Page 404 - Global Tectonics

386 CHAPTER 12

temperature profiles will be as shown to the right of assume uniform viscosity throughout the convecting

the figure. If there is no heating from below the tem- layer, a parallel-sided rather than a spherical layer,

perature in the interior of the fluid will be the same thermal convection alone and no phase changes within

as that at the base of the fluid layer (Fig. 12.5b). If the fluid. In the Earth’s mantle it is now thought that
there is some heating from below, in addition to inter- the viscosity increases with depth and that buoyancy is
nal heating (Fig. 12.5c), then the interior of the con- in part created by compositional variations. As discussed

vecting fluid will have an intermediate temperature in Section 12.9 these two factors appear to stabilize
between cases (a) and (b). This results in a greater the convective pattern for hundreds of millions of years,
drop in temperature across the upper boundary layer, whereas the convective patterns developed in the
and a lower drop in temperature across the lower models of Fig. 12.6 are clearly unstable over this period
boundary layer, compared to case (a). This effect of of time.
internal heating, whereby the top boundary layer is
strengthened and the bottom boundary layer weak-
ened, may therefore be applicable to the mantle. 12.5.2 Feasibility of
The effect of internal heating and the lack of a lower
thermal boundary layer is illustrated in Fig. 12.6. This mantle convection
shows the results of two numerical models with param-
eters appropriate to the mantle. The three frames on In order to gain insight into the feasibility and nature
the left relate to a model with heating from below and of convection within a spherical, rotating Earth, it is
no internal heating and those on the right to a model convenient to assume that the mantle approximates a

with internal heating and no lower boundary layer. In Newtonian fluid. Although this assumption may be

the first case one can clearly see cold sinking columns erroneous, it does allow simple calculations to be made
and hot rising columns analogous to Fig. 12.5a. In the on the convective process.
right hand case only downwellings are apparent and the The condition for the commencement of thermal
upwellings are passive and widely distributed (cf. Fig. convection is controlled by the magnitude of the dimen-
12.5b). sionless Rayleigh number (R a ), which is defi ned as the
Although instructive, these models probably do not ratio of the driving buoyancy forces to the resisting
accurately simulate convection in the mantle as they effects of the viscous forces and thermal diffusion.

218.3 Ma 349.6 Ma

441.9 Ma 587.0 Ma

536.7 Ma 738.7 Ma

0.0 Temperature 2840. 0.0 Temperature 2840.
Figure 12.6 Frames from numerical models illustrating (a) convection in a layer heated from below and (b)
convection in a layer heated internally and with no heat from below (from Davies, 1999. Copyright © Cambridge
University Press, reproduced with permission).