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\usepackage{amsthm}
\usepackage{amssymb}
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%\usepackage{textcomp}
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%\hypersetup{pdfpagemode=FullScreen}

\title{Heat flux and hydrography at the Main Endeavour vent field}
\subtitle{MGG seminar and Final Examination \\ May 8, 2003}
\author{Scott Veirs}
\email{scottv@ocean.washington.edu}
\institution{University of Washington School of Oceanography}
\slideCaption{}

\begin{document}

\maketitle

\begin{slide}{Motivation}
%\begin{figure}
\begin{tabular}{lc}
\begin{minipage} {5cm}
Plumes in cross flow: 
\begin{itemize}
\item{In the atmosphere $\longrightarrow$}
\item{In the ocean}
\end{itemize}

Flux \& form implications: 
\begin{itemize}
\item{Crustal formation}
\item{Ocean chemistry}
\item{Habitat \& dispersal}
\item{Global heat budget}
\end{itemize}
\end{minipage}
&
\begin{minipage} {10cm}
\includegraphics*[width=.5\textwidth]{baghdad_plumes.eps}

\tiny{NASA Earth Observatory}
\end{minipage}
\end{tabular}
\end{slide}

\begin{slide}{Outline ($\sim$45 minutes)}
\begin{itemize}
  \item{(10) The Flow Mow study}
  \item{(10) Current results}
  \item{(5) Model results}
  \item{(10) Heat flux results}
  \item{(5) Conclusions}
  \item{(5) Acknowledgements}
\end{itemize}
\end{slide}


\overlays{6}{
\begin{slide}{Endeavour study site}
\begin{tabular}{rc}
\begin{minipage}{4cm}

\begin{small}
Orientation:
\begin{itemstep}
\item Start: 47$^\circ$54.5'N
\item $\sim$300\,m relief; crest $\sim$2100\,m
\item Valley 10\,km long, 1\,km wide, 100\,m deep 
\item Saddle $\sim$2170\,m
\item Vent fields
\end{itemstep}
\end{small}

\end{minipage}
&
\begin{minipage}{12cm}
\includegraphics*[width=0.5\textwidth]{../figs/maps/field_location_map.eps}
\end{minipage}
\end{tabular}

\end{slide}
}


\begin{slide}{Main Endeavour vent field (MEF)}
\begin{center}
\includegraphics*[width=.5\textwidth]{finexsmoke_map.eps}
%\hfill
%\includegraphics*[width=.5\textwidth]{mefnamemap.eps}
\end{center}
\end{slide}


\begin{slide}{MEF heat flux puzzles}

Power loss per km of ridge: \\ 
$H_f+H_d \simeq H_R = Q_R (L_r + \int _{1200}^{200} c_r(T) dT) = 42$\,MW/km

\includegraphics*[width=.5\textwidth]{finexcrustbox.eps}
%\includegraphics*[width=.7\textwidth]{../figs/xfig/crustbox.eps} 

\begin{tiny}
\begin{tabular}{lrrr}
Study             & Estimate [MW] & Heat flux\\
\hline
Thomson et al., 1992   &  2500$\pm$1525  & $H_p$ \\
Baker \& Massoth, 1987 &  4250$\pm$2750  & $H_p$ \\
%Rosenberg et al., 1988 &  3000$\pm$2000  & $H_p$ \\
%Ginster et al., 1994   &  364$\pm$73    & $H_f$ \\     
Ginster et al., 1994   &  615$\pm$120    & $H_f$ \\
Schultz et al, 1992    & 9000$\pm$760    & $H_d$ \\
\end{tabular}
\end{tiny}
\end{slide}


\begin{slide}{Heat flux from a control volume}
\begin{center}
\includegraphics*[width=.5\textwidth]{fmcvfinex.eps}
\end{center}
\begin{itemize}
\item Net heat flux via \emph{advection} through $A$:
\end{itemize}
%\begin{tiny}
  \begin{equation*}
  \mathbf{H} = \int_A \rho c_p \theta \mathbf{ u \cdot \hat{n} } dA \simeq \rho {c_p} \sum_{i=1}^{N} \Delta_S\theta_i u_i \Delta A_i
  \end{equation*}

