\relax \citation{Elderfield1996} \citation{Kelley2002} \citation{Crone2005} \citation{Wilcock2004} \citation{Larson2007} \citation{Butterfield1997} \citation{Johnson2000} \citation{McDuff1995abstract} \citation{Schultz1996} \citation{Crone2005} \citation{Davis2004} \citation{Crone2006} \@writefile{toc}{\contentsline {chapter}{\numberline {\@textofChapter \ 4:}Measuring Black Smoker Flow Rates Using Optical Plume Velocimetry}{72}} \@writefile{lof}{\addvspace {5\p@ }} \@writefile{lot}{\addvspace {5\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {4.1}Introduction}{72}} \citation{Elderfield1996} \citation{Chevaldonne1991} \citation{Fornari1998} \citation{Larson2007} \citation{Shank1997abstract} \citation{Tivey2002} \citation{Jupp2000thesis} \citation{Pruis2004} \citation{Schultz1996} \citation{Bemis1993} \citation{Converse1984} \citation{Pruis2004} \citation{Coupland2000} \citation{Kraus1994} \citation{Adrian2005} \citation{Tokumaru1995} \citation{McDuff1990abstract} \citation{Wilcock2002} \citation{Delaney2000} \citation{McDuff1995} \citation{Morton1956} \citation{List1982} \citation{Turner1986} \citation{Papanicolaou1988} \citation{Shabbir1994} \citation{Ruden1933} \@writefile{toc}{\contentsline {section}{\numberline {4.2}General Concepts Related to Image-Based Jet Flow Measurement}{75}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.2.1}Theory of Turbulent Buoyant Jets and Plumes}{75}} \@writefile{lof}{\contentsline {figure}{\numberline {4.1}{\ignorespaces Conceptual flow diagram illustrating the stages of image-based jet flow measurement}}{76}} \newlabel{conceptflow}{{4.1}{76}} \citation{List1982} \citation{McDuff1995} \citation{Turner1986} \citation{Turner1986} \citation{Rodi1982book} \citation{Papanicolaou1988} \citation{Turner1986} \citation{List1982} \citation{Papanicolaou1988} \citation{Papanicolaou1988} \citation{Turner1986} \citation{Papanicolaou1988} \@writefile{toc}{\contentsline {subsection}{\numberline {4.2.2}The Visible Flow Field}{79}} \citation{Beauchemin1995} \citation{Beauchemin1995} \citation{Horn1981} \citation{Adelson1985} \citation{Anandan1989} \citation{Adrian2005} \citation{Meynart1983} \citation{Tokumaru1995} \@writefile{toc}{\contentsline {subsection}{\numberline {4.2.3}Two-Dimensional Projection and Video Capture}{80}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.2.4}The Time-Averaged Image-Velocity Field}{80}} \citation{Hovmoller1949} \@writefile{toc}{\contentsline {subsection}{\numberline {4.2.5}Flow Rate Metric}{81}} \@writefile{toc}{\contentsline {section}{\numberline {4.3}Laboratory Simulations}{82}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.3.1}Apparatus}{82}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.3.2}Simulations}{83}} \@writefile{lof}{\contentsline {figure}{\numberline {4.2}{\ignorespaces Schematic of simulated black smoker jet apparatus}}{84}} \newlabel{apparatus}{{4.2}{84}} \@writefile{lof}{\contentsline {figure}{\numberline {4.3}{\ignorespaces Simulated black smoker nozzle assembly}}{85}} \newlabel{nozzle}{{4.3}{85}} \citation{Holzbecher1998book} \citation{Dimotakis1983} \@writefile{lof}{\contentsline {figure}{\numberline {4.4}{\ignorespaces Photograph of laboratory apparatus during a simulation run}}{86}} \newlabel{tankplume}{{4.4}{86}} \@writefile{lof}{\contentsline {figure}{\numberline {4.5}{\ignorespaces Typical video image frame from black smoker simulation}}{87}} \newlabel{plumeimage}{{4.5}{87}} \@writefile{lot}{\contentsline {table}{\numberline {4.1}{\ignorespaces Flow rate measurements for laboratory simulations}}{88}} \newlabel{simulationmeasurements}{{4.1}{88}} \@writefile{lot}{\contentsline {table}{\numberline {4.2}{\ignorespaces Derived flow rate information for laboratory simulations}}{89}} \newlabel{simulationruns}{{4.2}{89}} \newlabel{eqn:taylorscaling}{{4.13}{90}} \citation{Bischoff1985} \citation{Bischoff1985} \citation{Tokumaru1995} \citation{Tokumaru1995} \citation{Tokumaru1995} \@writefile{toc}{\contentsline {section}{\numberline {4.4}Computational Methods}{91}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.4.1}Region-Based Matching}{91}} \@writefile{lof}{\contentsline {figure}{\numberline {4.6}{\ignorespaces Solutions of the normalized non-dimensional Morton length scale used for laboratory simulation