Report: Method
This commit is contained in:
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417a6640c4
commit
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GPG key ID:
9833D3C5A25BD227
5 changed files with 2899 additions and 16 deletions
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@ -115,6 +115,7 @@
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\DeclareMathOperator\cond{cond}
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\DeclareMathOperator\cond{cond}
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\DeclareMathOperator\erf{erf}
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\DeclareMathOperator\erf{erf}
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\DeclareMathOperator\erfc{erfc}
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\DeclareMathOperator\erfc{erfc}
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\DeclareMathOperator\sech{sech}
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%%% Vecteurs et Matrices
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%%% Vecteurs et Matrices
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\renewcommand\u[1]{\underline{#1}}
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\renewcommand\u[1]{\underline{#1}}
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684
report/fig/bathy.pgf
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684
report/fig/bathy.pgf
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@ -0,0 +1,684 @@
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%% Creator: Matplotlib, PGF backend
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%%
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%% To include the figure in your LaTeX document, write
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%% \input{<filename>.pgf}
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%%
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%% Make sure the required packages are loaded in your preamble
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%% \usepackage{pgf}
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%%
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%% Also ensure that all the required font packages are loaded; for instance,
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%% the lmodern package is sometimes necessary when using math font.
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%% \usepackage{lmodern}
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%%
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%% Figures using additional raster images can only be included by \input if
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%% they are in the same directory as the main LaTeX file. For loading figures
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%% from other directories you can use the `import` package
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%% \usepackage{import}
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%%
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%% and then include the figures with
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%% \import{<path to file>}{<filename>.pgf}
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%%
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%% Matplotlib used the following preamble
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%% \usepackage{fontspec}
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%% \setmainfont{DejaVuSerif.ttf}[Path=\detokenize{/home/edpibu/Code/openfoam_project/env/lib/python3.10/site-packages/matplotlib/mpl-data/fonts/ttf/}]
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%% \setsansfont{DejaVuSans.ttf}[Path=\detokenize{/home/edpibu/Code/openfoam_project/env/lib/python3.10/site-packages/matplotlib/mpl-data/fonts/ttf/}]
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%% \setmonofont{DejaVuSansMono.ttf}[Path=\detokenize{/home/edpibu/Code/openfoam_project/env/lib/python3.10/site-packages/matplotlib/mpl-data/fonts/ttf/}]
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%%
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\begingroup%
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\makeatletter%
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\begin{pgfpicture}%
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\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{6.000000in}{2.000000in}}%
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\pgfusepath{use as bounding box, clip}%
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\begin{pgfscope}%
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\pgfsetbuttcap%
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\pgfsetmiterjoin%
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\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}%
