An example of applying Lacey et al.’s (1981) model
Lacey et al.’s (1981) model relates volcano radius to flux rate and
viscosity as a function of time:
This can also be written as r0 as a function of volcano volume by noting
that V = Qot so that the variable of t can be removed.
Simulated volcanic shapes under various conditions. Note that the volcanic flanks
concave upwards, which is opposite to the concave-downward geometry commonly
observed for volcanoes.
Problem with actual applications: the geometry of volcanoes may incompletely preserved
Morphology and length of volcanic flows
Volcanic veins
Types of lava flows: (1) Cooling limited lava flows
Wilson and Head (1994, Review of Geophysics)
Types of lava flows: (1) volume limited lava flows
Volcanic veins
Pre-existing graben captured lava channel
Wilson and Head (1994, Review of Geophysics)
THEMIS image of Mars
(Mouginis-Mark and
Christensen, 2005)
Lave channel (20 m wide)
from Hawaii (Griffith , 2000)
Volcanic vein on Mars
1m
Ropy pahoehoe from Hawaii
Toey pahoehoe (30 cm across)
Pillow lave (each ~ 1 m across)
Rhyolite flow around an local
topographic high (2.8 km
across)
Lave dome, 850 m across and 130 m high.
Wilson and Head (1994)
Lava cooling via convection in atmosphere and radiation
Effect of convective cooling is negligible
Lava surface
temperature
(convection in atmosphere)
What determines the length of a long lava flow?
Rheology of lava flow follows the Bingham flow law:
Its 3-D case can be written in tensor form:
h is plastic
viscosity,
which is only
meaning full
when s > so.
Evidence for non-Newtonian flow regimes:
(1) linear crevasse structures, along which the material parts as it is slowly
extruded,
(2) irregular surfaces sometimes dominated by tall angular spines, smooth striated
extrusion surfaces,
(3) tearing of the surface lava in channel flows,
(4) formation of solidified levees that channelize Hawaiian lavas.
Viscous flow on a slope:
hs is the critical depth/lava
channel thickness at and above
which the flow will occur.
Depth-average velocity in the lava flow (h is the thickness of the flow and h > hs):
b
Flow velocity is faster on Earth than on Mars if all other parameters hold constant.
Maximum flow length:
Gzc has the critical value of a dimensionless parameter that is defined by
Note: e = n
Definition of hydraulic diameter
Water level
b
a
Area (A)
Height (h)
D = 4 x wetted cross-section area (A) /wetted perimeter (wetted river bank) (ab)
or
D = wetted cross-section area/wetted perimeter (wetted river bank)
So, n = D/h
Maximum flow length:
Gz is called Graz number, a dimensionless parameter that is defined the square of
the ratio of the thickness of a flow (h) to the distance (d) on which a thermal
cooling wave will have traveled into it since the flow left the vent.
Gzc is the critical Graz number, which is ~300.
Purely due to gravity difference, lava flows on Mars should be a factor of ~ 1.7
longer than those on Earth
Maximum flow length:
Gzc has the critical value of a dimensionless parameter that is defined by
If higher effusion rate of Mars “E” is considered, a factor of ~ 6 increase in
flow length would have occurred on Mars. On Earth, the maximum length of
60 km would be translated to ~360 km; if the flow length decides volcano
length, the size of largest volcano on Mars should ~ 720 km (Wilson and Head,
1994).
What controls the form/morphology of the lava flows?
For isothermal case, we define a dimensionless volume V of lava flow by
flow volume divided by
Slope = 12 degrees
Slope = 18 degrees
Define dimensionless solidification time scale:
For viscous case
For plastic case
Time scale ts is the time when the surface of lava flow first starts to be
solidified due to cooling from the vein. This parameter really measures
the role of flux or effusion rate in controlling lava flow morphology.
The value of ts depends on a dimensionless number qs = (Ts -Ta)/(Te -Te),
where Ta is temperature of the atmosphere; Ts, solidification
temperature; Te, eruption temperature. It also depends on the surface
heat flux and must be calculated via a heat transfer calculation
accounting for radiation and convection from the surface and
conduction from below.
Increasing
Form of lava domes as a function of dimensionless solidification time scale:
In real world, volcano shape depends on the spatial and temporal evolution of
intrusions (dikes and sills) and surface distribution of lava flows from linear and
point sourced veins. The paper listed below provides such a case. This process is
testable via geodetic and seismological data, by it is difficult to generalize for
inferring scaling relationships.
Deformation near a large volcano with ductile layer below
s is a measure of the cohesive strength
of the volcano and its underlying plate
Olympus Mons