
\subsection{Equilibration height}

% Lupton?85: They try to explain observed z*< expected z* by suggesting $B$
% decreased somehow -- this is good example of historical underestimation of
% the importance of U in the deep sea. 

In a quiescent, stratified ambient, the equilibration height ($z^*$) of a buoyant plume is 

\begin{equation}
z^* = c \frac{B^{1/4}}{N^{3/4}} = c (\frac{B}{N^3})^4
\label{hh}
\end{equation}

in which $N$ is the buoyancy frequency and $c$ is a constant \cite{morton+59}.
It is clear that the stratification, measured by the
buoyancy frequency $N$, exerts stronger control than does $B$.

This begs the question of how much $N$ and $B$ vary for the MEF case.
Furthermore, how should $N$ be quantified in such a variable environment?  What
is the typical fluid that a MEF plume rises through?  It might be fairly
uniform and constant within the axial valley, but could shift quickly between
axial and background above the ridge.

Note that the maximum rise height is given by a slightly different equation.

\subsection{MEF B, T, expected Z*}

\begin{sidewaystable}
\begin{tabular}{lrrrrr}
Name		&$\Delta\theta$	&$\Delta S$	&$\Delta\rho$	&$B$		& $z^*$	\\
		&$^\circ$C	&psu		&kg/m$^3$	& m$^4$/s$^3$	& 	\\
\hline
Sasquatch 	&               &               &               &	      	&       \\
Salty Dawg	&               &               &               &      		&       \\
High Rise	&               &               &               &      		&       \\
N MEF           &               &               &               &       	&       \\
S MEF           &               &               &               &       	&       \\
Mothra		&		&		&		&		&	\\

\label{rise_table}
\end{tabular} 

\caption[Typical Endeavour segment vent fluid properties and rise height]{
Typical Endeavour segment vent fluid properties and rise height}
\end{sidewaystable}

% Ginster (page 4946) observation of venting fissure at TP: $T=$333$^\circ$C, $w=$93\,cm/s
% width order decimeters, length order meters, spatial variability not assessed; unclear 
% whether above values are max or means, though there is tendency in article to use max.
%
% #s referenced in Ginster, pg 4948-- shultz diffuse: T=7--13, w=7--15cm/s, delaney diffuse T=8--15
% ==> Delaney 92 started the diffuse/focused categorization?
%

%\subsection{Cross flow}
%
% The assumption that plumes from high $B$ MEF sources are axisymmetric, and therefore represented by MTT theory,
% is called into question by the magnitude of cross flow measured near the MEF, within the axial valley.
% Little+87 argued the effect of 3--4\,cm/s cross flow at a site on the EPR was negligible because the 
% vertical velocity in the plume was much greater, ranging from 63\,cm/s at the source to 15\,cm/s at a height 
% of 24~mas.



