The plume mode of convection - Mantle Convection for Geologists - page 85

v

D

h

−Δρ

w

Figure 7.6. Sketch of two layers of fluid, the lower layer with a density lower by
ρ . The total depth of the two layers is D . An instability is developing, with a
width w and an amplitude h . The highest point of the instability is rising at velocity
v . This instability is known to fluid dynamicists as the Rayleigh-Taylor instability.

as ambient mantle, and there are demonstrations that compositional density will
considerably complicate the behaviour of plumes, whose buoyancy is affected by
both temperature and composition. Because the behaviours are complicated, and
have not yet been explored much, it is difficult to say that this accounts for the
observed complications, but a plausibility case can be made for some volcanism.
There is other localised volcanism that does not seem to have much connection
with plumes, so there may indeed be other phenomena occurring in the mantle, but
evidently they are not major sources of volcanism or tectonics.

7.3.1 Outline of plume dynamics
I will start by briefly outlining the theory of thermal plumes. Some of the details
are covered in following subsections, which you can read or skip, as you please.
Our understanding of thermal plumes begins with the instability of a layer of fluid
overlain by fluid of greater density, so the lower layer is buoyant (as sketched in
Figure 7.6). The buoyant layer will tend to rise, but there is a preferred horizontal
scale or spacing of the resulting upwellings. This scale is approximately the total
depth, D , of the two layers. Upwellings spaced much closer than D or much further
apart than D can grow, but only slowly, and they are overwhelmed by the faster
growth of upwellings spaced about D apart.
This preferred spacing of upwellings means that there will not be thousands
of tiny upwellings, nor one or two huge upwellings. In other words, it implies
that upwellings will tend to be of a certain size. Theoretical estimates and numer-
ical experiments for conditions in the lower mantle indicate that the spacing of
upwellings will be of the order of 1000 km, and they will initially form blobs about
400 km in diameter.
Experiments and some theory by Whitehead and Luther in 1975 [67] showed
that upwellings tend to take the form of columns rather than sheets. They also
showed that, if the upwelling fluid has a lower viscosity than the surrounding fluid,
the upwelling takes the form of a roughly spherical 'head' and a relatively narrow