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\pgfsetfillcolor{currentfill}%
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\pgfsetlinewidth{0.000000pt}%
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\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}%
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\pgfsetstrokecolor{currentstroke}%
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\pgfsetdash{}{0pt}%
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\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
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\pgfpathlineto{\pgfqpoint{6.000000in}{0.000000in}}%
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\pgfpathlineto{\pgfqpoint{6.000000in}{2.000000in}}%
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\pgfpathlineto{\pgfqpoint{0.000000in}{2.000000in}}%
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\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}%
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\pgfpathclose%
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\pgfusepath{fill}%
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\end{pgfscope}%
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\begin{pgfscope}%
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\pgfsetbuttcap%
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\pgfsetmiterjoin%
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\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}%
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\pgfsetfillcolor{currentfill}%
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\pgfsetlinewidth{0.000000pt}%
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\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
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\pgfsetstrokecolor{currentstroke}%
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\pgfsetstrokeopacity{0.000000}%
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\pgfsetdash{}{0pt}%
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\pgfpathmoveto{\pgfqpoint{0.750000in}{0.571935in}}%
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\pgfpathlineto{\pgfqpoint{5.400000in}{0.571935in}}%
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\pgfpathlineto{\pgfqpoint{5.400000in}{1.408065in}}%
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\pgfpathlineto{\pgfqpoint{0.750000in}{1.408065in}}%
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\pgfpathlineto{\pgfqpoint{0.750000in}{0.571935in}}%
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\pgfpathclose%
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\pgfusepath{fill}%
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\end{pgfscope}%
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\begin{pgfscope}%
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\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
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\pgfusepath{clip}%
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\pgfsetrectcap%
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\pgfsetroundjoin%
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\pgfsetlinewidth{0.803000pt}%
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\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
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\pgfsetstrokecolor{currentstroke}%
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\pgfsetdash{}{0pt}%
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\pgfpathmoveto{\pgfqpoint{0.750000in}{0.571935in}}%
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\pgfpathlineto{\pgfqpoint{0.750000in}{1.408065in}}%
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\pgfusepath{stroke}%
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\end{pgfscope}%
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\begin{pgfscope}%
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\pgfsetbuttcap%
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\pgfsetroundjoin%
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\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
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\pgfsetfillcolor{currentfill}%
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\pgfsetlinewidth{0.803000pt}%
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\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
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\pgfsetstrokecolor{currentstroke}%
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\pgfsetdash{}{0pt}%
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\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
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\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
