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%                    M I X I N G / D I S C U . T E X 
%                    doc: Tue Apr  4 17:15:58 2000
%                    dlm: Thu Jun  8 00:13:45 2000
%                    (c) 2000 A.M. Thurnherr
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Diapycnal-diffusivity estimates for the \A segments calculated from
heat budgets result in bulk values of \mmps*{3$--$8}{-3}. There are
significant uncertainties associated with the budgets, primarily
because the pathways of the rift-valley water are not well constrained
by our data, but even with conservative assumptions the diffusivities
remain of order \mmmps*{5}{-3}. Circumstantial evidence for strong
diapycnal mixing in the rift valley of the \A segments was presented in
\MakeLowercase\chaptersname~\ref{chap:HYD}, \ref{chap:CM}
and~\ref{chap:plume}. Without confirmation from more direct
measurements, such as microstructure profiles, the diffusivity
estimates (and, hence, the following discussion) must remain associated
with some doubt. The consistency of the picture which emerges from the
volume and heat budgets is encouraging, however. It is difficult to see
how an alternative view, e.g.\ additional inflow from \FAM, could yield
similarly consistent results.

The heat budgets indicate that the known geothermal contributions to
the rift-valley water column of the \A segments are not significant in
relation to other processes, even in the presence of the large heat
flux from the \R hydrothermal vent field. This is consistent with the
mutual consistency of the rift-valley \ThetaS properties along the \A
segments \rsec{F2-grad} and with the apparent lack of plume-related
dynamical signatures in the LADCP \rsec{LADCP} and current-meter data
\rsec{CM-pies}, implying that the rift-valley hydrography and dynamics
are dominated by processes which are not associated with the
hydrothermal plume. The observation that mixing within the rift valley
of the \MAR can have a much stronger effect on the density field than a
large hydrothermal plume supports the conclusion of
\citeN{Science/talley+johnson94} that hydrothermal plumes may not be
the (primary) driving mechanism for the westward mid-depth flows
observed in the Pacific and in the Atlantic ocean, and provides a
plausible explanation why hydrographic exploration of the \MAR rift
valley has failed to detect even large hydrothermal plumes
\citeEG{JGR/wilson+95}.

The mass budgets derived for the \A segments suggest that not all the
water entering the rift valley below \m{2000} flows out across the
deepest sills. There are three possibilities to account for the
observations:\begin{itemize}

\item uncertainties in the volume-flux estimates can result in false
apparent deficits;

\item the deficits can be caused by outflows across additional sills;

\item rift-valley water can be lost to the overlying water column.

\end{itemize} Our data do not rule out any of these possibilities.
Hydraulically controlled outflows across sills can balance the inflows
if there are sufficient density gradients in the off-ridge water column
between the inflows and the outflows to compensate the along-segment
hydrographic gradients within the rift-valley. Our profiles (e.g.\
\rfigNP{F-sigcompare}) as well as other data
\citeEG{Progress/fukumori+91} indicate that there is a (possibly
persistent) cross-MAR density gradient near \degN{36} which favors
inflow into the rift-valley from the east and outflow towards the west.
The magnitude of the cross-ridge density difference at \m{2000} is of
order \kgpmmm*{3}{-2} implying that an along-segment flow of
approximately \km{300} can be driven if the observed rift-valley
density gradient of \kgpmmmpkm{10^{-4}} \rsec{F2-grad} is
representative. Nevertheless, the deep rift-valley water must be
uplifted to any such outflow sill because below \m{2200} even the water
on the western ridge flank is denser than the rift-valley water at the
same depth \rfig{F-sigcompare}. If vertical transport is required it
does not seem unreasonable to suggest that some of the rift-valley
water may be mixed (``entrained'') into the overlying water column,
providing a ``diffuse'' pathway for the water and the associated
hydrothermal tracers out of the \A segments. 

\REM{Assuming the flow is northward throughout \A, the density
distribution within the rift valley shown in \rfigNP{sigsec} is
intriguing because of the asymmetric ``bowl-shape'' of the isopycnals
with a depth maximum in the vicinity of the downstream end of the rift
valley. Similar sections have been observed within other valleys as
well. The hydrographic sections of \citeN{JGR/wilson+95} a similar
pattern in the \FAM segment. (Their contour intervals are too large to
resolve the details within \A.) The hydrographic sections taken within
a canyon on the flank of the \MAR shown by \citeN{Nature/ledwell+00}
are also characterized by uniform bottom gradients and ``bowl-like''
shapes in the overlying water column near the downstream end of the
canyons.}