\begin{tiny}
%How best to measure $\theta$ (and $S$) and $u$ over $A$?
\end{tiny}
\end{slide}


\begin{slide}{Instruments: CTD \& ABE}
\includegraphics*[width=.43\textwidth]{../figs/ctd_on_deck.eps}\hfill
\includegraphics*[width=.43\textwidth]{../figs/abe_front.eps}
\end{slide}


\begin{slide}{Instruments: Current meters}
\includegraphics*[width=.85\textwidth]{../figs/setting/alongaxisbathy.eps}
\end{slide}


\begin{slide}{Mean flow}
\begin{center}
\includegraphics*[width=.65\textwidth]{../figs/cms/5cmmultipvd.eps}
\end{center}

%\tiny{Idea: measure heat flux in plume bent over by mean flow!}
\end{slide}

%\begin{slide}{MEF control volumes and heat fluxes}
%\begin{center}
%\end{center}


%\tiny{So, what might explain the difference?  $H_d$?  Change?  Errors?}
%\end{slide}


\begin{slide}{Oscillatory flow over ridge}
\begin{tabular}{ll}
\begin{minipage}{4cm}
\begin{tiny}
$\Delta x_c$ 
\begin{itemize}
\item{$\sim$2.2\,km above ridge}
\item{$\sim$1.3\,km in valley}
\end{itemize}

$\Delta x_{\overline{u}}$ in 12\,hr:
\begin{itemize}
\item{$\sim$2.2\,km at 5\,cm/s}
\item{$\sim$0.5\,km at 1\,cm/s}
\end{itemize}

%\href{notes.html}{\blue notes}

\href{run:cm250.fli}{Animation}
\end{tiny}
\end{minipage}
&
\begin{minipage}{13cm}
\includegraphics*[width=.4\textwidth]{../figs/cms/thomson/ellipses.eps}

\tiny{Figure courtesy Rick Thomson, IOS Canada}
\end{minipage}
\end{tabular}
\end{slide}


\begin{slide}{Oscillatory flow in valley}
\begin{center}
%\includegraphics*[width=0.6\textwidth]{../figs/cms/fm1_quiver.eps2} 
\includegraphics*[width=0.6\textwidth]{../figs/cms/fm1_v-tseries-all.eps}
\end{center}

\begin{tiny}
\href{run:3cms.fli}{Animation}
\end{tiny}
\end{slide}



\begin{slide}{Hydrography and heat flux in the valley}
\begin{center}
\includegraphics*[width=0.7\textwidth]{../figs/fm1/allabe_NSwalls.eps2}
\begin{tiny}
$H_h=\overline{H}_N+\overline{H}_S = \rho c_p \overline{u} A (\overline{\Delta\theta}_N - \overline{\Delta\theta}_S)=80\pm37$\,MW (46\%, $\sim$50\%)
\end{tiny}
\end{center}
% Changing dTh or v by 0.01 units alters heat flux by 10MW
\end{slide}

%\begin{slide}{CTD survey of north and south surfaces}
%\begin{center}
%\includegraphics*[width=.75\textwidth]{../figs/upper/allctd_NSwalls_fullz.eps2}
%\end{center}
%\end{slide}

%\begin{slide}{CTD time series north and south of MEF}
%\begin{center}
%\includegraphics*[width=.75\textwidth]{../figs/upper/Dth.nosomef.image.all2.eps}
%\end{center}
%\end{slide}

\begin{slide}{Hydrography and heat flux above the ridge}
\begin{center}
\includegraphics*[width=.75\textwidth]{../figs/upper/Dth35-39_annot.eps}
\begin{tiny}
%${H_{qs}}_j = \sum_{i=j}^{j+3} {H_h}_i$ for $j=$1..16 observed surfaces yields
$\overline{H_{qs}}=442\pm213$\,MW.  Max $H_{qs} \simeq +2000$\,MW
% Use corrected value!!
\end{tiny}
\end{center}
\end{slide}