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\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
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\pgfusepath{stroke,fill}%
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}%
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\begin{pgfscope}%
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\pgfsys@transformshift{0.750000in}{0.571935in}%
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\pgfsys@useobject{currentmarker}{}%
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\end{pgfscope}%
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\end{pgfscope}%
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\begin{pgfscope}%
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\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
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\pgfsetstrokecolor{textcolor}%
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\pgfsetfillcolor{textcolor}%
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\pgftext[x=0.750000in,y=0.474713in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 0}%
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\end{pgfscope}%
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\begin{pgfscope}%
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\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
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\pgfusepath{clip}%
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\pgfsetrectcap%
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\pgfsetroundjoin%
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\pgfsetlinewidth{0.803000pt}%
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\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
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\pgfsetstrokecolor{currentstroke}%
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\pgfsetdash{}{0pt}%
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\pgfpathlineto{\pgfqpoint{1.370000in}{1.408065in}}%
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\pgfusepath{stroke}%
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\end{pgfscope}%
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\begin{pgfscope}%
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\pgfsetbuttcap%
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\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
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\pgfsetfillcolor{currentfill}%
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\pgfsetlinewidth{0.803000pt}%
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\pgfsetstrokecolor{currentstroke}%
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\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
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\pgfusepath{stroke,fill}%
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}%
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\begin{pgfscope}%
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\pgfsys@transformshift{1.370000in}{0.571935in}%
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\pgfsys@useobject{currentmarker}{}%
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\end{pgfscope}%
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\end{pgfscope}%
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\begin{pgfscope}%
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\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
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\pgfsetstrokecolor{textcolor}%
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\pgftext[x=1.370000in,y=0.474713in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 20}%
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\end{pgfscope}%
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\begin{pgfscope}%
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\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
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\pgfusepath{clip}%
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\pgfsetrectcap%
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\pgfsetroundjoin%
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\pgfsetlinewidth{0.803000pt}%
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\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
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\pgfsetstrokecolor{currentstroke}%
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\pgfsetdash{}{0pt}%
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\pgfpathlineto{\pgfqpoint{1.990000in}{1.408065in}}%
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\pgfusepath{stroke}%
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\pgfsetstrokecolor{currentstroke}%
