Geology Reference
In-Depth Information
are 40 or more identified hotspots, all of them are weaker than Hawaii and many of
them are substantially weaker. The total heat flow of plumes is about 2.3
10
12
W
×
(2.3 TW), which is about 6% of the global heat flow.
Whereas the heat transported by plates accounts for nearly 90% of the heat
coming out of the mantle, heat transported by plumes is much less. This suggests
that plumes are a secondary form of convection. This conclusion is not surprising,
because we estimated the plume heat flow from hotspot swells, and the hotspot
swells are a secondary form of topography compared with the mid-ocean rise
system (Figure 2.4). We saw in the previous chapter that the mid-ocean rises
are intimately related with the plate mode of convection, being due to thermal
contraction of plates. In fact, one can relate the heat transported by plates with the
negative buoyancy of the plates, due to their thermal contraction, and arrive at the
same relationship as Eq. (7.8) [1].
7.2.3 Volume flow rates and eruption rates of plumes
The buoyancy flow rate of a plume was estimated from the swell size without
knowing the plume temperature. However, if we do have an estimate of plume
temperature, it is possible to estimate the volumetric flow rate of the plume. It is
instructive to compare this with the rate of volcanic eruption.
From Eq. (7.6), using Eq. (7.1) for the volumetric flow rate
φ
,weget
b
=
φgρ
m
αT
and thus
φ
=
b/gρ
m
αT.
(7.9)
From the petrology of erupted lavas, plumes are estimated to have a peak temper-
ature of 250-300
◦
C above that of normal mantle [56]. Taking
T
300
◦
Cand
=
10
4
N/s), with our usual values for
using our previous value for Hawaii (
b
=
7
×
7.4 km
3
/yr.
It is interesting to compare this with the rate at which the Hawaiian swell
is generated. The volume added every year is
wvh
, and using
h
=
=
240 m
3
/s
=
the other quantities, this yields
φ
1km,
w
=
100 mm/yr, we find that 0.1 km
3
of new swell is raised every
year. This is only 1.4% of the volumetric flow rate of the plume, which reflects the
fact that the uplift is due to the thermal expansion of the plume material.
We can make a rough estimate of the velocity of flow in the plume, based at this
stage only on the inference from the localisation of active volcanism that the plume
seems to be 100 km or less in diameter. Equation (7.1) gives us
1000 km and
v
=
φ/
π
r
2
,
u
=
(7.10)
