Geoscience Reference
In-Depth Information
normal mantle convection and the lateral dimen-
sions of plates. Sometimes geophysical plumes
are considered to be
the way the core gets
rid of its heat
. The corollary is that plate
tectonics is the way that the mantle gets rid of
its heat. Actually, the mantle and the surface and
boundaries layers are coupled.
If much of the upper mantle is at or near the
melting point, which seems unavoidable, then
there is a simple explanation for island chains,
extensive diking and large igneous provinces.
The criterion for diking is that the least com-
pressive axis in the lithosphere is horizontal and
that melt buoyancy can overcome the strength
of the plate. Magma can break the lithosphere at
lower deviatoric stresses than it would otherwise
take. Dikes propagate both vertically and along
strike, often driven by the hydrostatic head of an
elevated region. Dikes, like cracks, can propagate
laterally. Typical crack propagation velocities are
2to10cm/year,comparabletoplatevelocities.
These velocities are known from the study of
ridge propagators
and the penetration of ridges
into continents. These propagating cracks are
volcanicsotheyareprobablyexamplesofprop-
agating
plumes, based on unscaled laboratory simula-
tions, implausible for the mantle.
The critical dimension of lower-mantle ther-
mal instabilities is predicted to be about 10 times
larger than at the surface, or about 1000 km.
The timescale of deep thermal instabilities
scaled from the upper mantle value is
10
9
years. Radiative transfer and other effects may
increase thermal diffusivity, further increasing
timescales. The surface TBL cools rapidly and
becomes unstable quickly. The same theory,
scaled for the density and pressure increase
across the mantle, predicts large and long-lived
features above the core.
Geophysical plume theory is motivated by
experiments that inject narrow streams of hot
fluid into a stationary tank of low viscosity fluid.
These injected streams are not the same as the
natural instabilities that form at the base of
a fluid heated from below. Computer simula-
tions often mimic the laboratory experiments by
inserting a hot sphere at the base of the fluid and
watching it evolve with time during the period
that it rises to the surface. These are not cycli-
cal or steady-state convection experiments, and
they ignore the effects of pressure on physical
properties. Because of the inordinate sensitivity
of mantle convection and lithospheric stress to
surface conditions it is necessary to exhaust the
various plate-tectonic explanations for episodic-
ity, plate reorganization, volcanic chains, periods
of massive magmatism, continental breakup etc.
before one invokes unstable deep thermal layers
and narrow active upwellings.
∼
3
×
magma-filled
cracks
or
dikes
[
giant
radiating dikes
].
Geophysical plumes
One finds many kinds of plumes in the Earth
science literature; diapiric, cavity, starting, incu-
bating, plume heads, plume tails, zoned plumes,
plumelets, megaplumes and so on. When the
whole lower TBL goes unstable we have a
diapiric plume
. Scaling relations show that
these will be huge, slow to develop and long-
lived. When a thin low-viscosity layer near the
core feeds a plume head, we have a
cavity
plume
; the physics is similar to a hot-air balloon.
Temperature dependence of viscosity is essential
for the formation of cavity plumes with large
bulbous plume heads and narrow plume tails.
Temperature dependence and internal heating,
however, reduce the temperature drop across the
lower thermal boundary layer and the viscosity
contrasts essential for this kind of plume. Pres-
sure broadens the dimensions of diapiric plumes
andcavityplumeheads.Itisthis'pressure-
broadening' that makes intuitive concepts about
Boussinesq approximation
The
Boussinesq approximation
is widely
used in fluid dynamics. It simply means that all
physical properties are assumed to be indepen-
dent of depth and pressure and, except for den-
sity, independent of temperature. This is not a
good approximation for the deep mantle. Some
workers try to fix up the limitations of this
approximation by assigning depth or tempera-
ture dependence to some of the physical prop-
erties, but if this is not done in a thermody-
namically self-consistent way, it can make things
worse. High Prandtl number essentially means
high viscosity and low thermal conductivity, a
