Geology Reference
In-Depth Information
the mantle convection system. Thus the relationship between plates and mantle
convection is revealed, and it is a straightforward relationship, once we have a clear
understanding of what convection is.
We can say this in another way. The cycle, in which mantle material rises at
a mid-ocean ridge, cools at the surface to form a plate, moves horizontally and
subducts, and finally is warmed and reabsorbed into the mantle, is a form of
convection. The motion is driven by thermal buoyancy within the system, and it
transports heat, as we will see explicitly a little further on.
We have established the central result of this topic. The rest is tidying up
and looking at some implications. Convection has been, to many people, a rather
mysterious process. I hope this treatment has made convection a lot less mysterious.
It is also widely regarded as complicated, requiring supercomputers to model. The
simple theory here shows that, when approached with clear concepts and judicious
approximations, convection is not so complicated, and in fact good quantitative
agreement with observations can be obtained relatively easily.
5.6 The Rayleigh number and other fluid-dynamical beasts
Fluid dynamicists love to find dimensionless numbers that characterise fluid flow.
They then name them after each other. For example, you can't read anything about
convection without encountering the
Rayleigh number
. There will usually be a
complicated-looking expression for it and, possibly but not necessarily, a terse
explanation that you may or may not understand. Well, I'm being a little facetious
and a little unkind, though the explanations usually are terse, or absent.
We have been through a very nice theory of convection without needing to men-
tion the Rayleigh number, because I was more concerned with making the physics
clear. However, to give fluid dynamicists their due credit, the Rayleigh number is
extremely useful, because it gives a very concise summary of the convective system
that allows you to know whether the convection is languid or very vigorous, or
whether the convection in a laboratory tank is in any way similar to convection in
the ocean or in the mantle.
Here is one way to get at the Rayleigh number. Use Eq. (5.18) in (5.17) to get
an expression for
d
that doesn't involve
v
. Equation (5.17) is
(4
κD/v
)
1
/
2
.
d
=
Square both sides and substitute for
v
from (5.18):
2
/
3
4
κD
D
6
μ
gρ
0
αT
√
κ
d
2
=
.
