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%                    F L U X E S / D I S C U . T E X 
%                    doc: Wed Apr  8 09:18:03 1998
%                    dlm: Thu Jun  8 00:03:53 2000
%                    (c) 1998 A.M. Thurnherr
%                    uE-Info: 57 22 NIL 0 0 72 3 2 4 ofnI
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Two estimates for the heat flux associated with the hydrothermal
particle plume of the 1997 data set differing by an order of magnitude
have been calculated. Because the plume rise height is not
significantly larger than the horizontal extent of the hydrothermal
vent field the point-source assumption required for the height-of-rise
estimate is violated and the resulting \GW{0.3} are not considered to
be accurate. \REM{The vertical thickness of the mean near-source plume
\rfig{F-bulkplumes} is of the order of the rise height, consistent with
the scaling analysis of \citeN{JMR/speer+marshall95}, providing another
indication that the height-of-rise method does not yield appropriate
values for the source buoyancy and heat fluxes at \R.}

The hydrographic anomalies associated with the near-source particle
plume together with the boundary current observations from the western
slope of \RR allow the heat flux to be estimated using an alternative
method. Because of the simplicity of the near-source flow field
advecting the plume unidirectionally along the western slope of \RR and
because of the consistency of the relationship between the temperature
and the nephelometry anomalies in the near-source profiles, implying
accurate temperature-anomaly estimates, the value of \GW{2.3}
derived with this method is much more likely to represent the
integrated high-temperature heat flux from the vent field during the
1997 survey.

The factor-10 difference between the two estimates is interesting.
\citeN{misc/fouquet+98} describe the distribution of the vent chimneys
at \R as \emph{``about ten major groups of extremely active black
smokers''.} The two heat-flux estimates are mutually consistent if the
plumes from the different groups coalesce high enough in the water
column so that they have already lost much of their buoyancy, i.e.\ the
height-of-rise method yields a heat flux consistent with a single group
of vents.

A third method to derive a rough estimate of the heat flux consists in
taking a ``canonical'' value expected for a single vent chimney
(\GW{0.05}, e.g.\ \citeNP{JGR/speer+rona89,review/lupton95})\REM{based
on source measurements} and extrapolating that value to a group of
vents (4--5, estimated from a video tape recorded during a submersible
dive at the \R hydrothermal site), resulting in a value of
\GW{0.2$--$0.25}, close to the value derived from height-of-rise
modeling. Extrapolating this value to the entire vent field (10 groups
of chimneys) yields \GW{2$--$2.5}, consistent with the estimate derived
from the advective temperature-anomaly flux.

Hydrothermal vent fields are commonly composed of numerous individual
sources, indicating that heat fluxes derived using the height-of-rise
method at other sites may be underestimates as well. The simplicity of
the flow field in the vicinity of the \R vent field allows the
advective temperature-anomaly flux to be calculated with a high degree
of confidence. At other sites (e.g.\ TAG, where there is no strong mean
flow) this method may not be as useful, indicating that it can be
extremely difficult to estimate heat fluxes from physical measurements
in the equilibrium plumes.