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\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
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\pgfusepath{stroke,fill}%
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}%
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\begin{pgfscope}%
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\pgfsys@transformshift{1.990000in}{0.571935in}%
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\pgfsetlinewidth{0.803000pt}%
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\pgfsetstrokecolor{currentstroke}%
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\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
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\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
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\pgfusepath{stroke,fill}%
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}%
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\begin{pgfscope}%
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\pgfusepath{stroke}%
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}%
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|
\pgfusepath{stroke,fill}%
|
||||||
|
}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfsys@transformshift{3.850000in}{0.571935in}%
|
||||||
|
\pgfsys@useobject{currentmarker}{}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetstrokecolor{textcolor}%
|
||||||
|
\pgfsetfillcolor{textcolor}%
|
||||||
|
\pgftext[x=3.850000in,y=0.474713in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 100}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
|
||||||
|
\pgfusepath{clip}%
|
||||||
|
\pgfsetrectcap%
|
||||||
|
\pgfsetroundjoin%
|
||||||
|
\pgfsetlinewidth{0.803000pt}%
|
||||||
|
\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
|
||||||
|
\pgfsetstrokecolor{currentstroke}%
|
||||||
|
\pgfsetdash{}{0pt}%
|
||||||
|
\pgfpathmoveto{\pgfqpoint{4.470000in}{0.571935in}}%
|
||||||
|
\pgfpathlineto{\pgfqpoint{4.470000in}{1.408065in}}%
|
||||||
|
\pgfusepath{stroke}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfsetbuttcap%
|
||||||
|
\pgfsetroundjoin%
|
||||||
|
\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetfillcolor{currentfill}%
|
||||||
|
\pgfsetlinewidth{0.803000pt}%
|
||||||
|
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetstrokecolor{currentstroke}%
|
||||||
|
\pgfsetdash{}{0pt}%
|
||||||
|
\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
|
||||||
|
\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
|
||||||
|
\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
|
||||||
|
\pgfusepath{stroke,fill}%
|
||||||
|
}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfsys@transformshift{4.470000in}{0.571935in}%
|
||||||
|
\pgfsys@useobject{currentmarker}{}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetstrokecolor{textcolor}%
|
||||||
|
\pgfsetfillcolor{textcolor}%
|
||||||
|
\pgftext[x=4.470000in,y=0.474713in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 120}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
|
||||||
|
\pgfusepath{clip}%
|
||||||
|
\pgfsetrectcap%
|
||||||
|
\pgfsetroundjoin%
|
||||||
|
\pgfsetlinewidth{0.803000pt}%
|
||||||
|
\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
|
||||||
|
\pgfsetstrokecolor{currentstroke}%
|
||||||
|
\pgfsetdash{}{0pt}%
|
||||||
|
\pgfpathmoveto{\pgfqpoint{5.090000in}{0.571935in}}%
|
||||||
|
\pgfpathlineto{\pgfqpoint{5.090000in}{1.408065in}}%
|
||||||
|
\pgfusepath{stroke}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfsetbuttcap%
|
||||||
|
\pgfsetroundjoin%
|
||||||
|
\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetfillcolor{currentfill}%
|
||||||
|
\pgfsetlinewidth{0.803000pt}%
|
||||||
|
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetstrokecolor{currentstroke}%
|
||||||
|
\pgfsetdash{}{0pt}%
|
||||||
|
\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
|
||||||
|
\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
|
||||||
|
\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
|
||||||
|
\pgfusepath{stroke,fill}%
|
||||||
|
}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfsys@transformshift{5.090000in}{0.571935in}%
|
||||||
|
\pgfsys@useobject{currentmarker}{}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetstrokecolor{textcolor}%
|
||||||
|
\pgfsetfillcolor{textcolor}%
|
||||||
|
\pgftext[x=5.090000in,y=0.474713in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 140}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetstrokecolor{textcolor}%
|
||||||
|
\pgfsetfillcolor{textcolor}%
|
||||||
|
\pgftext[x=3.075000in,y=0.284744in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont x (m)}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
|
||||||
|
\pgfusepath{clip}%
|
||||||
|
\pgfsetrectcap%
|
||||||
|
\pgfsetroundjoin%
|
||||||
|
\pgfsetlinewidth{0.803000pt}%
|
||||||
