Page 405 - Global Tectonics

THE MECHANISM OF PLATE TECTONICS 387

R a = αβρgd /kη very little heat is transferred by convection. At R a values
4
6
10 or greater, appropriate to the mantle, Nu is about
where α is the coefficient of thermal expansion, β the 100, indicating the predominance of heat transfer by

superadiabatic temperature gradient (the gradient in convection.
excess of that expected to be associated with the increas-
ing pressure), ρ the density of the fl uid, g the accelera-
tion due to gravity, d the thickness of the convecting 12.5.3 The vertical extent
fl uid, k the thermal diffusivity (the ratio of the thermal
conductivity to the product of density and specifi c heat of convection
at constant volume), and η the dynamic viscosity
(Section 2.10.3). For convection in the mantle, the Ray- The mantle transition zone (Section 2.8.5) may well
leigh number corresponding to the onset of convection infl uence the nature or even the vertical extent of con-
3
is approximately 10 . This corresponds to the minimum vection in the mantle. If this zone represents a change
temperature gradient required for convection to occur. in chemical composition, then it implies that convection
For the actual temperature gradient the Rayleigh currents do not cross it. In this case separate layers of
6
number is of the order of 10 or greater. This implies convective circulation would occur above and below the
very favorable conditions for convection and, as a con- transition zone, with heat transported by conduction
sequence, thin boundary layers compared to the total across a thermal boundary layer within all or part of
layer thickness. the transition zone.

The nature of the flow in a convecting fluid can be The nature of the mantle transition zone is equivo-
judged by the magnitude of the Reynolds number (Re), cal, but the majority view appears to be that it repre-
which allows discrimination between laminar and sents a region in which solid state phase changes take
turbulent fl ow. Re is defi ned: place, whereby the mineralogy of mantle material
changes to higher pressure forms with depth, rather
Re = vd/v than representing a change in chemical composition
(Section 2.8.5). For example, Watt & Shankland (1975)
where v is the velocity of fl ow and ν is the kinematic have shown, from an inversion of velocity–density data,
viscosity (the ratio of the dynamic viscosity, η, to that the mean atomic weight of the mantle shows no
density). Taking v = 200 mm a = 6 × 10 ms , d = change across the transition zone. If this is the case,
−9
−1
−1
3000 km = 3 × 10 m and ν = 2 × 10 m s , Re = 9 × convection currents could cross the transition zone, as
17
2 −1
6
−20
10 . This very low value indicates that viscous forces long as the phase changes take place very rapidly, and
dominate and hence the flow is laminar. The effect of convection cells would then be mantle wide. The phase

the Earth’s rotation on convection can be judged by the changes would have two important effects on convec-
magnitude of the Taylor number (T), which is tion, as they are temperature and pressure dependent
defi ned: and involve latent heat. In the case of olivine to spinel
the change from low pressure to high pressure forms
2
T = (2wd /ν) 2 takes place at shallower than average depths in the
cold descending currents and at greater than average
where w is the angular velocity of rotation. Putting depths in the hot ascending currents. Consequently,
w = 7.27 × 10 rad s and other values as above, T ≈ 4 low-density minerals are created deeper on ascent and
−5
−1
−17
× 10 . A value of T less than unity implies no signifi - denser, high-pressure forms at shallower depths on
cant effect of rotation on convection and so the Earth’s descent. Their positive and negative buoyancies respec-
rotation should have no effect on the pattern of mantle tively then help to drive the convection cells. The phase
convection. change is also associated with a release or absorption of

The efficiency of convection is measured by the latent heat, the high- to low-pressure reaction being
Nusselt number (Nu), which is the ratio of the total heat exothermic and the low to high-pressure reaction being
transferred to that transferred by thermal conduction endothermic. This causes steepening of the thermal
alone. Elder (1965) computed experimentally the rela- gradient across the transition zone, so that the tem-
tionship between Nu and R a . He found that at values of perature in the lower mantle is 100–150°C higher than
R a appropriate to marginal convection Nu is unity and if the zone did not exist.