,landscape]{article}
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\documentclass[landscape]{article}
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\usepackage[utf8]{inputenc}
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\usepackage{multicol}
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\usepackage{calc}
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\usepackage{bookmark}
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@ -13,12 +14,15 @@
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\usepackage{xcolor}
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\usepackage{float}
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\usepackage{apacite}
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\usepackage{physics}
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\usepackage[style=authoryear]{biblatex}
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\usepackage[
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type={CC},
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modifier={by-sa},
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version={3.0}
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]{doclicense}
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\addbibresource{main.bib}
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\graphicspath{{./img/}}
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\definecolor{codegreen}{rgb}{0,0.6,0}
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@ -148,12 +152,12 @@
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\subsection{Fundamental equations}
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\subsubsection{Navier-Stokes}
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\begin{equation}
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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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\frac{D\vb{u}}{Dt} = \underbrace{-\frac{1}{\rho}\nabla p}_\mathrm{Pressure} - \underbrace{(2\Omega \times \vb{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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\frac{D \rho}{Dt} + \rho(\nabla \vb{u}) = 0
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\end{equation}
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\subsubsection{First law of thermodynamics}
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@ -182,13 +186,30 @@ if $\mathcal{H} = 0$, the process is \textit{adiabatic}
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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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\subsection{Geostrophic streamfunction}
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\begin{equation}
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\nabla_h \psi = \zeta_G
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\end{equation}
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\subsection{Wave theory}
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\subsubsection*{Pertubation tendency}
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\begin{equation}
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\psi = \underbrace{\bar{\psi}(y,z)}_\mathrm{Mean \, meridional \, flow} + \underbrace{\psi'(x,y,z,t)}_\mathrm{Pertubation}
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\end{equation}
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assuming $|\psi'| \ll |\bar{\psi}|$
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\begin{equation}
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\bigg(\frac{\partial}{\partial t} + \mathcal{U} \bigg) q' + v'(\frac{\partial}{\partial y} \bar{q} + \beta) = 0
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\end{equation}
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with $\mathcal{U} = - \frac{\partial \bar{\psi}}{\partial y}$
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\section{Concepts}
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\subsection{Thermal wind}
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\textit{Thermal wind} describes the vertical change of geostrophic (i.e. horizontal) wind
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\begin{equation}
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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} \vb{v_G} = \bigg(\frac{1}{f}\frac{g}{\theta_0}\bigg)(\vb{k} \times \nabla_h \theta^*)
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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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@ -199,10 +220,28 @@ How to determine the $Q$-Vector on weather charts:
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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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\item Determine wind-change vector along $\eta$ (warm to the right, see Figure~\ref{Q-eta})
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\item Rotate that vector by $-90^\circ$
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\end{enumerate}
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\begin{figure}[H]
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\centering
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\includegraphics[width=0.1\textwidth]{eta.png}
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\caption{Direction of $\eta$}
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\label{Q-eta}
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\end{figure}
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\begin{equation}
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\vb{Q} = -\frac{g}{\theta_0}|\nabla_h\theta^{*}|(\vb{k} \wedge \frac{\partial}{\partial \xi}\vb{v_G})
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\end{equation}
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\subsection{PV streamer}
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\begin{itemize}
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\item is an upper level positive PV anomaly
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\item induces cyclonal flow
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\end{itemize}
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\scriptsize
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\section*{Copyleft}
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@ -213,14 +252,11 @@ This document is released under (CC BY-SA 3.0) \\
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\faGit \kern 0.88em \url{https://git.thisfro.ch/thisfro/lsd-zf} \\
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Jannis Portmann, HS22
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\section*{References}
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\begin{enumerate}
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\item Script: LSD\_22.pdf
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\end{enumerate}
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\printbibliography
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\section*{Image sources}
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\begin{itemize}
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\item Bild
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\item Figure~\ref{Q-eta} (Skript, \cite{wernliLectureScript})
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\end{itemize}
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\end{multicols*}
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