|
\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
|
||||||
|
\pgfsetstrokecolor{currentstroke}%
|
||||||
|
\pgfsetdash{}{0pt}%
|
||||||
|
\pgfpathmoveto{\pgfqpoint{0.750000in}{0.805859in}}%
|
||||||
|
\pgfpathlineto{\pgfqpoint{5.400000in}{0.805859in}}%
|
||||||
|
\pgfusepath{stroke}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfsetbuttcap%
|
||||||
|
\pgfsetroundjoin%
|
||||||
|
\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetfillcolor{currentfill}%
|
||||||
|
\pgfsetlinewidth{0.803000pt}%
|
||||||
|
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetstrokecolor{currentstroke}%
|
||||||
|
\pgfsetdash{}{0pt}%
|
||||||
|
\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
|
||||||
|
\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
|
||||||
|
\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
|
||||||
|
\pgfusepath{stroke,fill}%
|
||||||
|
}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfsys@transformshift{0.750000in}{0.805859in}%
|
||||||
|
\pgfsys@useobject{currentmarker}{}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetstrokecolor{textcolor}%
|
||||||
|
\pgfsetfillcolor{textcolor}%
|
||||||
|
\pgftext[x=0.368022in, y=0.753098in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \ensuremath{-}10}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
|
||||||
|
\pgfusepath{clip}%
|
||||||
|
\pgfsetrectcap%
|
||||||
|
\pgfsetroundjoin%
|
||||||
|
\pgfsetlinewidth{0.803000pt}%
|
||||||
|
\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
|
||||||
|
\pgfsetstrokecolor{currentstroke}%
|
||||||
|
\pgfsetdash{}{0pt}%
|
||||||
|
\pgfpathmoveto{\pgfqpoint{0.750000in}{1.115859in}}%
|
||||||
|
\pgfpathlineto{\pgfqpoint{5.400000in}{1.115859in}}%
|
||||||
|
\pgfusepath{stroke}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfsetbuttcap%
|
||||||
|
\pgfsetroundjoin%
|
||||||
|
\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetfillcolor{currentfill}%
|
||||||
|
\pgfsetlinewidth{0.803000pt}%
|
||||||
|
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetstrokecolor{currentstroke}%
|
||||||
|
\pgfsetdash{}{0pt}%
|
||||||
|
\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
|
||||||
|
\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
|
||||||
|
\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
|
||||||
|
\pgfusepath{stroke,fill}%
|
||||||
|
}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfsys@transformshift{0.750000in}{1.115859in}%
|
||||||
|
\pgfsys@useobject{currentmarker}{}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetstrokecolor{textcolor}%
|
||||||
|
\pgfsetfillcolor{textcolor}%
|
||||||
|
\pgftext[x=0.564412in, y=1.063098in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 0}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetstrokecolor{textcolor}%
|
||||||
|
\pgfsetfillcolor{textcolor}%
|
||||||
|
\pgftext[x=0.312467in,y=0.990000in,,bottom,rotate=90.000000]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont y (m)}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfsetrectcap%
|
||||||
|
\pgfsetmiterjoin%
|
||||||
|
\pgfsetlinewidth{0.803000pt}%
|
||||||
|
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetstrokecolor{currentstroke}%
|
||||||
|
\pgfsetdash{}{0pt}%
|
||||||
|
\pgfpathmoveto{\pgfqpoint{0.750000in}{0.571935in}}%
|
||||||
|
\pgfpathlineto{\pgfqpoint{0.750000in}{1.408065in}}%
|
||||||
|
\pgfusepath{stroke}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfsetrectcap%
|
||||||
|
\pgfsetmiterjoin%
|
||||||
|
\pgfsetlinewidth{0.803000pt}%
|
||||||
|
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetstrokecolor{currentstroke}%
|
||||||
|
\pgfsetdash{}{0pt}%
|
||||||
|
\pgfpathmoveto{\pgfqpoint{5.400000in}{0.571935in}}%
|
||||||
|
\pgfpathlineto{\pgfqpoint{5.400000in}{1.408065in}}%
|
||||||
|
\pgfusepath{stroke}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfsetrectcap%
|
||||||
|
\pgfsetmiterjoin%
|
||||||
|
\pgfsetlinewidth{0.803000pt}%
|
||||||
|
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetstrokecolor{currentstroke}%
|
||||||
|
\pgfsetdash{}{0pt}%
|
||||||
|
\pgfpathmoveto{\pgfqpoint{0.750000in}{0.571935in}}%
|
||||||
|
\pgfpathlineto{\pgfqpoint{5.400000in}{0.571935in}}%
|
||||||
|
\pgfusepath{stroke}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfsetrectcap%
|
||||||
|
\pgfsetmiterjoin%
|
||||||
|
\pgfsetlinewidth{0.803000pt}%
|
||||||
|
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetstrokecolor{currentstroke}%
|
||||||
|
\pgfsetdash{}{0pt}%
|
||||||
|
\pgfpathmoveto{\pgfqpoint{0.750000in}{1.408065in}}%
|
||||||
|
\pgfpathlineto{\pgfqpoint{5.400000in}{1.408065in}}%
|
||||||
|
\pgfusepath{stroke}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfsetbuttcap%
|
||||||
|
\pgfsetmiterjoin%
|
||||||
|
\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}%
|
||||||
|
\pgfsetfillcolor{currentfill}%
|