%\begin{center}
%\includegraphics*[width=.75\textwidth]{../figs/setting/NoSoMEF_5m_meanDTh2.allstns.eps2}
%\end{center}


\begin{slide}{Lower heat flux budget: \\ $H_d + H_f = H_v + H_h$}
%\includegraphics*[width=.75\textwidth]{../figs/xfig/crustbox.eps} 
\begin{center}
%$H_d + H_f = H_v + H_h$
%
\includegraphics*[width=.4\textwidth]{../figs/xfig/fmcv.eps}
\end{center}

\begin{tiny}
\begin{itemize}
\item $H_h=80\pm37$\,MW, $H_v=640\pm115$\,MW, $H_f=615\pm120$\,MW

\item $H_d \simeq 105$\,MW versus \\
$9000\pm760$\,MW (Schultz et al, 1992) and $\sim$150\,MW (Johnson et al, 2002)

\item Partitioning of heat flux between sources: \\
$H_d$:$H_f\simeq$100:615$\simeq$1:6, 
%$=$0.17 ($<$1) 
rather than $\sim$10:1
\end{itemize}
\end{tiny}
\end{slide}


\begin{slide}{Upper heat flux budget: \\ $H_v=H_p\simeq \overline{H_{qs}}$
}
%\includegraphics*[width=.75\textwidth]{../figs/xfig/crustbox.eps} 
\begin{center}
%$H_v=H_p\simeq \overline{H_{qs}}$
%
\includegraphics*[width=.4\textwidth]{../figs/xfig/fmcv.eps}
\end{center}
\begin{tiny}
\begin{tabular}{lrrr}
Study             & Estimate [MW] & Heat flux\\
\hline
%Stahr et al, 2003     &  550$\pm$100   & $H_v$ 
Stahr et al, 2003     &  640$\pm$115   & $H_v$ \\ 
Veirs et al, 2003     &  442$\pm$213   & $\overline{H_{qs}}$ \\
% use corrected $H_p$ values??!
Thomson et al, 1992   &  2500$\pm$1525   & $H_p$ \\
Baker \& Massoth, 1987 &  4250$\pm$2750 & $H_p$ \\
Rosenberg et al, 1988 &  3000$\pm$2000  & $H_p$ \\
%Ginster et al, 1994   &  364$\pm$73    & $H_f$ \\     
%Ginster et al, 1994   &  615$\pm$120    & $H_f$ \\
%Stahr et al, 2003     &  550$\pm$100   & $H_v$ 
\end{tabular}
\end{tiny}

\end{slide}

\begin{slide}{Conclusions}

\begin{itemize}
\item{Net heat flux at MEF is $\sim$720\,MW \\ $\sim$10$\times$ geologic mean of $\sim$82\,MW/2\,km}
\item{MEF $H_d$:$H_f\sim$1:6, rather than 10:1}
\item{Expect multidirectional flow above ridge (High heat flux variance \& $\Delta x_c=2.2$\,km)}
\item{When oscillatory currents disperse plumes, use a control volume to calculate \emph{net} flux}
\item{Expect rectilinear tidal flow and mean inflows in valley (Sea Breeze hypothesis)}
%($\Delta x\simeq$1\,km).}
\end{itemize}
\end{slide}


\begin{slide}{Acknowledgements}

  \begin{minipage}{5cm}
   \begin{tiny}
    \begin{itemstep}
    \item {Russ McDuff}
    \item {Bill Lavelle}
    \item {Supervisory committee members \\
          \begin{tabular}{l}
           Jeff Parsons   \\
           Glenn Cannon   \\
           Susan Hautala  \\
           Will Wilcock   \\
           Stephen Porter 
           \end{tabular}
          }
    \item {Family \\
          \begin{tabular}{l}
           Annie Reese and Mila\\ 
           Val, Leslie, Laura, Pete\\
          \end{tabular}
          }
    \item {Friends\\
          \begin{tabular}{l}
           \emph{Many} kind friends\\
           Fritz and Christian\\
           Graduate compatriots\\
          \end{tabular}
          }
    \end{itemstep}
    \end{tiny}
   \end{minipage}
\end{slide}

\overlays{3}{%
\begin{slide}{Acknowledgements}

   %\begin{minipage}{10cm}
    \onlySlide*{1}{\includegraphics*[width=.5\textwidth]{pix/russ.eps}}%
    \onlySlide*{2}{\includegraphics*[width=.5\textwidth]{pix/fam.eps}}%
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   %\end{minipage}
\end{slide}}

\end{document}
