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are controlled by mantle temperature and con-
vection, not the stress state of the lithosphere.
It was then recognized that plates could drive
themselves and could also organize the underly-
ing mantle convection. Plates and the architec-
ture of the lithosphere provided the template
and stress conditions for midplate magmatism
and tectonics, phenomena not obviously related
to plate tectonics or plate boundaries in the con-
text of rigid plates. Variations in the thickness
of the crust and the ages of continents, and the
cooling of oceanic plates, set up lateral tempera-
ture gradients which can be just as important in
driving mantle convection as the non-adiabatic
temperature gradients in TBLs. Secular cooling of
the Earth maintains a surface TBL; cooling from
above can initiate and maintain mantle convec-
tion and plate tectonics. Although the mantle is,
to some extent, heated from within, and from
below, it is basically a system that is driven from
the top.
The tectonic plate system can be viewed as an
open, far-from-equilibrium, dissipative and self-
organizing system that takes matter and energy
from the mantle and converts it to mechanical
forces (ridge push, slab pull), which drive the
plates. Subducting slabs, delamination and cra-
tonic roots cool the mantle and create pressure
and temperature gradients that drive mantle con-
vection. The plate system thus acts as a template
to organize mantle convection. In contrast, in the
conventional view, the lithosphere is simply the
surface boundary layer of mantle convection and
the mantle is the self-organizing dissipative sys-
tem. If most of the buoyancy and dissipation --
the alternative to mantle viscosity -- is provided
by the plates while the mantle simply provides
heat, gravity, matter, and an entropy dump, then
plate tectonics is a candidate for a self-organized
system, in contrast to being organized by mantle
convection or heat from the core. Stress fluctu-
ations in such a system cause global reorganiza-
tions without a causative convective event in the
mantle. Changes in stress affect plate permeabil-
ity and can initiate or turn off fractures, dikes
and volcanic chains. The mantle itself need play
no active role in plate tectonic 'catastrophes.'
The traditional view of mantle geodynam-
ics and geochemistry is that magmatism, and
phenomena such as continental break-up and
plate reorganization, are due to convection cur-
rents in the mantle, and the importation of core
heat, via plumes, into the upper mantle. Mantle
convection by-and-large controls itself, and can
experience massive overturns called
mantle
avalanches
. But mantle dynamics may be
almost entirely a top-down system and it is likely
that mantle convection of various scales is con-
trolled by plates and plate tectonics, not vice
versa. The surface boundary layer is the active ele-
ment, the 'convecting mantle' is the passive ele-
ment. When a plate tectonic and continental tem-
plate is placed on top of the convecting system,
it organizes the convective flow and the plates
themselves become the dissipative self-organized
system.
Plate driven flow
Marangoni convection is driven by surface ten-
sion. Since surface tension is isotropic, the fluid
flows radially from regions of low surface tension
to the cell boundaries, which are hexagonal in
planform, where linear downwellings form. The
equivalent surface force in mantle convection is
the
ridge-push--slab-pull
gravitational force which
has the same units as surface tension. Since
plates are not fluids the forces are not isotropic.
Plates move from ridge to trench, pulling up
material at diverging regions, which are the
equivalent of the centers of Bénard--Marangoni
hexagons, and inserting cold material at sub-
duction zones. The other difference between
Marangoni and plate-driven convection is that
plates are held together by lateral compression
and fail in lateral extension. Cell boundaries are
convergent and elevated and are regions of com-
pressive stress in Marangoni convection.
The plate-tectonic equivalent of the
Maran-
goni number
can be derived by replacing sur-
face tension by plate forces. I define the plate
tectonic or Platonic number
Pl
=
g
α
TL
2
/
U
D
where
L
is
a
characteristic
length
(e.g.
ridge-
trench distance) and
U
is plate velocity.
is a
dissipation function, which accounts for plate
deformation, intraplate resistance and mantle vis-
cosity. It is a rheological parameter. The
roles
D
