Geoscience Reference
In-Depth Information
depth is more important than the increasing
pressure. The melting point increases with pres-
sure, as does viscosity, density and thermal
conductivity. For a homogenous mantle, there
should be a minimum in viscosity, density, seis-
mic velocities and thermal conductivity near
100--200 km depth. This region is known as the
asthenosphere
. Below this depth, the temperature
ofthemantledivergesfromthemeltingpoint.
The coefficient of thermal expansion also goes
through a minimum, and this plus the effects of
partial melting and other phase changes in the
shallow mantle means that small changes in tem-
perature cause large changes in buoyancy. The
minimum in thermal conductivity means that
this region will have a steep thermal gradient
until it starts to convect. The minimum in viscos-
ity means that it will flow easily. Pressure stiffens
the mantle, raises the melting point and makes it
easier to conduct heat. All of these effects serve
to concentrate deformation in the upper man-
tle, and serve to at least partially decouple plate
motions from the interior. They also explain why
the
seismic low-velocity zone
is roughly equivalent
to the
asthenosphere
.
are intrinsically buoyant) and because the viscos-
ity, conductivity and
˙
at low
P
are strongly
T
-
dependent. For parameters appropriate for the
top of the mantle, treated as a constant vis-
cosity fluid, the surface TBL becomes unstable
at a thickness of about 100 km. The time-scale
is about 10
8
years, approximately the lifetime
of surface oceanic plates. The top boundary is
very viscous, stiff and partly buoyant, and the
instability (called subduction or delamination) is
controlled, in part, by faulting; a viscous instabil-
ity calculation is not entirely appropriate. For the
bottom boundary layer the deformation is more
likely to be purely viscous but there may also be
intrinsic stabilizing density effects. Realistic con-
vection simulations must include all of the above
effects plus self-consistent thermodynamics.
The critical thickness of the lower TBL, ignor-
ing radiative transfer, is about ten times larger
than at the surface, or about 1000 km. If there
is an appreciable radiative component to ther-
mal conductivity, or if there is a chemical com-
ponent to the density, then the scale-lengths at
the base of the mantle can be greater than this.
Tomographic anomalies in the lower third of the
mantle are very large, much larger than upper
mantle slabs (cold plumes), consistent with scal-
ing theory. The lifetime of the lower TBL, scaled
from the upper mantle value, is about 3 billion
years. The surface TBL cools rapidly and becomes
unstable quickly because of the magnitude of the
thermal properties. The same theory, scaled for
the density increase across the mantle, predicts
large scale and long-lived features in the deep
mantle.
α
Thermal boundary layers
The thermal boundary layer (TBL) thickness of a
fluid cooled from above or heated from below
grows as
t
)
1
/
2
h
∼
(
κ
where
is thermal diffusivity, and
t
is time. The
TBL becomes unstable, and detaches when the
local or sublayer Rayleigh
number
κ
Slabs
T
)
h
3
Ra
c
=
α
g
(
δ
/κν
exceeds
about
1000
(
g
is
acceleration
due
to
When a plate starts to sink it is called a
slab
.
In fluid dynamics, both cold sinking features
and hot rising features are called
plumes
.Slabs
are cold when they enter the mantle but they
immediately start to warm up toward ambi-
ent temperature; they get warmed up from
both sides. The cold portions of slabs may have
high seismic velocities, compared with mantle of
the same composition, and can be denser than
normal mantle. Slabs are composed of oceanic
gravity;
T
is the tem-
perature increase across the TBL). The combina-
tion
ν
is kinematic viscosity and
δ
decreases with
V
, thereby lowering Ra
c
at high
P
or low
T
.
The local Rayleigh number is based on TBL
thickness. At the surface of the Earth the issue
is complicated because of water and because the
crust and refractory peridotite part of the outer
shell are not formed by conductive cooling (they
α/κν