||||||
|
\pgfsetfillopacity{0.800000}%
|
||||||
|
\pgfsetlinewidth{1.003750pt}%
|
||||||
|
\definecolor{currentstroke}{rgb}{0.800000,0.800000,0.800000}%
|
||||||
|
\pgfsetstrokecolor{currentstroke}%
|
||||||
|
\pgfsetstrokeopacity{0.800000}%
|
||||||
|
\pgfsetdash{}{0pt}%
|
||||||
|
\pgfpathmoveto{\pgfqpoint{0.847222in}{0.889240in}}%
|
||||||
|
\pgfpathlineto{\pgfqpoint{2.111233in}{0.889240in}}%
|
||||||
|
\pgfpathquadraticcurveto{\pgfqpoint{2.139011in}{0.889240in}}{\pgfqpoint{2.139011in}{0.917017in}}%
|
||||||
|
\pgfpathlineto{\pgfqpoint{2.139011in}{1.310843in}}%
|
||||||
|
\pgfpathquadraticcurveto{\pgfqpoint{2.139011in}{1.338621in}}{\pgfqpoint{2.111233in}{1.338621in}}%
|
||||||
|
\pgfpathlineto{\pgfqpoint{0.847222in}{1.338621in}}%
|
||||||
|
\pgfpathquadraticcurveto{\pgfqpoint{0.819444in}{1.338621in}}{\pgfqpoint{0.819444in}{1.310843in}}%
|
||||||
|
\pgfpathlineto{\pgfqpoint{0.819444in}{0.917017in}}%
|
||||||
|
\pgfpathquadraticcurveto{\pgfqpoint{0.819444in}{0.889240in}}{\pgfqpoint{0.847222in}{0.889240in}}%
|
||||||
|
\pgfpathlineto{\pgfqpoint{0.847222in}{0.889240in}}%
|
||||||
|
\pgfpathclose%
|
||||||
|
\pgfusepath{stroke,fill}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfsetrectcap%
|
||||||
|
\pgfsetroundjoin%
|
||||||
|
\pgfsetlinewidth{1.003750pt}%
|
||||||
|
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetstrokecolor{currentstroke}%
|
||||||
|
\pgfsetdash{}{0pt}%
|
||||||
|
\pgfpathmoveto{\pgfqpoint{0.875000in}{1.226153in}}%
|
||||||
|
\pgfpathlineto{\pgfqpoint{1.013889in}{1.226153in}}%
|
||||||
|
\pgfpathlineto{\pgfqpoint{1.152778in}{1.226153in}}%
|
||||||
|
\pgfusepath{stroke}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetstrokecolor{textcolor}%
|
||||||
|
\pgfsetfillcolor{textcolor}%
|
||||||
|
\pgftext[x=1.263889in,y=1.177542in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont Bathymetry}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfsetrectcap%
|
||||||
|
\pgfsetroundjoin%
|
||||||
|
\pgfsetlinewidth{1.003750pt}%
|
||||||
|
\definecolor{currentstroke}{rgb}{1.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetstrokecolor{currentstroke}%
|
||||||
|
\pgfsetdash{}{0pt}%
|
||||||
|
\pgfpathmoveto{\pgfqpoint{0.875000in}{1.022296in}}%
|
||||||
|
\pgfpathlineto{\pgfqpoint{1.013889in}{1.022296in}}%
|
||||||
|
\pgfpathlineto{\pgfqpoint{1.152778in}{1.022296in}}%
|
||||||
|
\pgfusepath{stroke}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetstrokecolor{textcolor}%
|
||||||
|
\pgfsetfillcolor{textcolor}%
|
||||||
|
\pgftext[x=1.263889in,y=0.973685in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont Armour}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
|
||||||
|
\pgfusepath{clip}%
|
||||||
|
\pgfsetrectcap%
|
||||||
|
\pgfsetroundjoin%
|
||||||
|
\pgfsetlinewidth{1.003750pt}%
|
||||||
|
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||||
|
\pgfsetstrokecolor{currentstroke}%
|
||||||
|
\pgfsetdash{}{0pt}%
|
||||||
|
\pgfpathmoveto{\pgfqpoint{0.750000in}{0.626923in}}%
|
||||||
|
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\begin{pgfscope}%
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\pgfpathclose%
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\pgfusepath{stroke,fill}%
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|
}%
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\begin{pgfscope}%
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|
\pgfsys@transformshift{0.000000in}{0.000000in}%
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|
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|
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|
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\begin{pgfscope}%
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\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
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\pgfsetbuttcap%
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\pgfsetlinewidth{1.003750pt}%
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\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
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\pgfsetstrokecolor{currentstroke}%
|
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\pgfsetdash{}{0pt}%
|
||||||
|
\pgfsys@defobject{currentmarker}{\pgfqpoint{3.952300in}{1.100359in}}{\pgfqpoint{4.183250in}{1.263109in}}{%
|
||||||
|
\pgfpathmoveto{\pgfqpoint{4.183250in}{1.115859in}}%
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||||||
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\pgfpathlineto{\pgfqpoint{4.183250in}{1.100359in}}%
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|
\pgfpathlineto{\pgfqpoint{3.952300in}{1.263109in}}%
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||||||
|
\pgfpathlineto{\pgfqpoint{3.955400in}{1.115859in}}%
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\pgfpathlineto{\pgfqpoint{3.952300in}{1.115859in}}%
