Geoscience Reference
In-Depth Information
may
help
explain
the
unusual
characteristics
temporal scale of core--mantle--boundary instabil-
ities are orders of magnitude larger than those
at the surface. This physics is not captured in
laboratory simulations or calculations that adopt
the popular Boussinesq approximation. Pressure
also makes it easier to irreversibly chemically
stratify the mantle. A small intrinsic density
difference due to subtle changes in chemistry
can keep a deep layer trapped since it requires
such large temperature increases to make it
buoyant. Layered-mantle convection is the likely
outcome.
of D
.
Although convection in the mantle can be
described in general terms as thermal con-
vection, it differs considerably from convec-
tion in a homogenous Newtonian fluid, heated
from below, with constant viscosity and thermal
expansion. The temperature dependence of vis-
cosity gives a 'strong' cold surface layer. This layer
mustbreakorfoldinordertoreturntotheinte-
rior. When it does, it can drag the attached 'plate'
with it, a sort of surface tension that is gen-
erally not important in normal convection. The
deformation also introduces dissipation, a role
played by internal viscosity in normal convec-
tion. In addition, light crust and depleted litho-
sphere serve to decrease the average density of
the cold thermal boundary layer, helping to keep
it at the surface. Buoyant continents and their
attached, probably also buoyant, lithospheric
roots move about and affect the underlying con-
vection. The stress dependence of the strain rate
in solids gives a stress-dependent viscosity. This
concentrates the flow in highly stressed regions;
regions of low stress flow slowly. Mantle miner-
als are anisotropic, tending to recrystallize with
a preferred orientation dictated by the local
stresses. This in turn gives an anisotropic viscos-
ity, probably with the easy flow direction lined
up with the actual flow direction. The viscos-
ity controlling convection may therefore be dif-
ferent from the viscosity controlling postglacial
rebound.
Dimensionless scaling relations
The theory of convection is littered with dimen-
sionless numbers named after prominent dead
physicists. The importance of these numbers to
Earth scientists is that they tell us what kinds
of experiments and observations may be rele-
vant to the mantle. Experiments and calculations
that are in a different parameter space from the
mantle are not realistic. Atmospheric thunder-
heads and smoke-stack plumes cannot be used as
analogs to what might happen in the mantle.
The relative importance of conduction and
convection is given by the Peclet number
Pe
=
vL
/κ
where
v
is a characteristic velocity,
L
a character-
istic length and
κ
the thermal diffusivity,
κ
=
K
/ρ
C
P
expressed in terms of conductivity, density and
specific heat at constant pressure. The Peclet
number gives the ratio of convected to con-
ducted heat transport. For the Earth
Pe
is about
10
3
and convection dominates conduction. For a
much smaller body (
L
small), conduction would
dominate; this is an example of the scale as well
as the physical properties being important in the
physics. There are regions of the Earth, however,
where conduction dominates, such as at the sur-
face where the vertical velocity vanishes.
Dynamic similarity depends on two other
non-dimensional parameters: the Grashof num-
ber, which involves the buoyancy forces and the
resisting forces,
The core--mantle boundary region
The TBL at the base of the mantle generates a
potentially unstable situation. The effects of pres-
sure increase the thermal conductivity, decrease
the thermal expansion and increase the viscosity.
This means that conductive heat transfer from
below is more efficient than at the surface, that
temperature increases have little effect on den-
sity and that any convection will be sluggish.
Although the amount of heat coming out of
the core may be appreciable, it is certainly less
(
10%) than that flowing through the surface.
The net result is that lower-mantle upwellings
takealongtimetodevelopandtheymustbevery
large in order to accumulate enough buoyancy
to overcome viscous resistance. The spatial and
∼
=
α
TL
3
/ν
2
Gr
g
