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\begin{document}
\frontmatter
\thispagestyle{empty}
\begin{center}
\vspace*{3cm}
{\Huge\bfseries A Study in the Mathematics of Flow}\\[1cm]
{\large First Last}\\[3cm]
{\large Exampleworth College}\\[0.5cm]
{\large University of Oxbridge}\\[3cm]
{\large A thesis submitted for the degree of}\\
{\itshape Doctor of Philosophy}\\[1cm]
{\large Hilary \the\year}
\end{center}
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\chapter*{Abstract}
We investigate the dynamics of incompressible flow around bluff bodies at
moderate Reynolds numbers, combining direct numerical simulation with a new
asymptotic expansion valid at the boundary of the laminar-turbulent transition.
\cleardoublepage
\chapter*{Acknowledgements}
I thank my supervisor, colleagues, and funding bodies.
\cleardoublepage
\tableofcontents
\listoffigures
\listoftables
\mainmatter
\chapter{Introduction}
This thesis is concerned with the hydrodynamics of bluff-body wakes.
\section{Background}
The problem dates to early 20th-century experiments.
\section{Outline}
Chapter~\ref{ch:theory} develops the theory; Chapter~\ref{ch:num} describes numerical methods.
\chapter{Theoretical Framework}
\label{ch:theory}
\begin{equation}
\partial_t u + (u \cdot \nabla)u = -\nabla p + \nu \Delta u, \qquad \nabla \cdot u = 0.
\end{equation}
We seek weak solutions in the Leray sense.
\chapter{Numerical Methods}
\label{ch:num}
We use a second-order projection scheme on staggered grids.
\chapter{Results}
\begin{table}[h]
\centering
\caption{Drag coefficients at various $Re$.}
\begin{tabular}{rcc}
\toprule
$Re$ & $C_D$ (ours) & $C_D$ (literature) \\
\midrule
40 & 1.54 & 1.56 \\
100 & 1.35 & 1.34 \\
200 & 1.32 & 1.31 \\
\bottomrule
\end{tabular}
\end{table}
\chapter{Conclusion}
The numerical results corroborate the asymptotic predictions to within 2\%.
\backmatter
\printbibliography
\end{document}

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