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\pgfpathlineto{\pgfqpoint{4.183250in}{1.115859in}}%
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\pgfpathlineto{\pgfqpoint{4.183250in}{1.115859in}}%
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\pgfpathlineto{\pgfqpoint{4.183250in}{1.115859in}}%
|
||||||
|
\pgfpathclose%
|
||||||
|
\pgfusepath{stroke,fill}%
|
||||||
|
}%
|
||||||
|
\begin{pgfscope}%
|
||||||
|
\pgfsys@transformshift{0.000000in}{0.000000in}%
|
||||||
|
\pgfsys@useobject{currentmarker}{}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\end{pgfscope}%
|
||||||
|
\end{pgfpicture}%
|
||||||
|
\makeatother%
|
||||||
|
\endgroup%
|
||||||
2096
report/fig/map.pgf
Normal file
2096
report/fig/map.pgf
Normal file
File diff suppressed because it is too large
Load diff
|
|
@ -48,23 +48,31 @@
|
||||||
}
|
}
|
||||||
|
|
||||||
@article{nott2003waves,
|
@article{nott2003waves,
|
||||||
title={Waves, coastal boulder deposits and the importance of the pre-transport setting},
|
title={Waves, coastal boulder deposits and the importance of the pre-transport setting},
|
||||||
author={Nott, Jonathan},
|
author={Nott, Jonathan},
|
||||||
journal={Earth and Planetary Science Letters},
|
journal={Earth and Planetary Science Letters},
|
||||||
volume={210},
|
volume={210},
|
||||||
number={1-2},
|
number={1-2},
|
||||||
pages={269--276},
|
pages={269--276},
|
||||||
year={2003},
|
year={2003},
|
||||||
publisher={Elsevier}
|
publisher={Elsevier}
|
||||||
}
|
}
|
||||||
|
|
||||||
@article{zijlema2011swash,
|
@article{zijlema2011swash,
|
||||||
title={SWASH: An operational public domain code for simulating wave fields and rapidly varied flows in coastal waters},
|
title={SWASH: An operational public domain code for simulating wave fields and rapidly varied flows in coastal waters},
|
||||||
author={Zijlema, Marcel and Stelling, Guus and Smit, Pieter},
|
author={Zijlema, Marcel and Stelling, Guus and Smit, Pieter},
|
||||||
journal={Coastal Engineering},
|
journal={Coastal Engineering},
|
||||||
volume={58},
|
volume={58},
|
||||||
number={10},
|
number={10},
|
||||||
pages={992--1012},
|
pages={992--1012},
|
||||||
year={2011},
|
year={2011},
|
||||||
publisher={Elsevier}
|
publisher={Elsevier}
|
||||||
|
}
|
||||||
|
|
||||||
|
@misc{shomsjl,
|
||||||
|
author="SHOM",
|
||||||
|
title="MNT topo-bathymétrique côtier de la baie de Saint-Jean-de-Luz et de ses abords a 20m (Projet TANDEM).",
|
||||||
|
year="2016",
|
||||||
|
doi={10.17183/MNT_COTIER_BAIE_SJL_TANDEM_20m_WGS84},
|
||||||
|
url={http://dx.doi.org/10.17183/MNT_COTIER_BAIE_SJL_TANDEM_20m_WGS84},
|
||||||
}
|
}
|
||||||
|
|
|
||||||
|
|
@ -89,6 +89,100 @@ following computations, as it represents the expected porosity of such a
|
||||||
block armour.
|
block armour.
|
||||||
|
|
||||||
\section{Methods}
|
\section{Methods}
|
||||||
|
\subsection{Model}
|
||||||
|
In this project, we will model the transformation of a storm wave over the
|
||||||
|
Artha breakwater using the olaFlow (\cite{olaFlow}) model in a two-dimensionnal
|
||||||
|
domain. This model has several features that will be important for this study.
|
||||||
|
It provides powerful wave-generation and wave absorption capabilities, as well
|
||||||
|
as the ability to study two-phase flow through porous media.
|
||||||
|
|
||||||
|
The olaFlow model is based on VARANS equations\footnote{Volume-Averaged
|
||||||
|
Reynolds-Averaged Navier-Stokes equations}. This model is based on a
|
||||||
|
finite-volume approach, and provides multiple volume-averaging methods for
|
||||||
|
turbulence: the $k-\varepsilon$ model and the $k-\omega$ sst model. The
|
||||||
|
$k-\omega$ sst model should provide better results in situations where strong
|
||||||
|
pressure gradients are present, at the cost of computing power.
|
||||||
|
For the purposes of this initial sensibility study, the $k-\omega$ model will
|
||||||
|
be used.
|
||||||
|
|
||||||
|
\subsection{Domain}
|
||||||
|
The studied domain will be a two-dimensionnal vertical slice going through the
|
||||||
|
Artha breakwater. In order to provide accurate results while keeping
|
||||||
|
computation times acceptable, a domain length of \SI{150}{\m} was chosen, with
|
||||||
|
a length of \SI{120}{\m} towards the offshore and \SI{30}{\m} towards the
|
||||||
|
inside of the Saint-Jean-de-Luz bay, as shown in \autoref{fig:map}.
|
||||||
|
|
||||||
|
\begin{figure}
|
||||||
|
\centering
|
||||||
|
\input{fig/map.pgf}
|
||||||
|
\caption{Studied domain.}\label{fig:map}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
The bathymetry was generated using bathymetric data from the SHOM
|
||||||
|
(\cite{shomsjl}). Although the density of points is fairly low in this data,
|
||||||
|
it should be precise enough for the purposes of this project.
