Geoscience Reference
In-Depth Information
temperature-dependent and may change by as much as an order of magnitude for
each change by 100
◦
Cintemperature.
8.2.3 Models of convection in the mantle
Patterns of mantle convection can be investigated in two ways. Numerical models
can be simulated on a computer, or physical laboratory models can be made by
choosing material of an appropriate viscosity to yield observable flow at appro-
priate Rayleigh numbers on a measurable timescale. The dimensionless numbers
described in Section 8.2.2 are particularly important because they control the
fluid behaviour. Therefore, by careful choice of appropriate fluids, it is possible
to conduct laboratory experiments at Rayleigh numbers that are appropriate for
the mantle - Tate and Lyle's golden syrup, glycerine and silicone oil are frequent
choices. The dynamic viscosity of water is 10
−
3
Pa s and that of thick syrup is
perhaps 10 Pa s; compare these values with the values of 10
21
Pa s for the mantle
(Section 5.7.2).
Simple two-dimensional numerical models of flow in rectangular boxes at
high Rayleigh numbers (10
4
-10
6
) appropriate for the upper mantle cannot be
compared directly with the Earth. The problem with these numerical models is
that the exact form of instabilities and secondary flow depends upon the particular
boundary conditions used. Figure 8.14(a) shows an example of the temperature
and flow lines for a numerical model with heat supplied from below and the
temperature fixed on the upper boundary. There is a cold thermal boundary layer
at the surface that could represent the lithospheric plates. This cold material,
which sinks and descends almost to the base of the box, could represent the
descending plate at a convergent plate boundary. A hot thermal boundary layer
at the base of the box rises as hot material at the 'ridges'. Therefore, if the flows
in the upper and lower mantle are indeed separate, then simple models such as
this imply that the horizontal scale of the cells in the upper mantle should be
of the order of their depth (the aspect ratio of the cells is about unity). Cells
with a large aspect ratio were unstable with these boundary conditions. Thus,
this particular model implies that it is not possible for convection in the upper
mantle to be directly related to the motions of the plates, with the downgoing cold
flow representing the descending plates along the convergent boundary and the
upwelling hot flow representing the mid-ocean-ridge system, because such a flow
would have an aspect ratio much greater than unity (the horizontal scale of these
motions is
10 000 km). However, changing the boundary conditions results in a
dramatic change in the flow. Figure 8.14(b) shows the flow that results when there
is a constant heat flow across the upper boundary instead of a constant temperature
on the upper boundary. In this case with constant heat flow across both the upper
and the lower boundary, large-aspect-ratio convection cells are stable. The small-
scale instabilities that develop on both boundaries of this model do not break up
the large-scale flow. Figure 8.14(c) shows the results of the same experiment but
∼