scaling}}{92}} \newlabel{taylorscaling}{{4.6}{92}} \citation{Hovmoller1949} \citation{Harris1978} \citation{Harris1978} \@writefile{toc}{\contentsline {subsection}{\numberline {4.4.2}Hovm\"{o}ller Diagram Spectral Analysis}{94}} \@writefile{lof}{\contentsline {figure}{\numberline {4.7}{\ignorespaces Normalized standard error of the mean of the mean image velocity}}{95}} \newlabel{stdmean}{{4.7}{95}} \@writefile{lof}{\contentsline {figure}{\numberline {4.8}{\ignorespaces Typical Hovm\"{o}ller diagram and Hovm\"{o}ller FFT}}{96}} \newlabel{hovslope}{{4.8}{96}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.4.3}Temporal Cross-Correlation}{97}} \citation{Otsu1979} \@writefile{toc}{\contentsline {subsection}{\numberline {4.4.4}Flow Rate Metric}{98}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.4.5}Optical Plume Velocimetry}{99}} \@writefile{toc}{\contentsline {section}{\numberline {4.5}Results}{99}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.5.1}Region-Based Matching}{99}} \newlabel{RF2}{{4.5.1}{100}} \@writefile{lof}{\contentsline {figure}{\numberline {4.9}{\ignorespaces Typical image-velocity fields computed using region-based matching}}{100}} \newlabel{imspace}{{4.9}{100}} \@writefile{lof}{\contentsline {figure}{\numberline {4.10}{\ignorespaces Flow rate metric from region-based matching versus measured flow}}{101}} \newlabel{spacemetric}{{4.10}{101}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.5.2}Hovm\"{o}ller Diagram Spectral Analysis}{102}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.5.3}Temporal Cross-Correlation}{102}} \newlabel{RF3}{{4.5.2}{103}} \@writefile{lof}{\contentsline {figure}{\numberline {4.11}{\ignorespaces Typical image-velocity fields computed using Hovm\"{o}ller diagram spectral analysis}}{103}} \newlabel{imhov}{{4.11}{103}} \@writefile{lof}{\contentsline {figure}{\numberline {4.12}{\ignorespaces Flow rate metric from Hovm\"{o}ller diagram spectral analysis}}{104}} \newlabel{hovmetric}{{4.12}{104}} \newlabel{RF4}{{4.5.3}{105}} \@writefile{lof}{\contentsline {figure}{\numberline {4.13}{\ignorespaces Typical image-velocity fields computed using temporal cross-correlation}}{105}} \newlabel{imtime}{{4.13}{105}} \@writefile{lof}{\contentsline {figure}{\numberline {4.14}{\ignorespaces Flow rate metric from temporal cross-correlation versus measured flow}}{106}} \newlabel{timemetric}{{4.14}{106}} \@writefile{toc}{\contentsline {section}{\numberline {4.6}Discussion}{106}} \citation{Draper1981book} \citation{Wilcock1991} \citation{Anandan1989} \citation{Dimotakis1983} \@writefile{toc}{\contentsline {subsection}{\numberline {4.6.1}Region-Based Matching}{107}} \@writefile{lof}{\contentsline {figure}{\numberline {4.15}{\ignorespaces Plume edge position example}}{109}} \newlabel{edgeimage}{{4.15}{109}} \@writefile{lof}{\contentsline {figure}{\numberline {4.16}{\ignorespaces Plume edge standard deviations as a function of nozzle flow rate}}{110}} \newlabel{edgestats}{{4.16}{110}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.6.2}Hovm\"{o}ller Diagram Spectral Analysis}{111}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.6.3}Temporal Cross-Correlation}{111}} \@writefile{lof}{\contentsline {figure}{\numberline {4.17}{\ignorespaces Flow feature wavelength filtering as a function of Nyquist frequency fraction and image-velocity}}{112}} \newlabel{nyquistfrac}{{4.17}{112}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.6.4}Implications for Real Systems and Future Instrumentation}{113}} \@writefile{lof}{\contentsline {figure}{\numberline {4.18}{\ignorespaces Transition regions for two black smokers}}{114}} \newlabel{bstrans}{{4.18}{114}} \@writefile{toc}{\contentsline {section}{\numberline {4.7}Conclusions}{115}} \@writefile{toc}{\contentsline {section}{\numberline {4.8}Supplementary Materials}{116}} \@setckpt{chap4}{ \setcounter{page}{118} \setcounter{equation}{16} \setcounter{enumi}{0} \setcounter{enumii}{0} \setcounter{enumiii}{0} \setcounter{enumiv}{0} \setcounter{footnote}{0} \setcounter{mpfootnote}{0} \setcounter{part}{0} \setcounter{chapter}{4} \setcounter{section}{8} \setcounter{subsection}{0} \setcounter{subsubsection}{0} \setcounter{paragraph}{0} \setcounter{subparagraph}{0} \setcounter{figure}{18} \setcounter{table}{2} \setcounter{NAT@ctr}{0} \setcounter{parentequation}{0} \setcounter{LT@tables}{0} \setcounter{LT@chunks}{0} \setcounter{r@tfl@t}{4} \setcounter{tablenotecounter}{1} }