Geology Reference
In-Depth Information
(a)
T =
0
d
v
d
T
v
D
(b)
T =
0
d
v
v
T
μ
v
D
v
d
D
Figure 5.2. (a) Sketch of a subducting plate and the mantle flow it induces.
(b) Simplification of the situation in (a).
values carefully, this estimate is likely to be within an order of magnitude or less
of the accurate answer.
So, in Figure 5.2(b), the cooler, denser fluid in the sheet on the right-hand side
of the box will sink. This will displace fluid within the box and thus induce a
circulation in the box. It will also drag the surface plate along behind it. Referring
back to Figure 5.2(a), the idea is that, as the sheet reaches the bottom, it spreads
across the bottom, and, as the surface plate moves to the right, material is added to
it at the spreading centre on the left. In this way the surface plate and its sinking
component are continuously renewed and the picture remains basically unchanged.
I have stated that the vertical sheet will sink because it is heavy - in other words,
it has negative buoyancy. As portrayed in Figure 5.2(b), there is nothing else that
might drive flow in the fluid. Therefore the sinking sheet is the active component,
and it will exert a force on the adjacent fluid. The fluid will resist motion because
it is viscous. Therefore, there will be a resisting force exerted on the sinking sheet.
Because mantle motion is so slow, accelerations are negligible, as discussed in
Chapter 4. If the acceleration is zero, Newton's second law says that the net force
on the sinking sheet must be zero. In other words, the resisting force,
F
R
,must
balance the driving buoyancy force,
B
:
B
+
F
R
=
0
.
(5.6)