|
||||||
|
In addition to this data, the geometry of the superstructure was taken from
|
||||||
|
\cite{amir}, and the size of the porous armor layer was inspired from
|
||||||
|
\cite{poncet2021characterization}. The necessary stl files that are used by
|
||||||
|
snappyHexMesh for the solid boundaries and olaFlow for the porosity
|
||||||
|
configuration were generated using a custom python script, and the resulting
|
||||||
|
case is plotted in \autoref{fig:conf}.
|
||||||
|
|
||||||
|
\begin{figure}
|
||||||
|
\centering
|
||||||
|
\input{fig/bathy.pgf}
|
||||||
|
\caption{Studied configuration (bathymetry and porosity).}\label{fig:conf}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
\subsection{Mesh}
|
||||||
|
In order to provide accurate results with an acceptable computation time, a
|
||||||
|
mesh with \SI{1}{\m} cells was generated on the domain. It seems like olaFlow
|
||||||
|
cannot use variable mesh sizing, which meant that the mesh was still fairly
|
||||||
|
coarse near the edges of the domain.
|
||||||
|
|
||||||
|
The boundary conditions were set to a wave generator on the offshore boundary,
|
||||||
|
and a wave absorption boundary on the bay side. The bottom and the caisson were
|
||||||
|
set to wall boundaries, and the top side of the domain was set to an
|
||||||
|
atmospheric boundary.
|
||||||
|
|
||||||
|
\subsection{Model setup}
|
||||||
|
In an attempt to model the event of February 2017 in Saint-Jean-de-Luz, the
|
||||||
|
water level was set to \SI{5}{\m}. The inbound wave on the offshore side of
|
||||||
|
the domain was set as a solitary Boussinesq wave, with a wave height
|
||||||
|
$H=\SI{7.5}{\m}$. The wave equation is the following:
|
||||||
|
\begin{equation}
|
||||||
|
\eta=H\left[\sech\sqrt{\frac 34\frac Hh\frac{x-ct}h}\right]^2
|
||||||
|
\end{equation}
|
||||||
|
|
||||||
|
\subsection{Porosity setup}
|
||||||
|
The goal of the study is to find out the influence of the porosity parameters
|
||||||
|
on the model results. Porosity in the olaFlow model is goverened by five
|
||||||
|
parameters: a, b, c are tuning parameters that represent friction inside
|
||||||
|
the porous material, D50 is the mean nominal diameter of blocks, and porosity.
|
||||||
|
|
||||||
|
In this study, we will focus on the D50 and porosity parameters, as a, b and c
|
||||||
|
should be tuned according to experimental data. The friction parameters will be
|
||||||
|
set to the default from the breakwater example in the olaFlow model.
|
||||||
|
|
||||||
|
Four cases will be run, with all combinations of the parameters in
|
||||||
|
\autoref{tab:params}. The D50 parameters is based on the smallest and largest
|
||||||
|
edge size of the blocks that make up the breakwater armour. The porosity
|
||||||
|
parameters are based on the work of \cite{poncet2021characterization}, with
|
||||||
|
\num{0.40} being the value that he used for the numerical study, and \num{0.25}
|
||||||
|
being the value that yielded the lowest error in the model calibration.
|
||||||
|
|
||||||
|
\begin{table}
|
||||||
|
\centering
|
||||||
|
\begin{tabular}{lcc}
|
||||||
|
\toprule
|
||||||
|
\bfseries Parameters & & \\
|
||||||
|
\midrule
|
||||||
|
D50 & \SI{4}{\m} & \SI{2}{\m} \\
|
||||||
|
Porosity & \num{0.40} & \num{0.25} \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
|
\caption{Parameter values.}\label{tab:params}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
\section{Results}
|
\section{Results}
|
||||||
|
|
||||||
|
|
|
||||||
Reference in a new issue