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%                    M I X I N G / S A U N D E R S . T E X 
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\begin{figure}[t]

\placeFig[1.2]{mixing/sigsec}

\caption[\A density section]{Rift-valley density section of the \A
segments and current meter observations (mean along-valley velocities
recorded at moorings G, B and F during the final week of deployment);
black triangles indicate the bathymetry rising above \m{2550}; sills
are labeled as in \protect\rfigNP{mix-sills}; shading
($\SigmaTwo\leq36.9449$) and non-uniformly spaced contours are the same
as in \protect\rfigNP{F2-inflow} (p.\pageref{fig:F2-inflow}).}

\labelFig{sigsec}

\end{figure}
%--------------------

\rFigNP{sigsec} shows an along-segment density section of the rift
valley between sills ``I'' and ``F''. The shaded area indicates
densities corresponding to the water flowing into \sA below \m{2000}
(i.e.\ the lower layer of the hydraulic calculation of
\rsecNP{F2-inflow}). Apart from sill ``I'' the rift valley is closed
below \m{2200} \rsec{AMAR}, indicating that lower-layer water does not
flow out of \A north of \degN{36}. South of \degN{36} there may be
outflow across sill ``O'' connecting \sA to the \emph{North
Oceanographer} segment. (The hydrographic sections of
\citeN{JGR/wilson+95} appear more consistent with flow from \emph{North
Oceanographer} into \A, however.) Extrapolating the depth trend of the
interface between the inflow (\m{2000}) and the westernmost station
(\m{2134}) occupied during the 1998 survey \rfig{F2-stations} to sill
``O'' yields a value of \m{2320}, i.e.\ below the sill depth of
\m{2200}. It is therefore tentatively assumed that there is no outflow
of lower-layer water from the \A segments, i.e.\ the isopycnal
associated with the interface at the inflow grounds within the \A
segments. Even if this assumption is violated, the volume flux
estimates across sills ``I'' \rsec{F2-inflow} and ``R''
\rsecs{hydraulics}{CM-asflow} indicate that it is unlikely that more
than a third of the water entering \sA below \m{2000} is lost across
sill ``O'' (see also \rsecNP{mix-2000}).

The heat budget beneath the grounding isopycnal is given by
 %
\begin{equation}
 %
\rho_0 c_p \BQi \overline{\Delta\theta}
	= \BHc + \BHp + \rho_0 c_p \BAisopycnal \Kv \theta_z
												\labelEqn{mix-saunders}
 %
\end{equation}
 %
\citeEG{JPO/saunders87}, where \BQi is the lower-layer volume flux
entering \sA and $\overline{\Delta\theta}$\ls{mdt} denotes the mean
temperature by which the inflowing water must be heated to cross the
grounding isopycnal. \lsym{BHc} and \lsym{BHp} are the conductive and
convective geothermal heat fluxes into the lower layer.
\lsym{BAisopycnal} is the horizontal area of the interface, and
$\theta_z$ is the mean vertical temperature gradient at the grounding
isopycnal. The mean lower-layer temperature deficit
\degC{\overline{\Delta\theta}=0.13} is taken from the CTD tow-yo at
sill ``I'' assuming an interface depth of \m{2000}
\rsec{F2-inflow}.\REM{It's 0.097 taking 2050m.} With the corresponding
volume flux estimate \mmmps*{\BQi=95}{3} the heat flux which must be
supplied by geothermal heating and diapycnal diffusion becomes
\W*{5.2}{10}.

The conductive heat flux
\W*{\BHc\approx328}{6}\REM{\degCmmmps{\BHc\approx70}} is calculated
from the near-axial heat flow value of \Wpmm*{131}{-3}
\cite{JGR/stein+stein94}\REM{TABLE 1} and \mm*{\BAisopycnal=2.5}{9},
estimated from the area enclosed by the \m{2250} bathymetric contour
\rfig{mix-sills}, the mean depth of the grounding isopycnal. The small
contribution of \BHc to the overall budget of \rexpr{mix-saunders} is
consistent with the lack of geothermal heating signatures in the
along-segment hydrographic properties \rsec{F2-grad}. Near \RS the
depth of the grounding isopycnal is approximately \m{2300}
\rfig{sigsec}, implying that the bulk of the convective heat flux from
the \R hydrothermal vent field (at \m{2300}) does not contribute to the
heat balance of the lower layer (c.f.\ \rfigNP{F-bulkplumes}). Even the
entire convective heat flux of \W*{2.5}{9}\REM{\degCmmmps{550}}
calculated from the 1997 data \rsec{HF-advective} does not
significantly change the balance of \rexpr{mix-saunders}, indicating
that geothermal contributions have a minor impact on the heat budget of
the \A segments, provided there are no additional major undetected heat
sources such as significant low-temperature hydrothermal circulation.
The mean temperature gradient at the interface
\degCpm*{\theta_z=6.2}{-4} is estimated from \m{100}-thick layers
centered at the grounding isopycnal in the deep rift-valley profiles of
the 1998 survey \rsec{F2-grad}. Using these estimates
\rexpr{mix-saunders} yields \mmps*{\Kv=8.4}{-3}. This value is reduced
by half if the lower bound of the volume flux estimate at sill ``I''
\rsec{F2-inflow}, and a correspondingly re-defined mean lower-layer
temperature deficit \degC{\overline{\Delta\theta}=0.10}, is used (i.e.\
assuming an interface depth of \m{2050}) or if it is assumed that half
of the inflow across sill ``I'' is lost by outflow across sill ``O''.

\enlargethispage\baselineskip The same method has been used to estimate
diapycnal mixing coefficients before, e.g.\ by
\citeN{JGR/whitehead+worthington82} for Antarctic Bottom Water (AABW)
in the North Atlantic (\mmps*{K_v=0.7}{-4} and \mmps*{K_v=3.7}{-4}
based on two different volume flux estimates), by \citeN{JMR/hogg+82}
for AABW in the Brazil Basin (\mmps*{K_v=3$--$4}{-4}), and by
\citeN{JPO/saunders87} for the water flowing through Discovery Gap into
the Iberian Abyssal Plane (\mmps*{K_v=2}{-4}). Using a different method
based on a vertical advection/diffusion balance
\citeN{JGR/read+pollard99} calculated a basin-wide diffusivity average
\mmps{K_v=10^{-3}} from the hydrography of the Mozambique basin. In
regions of strong flow much higher mean values are possible as shown by
\citeN{Nature/polzin+96} who estimated a mean vertical diffusivity
\mmps*{K_v=1.5}{-2} from temperature microstructure profiles in the
rapidly flowing (\mps{0.1$--$0.5}) bottom layer of the Romanche
Fracture Zone.

