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 r 0 as a function of volcano volume by noting that V = Q o t 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

Wilson and Head (1994, Review of Geophysics) Volcanic veins Types of lava flows: (1) Cooling limited lava flows

Wilson and Head (1994, Review of Geophysics) Volcanic veins Pre-existing graben captured lava channel Types of lava flows: (1) volume limited lava flows

THEMIS image of Mars (Mouginis-Mark and Christensen, 2005) Lave channel (20 m wide) from Hawaii (Griffith, 2000) Volcanic vein on Mars

Ropy pahoehoe from Hawaii 1 m

Toey pahoehoe (30 cm across) Pillow lave (each ~ 1 m across)

Lave dome, 850 m across and 130 m high. Rhyolite flow around an local topographic high (2.8 km across)

Wilson and Head (1994)

(convection in atmosphere) Effect of convective cooling is negligible Lava surface temperature Lava cooling via convection in atmosphere and radiation

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:   is plastic viscosity, which is only meaning full when  >  o.

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:  h s 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 > h s ): 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

Area (A) Water level 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 Height (h) a b Definition of hydraulic diameter

Maximum flow length: Purely due to gravity difference, lava flows on Mars should be a factor of ~ 1.7 longer than those on Earth 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.

Gzc has the critical value of a dimensionless parameter that is defined by Maximum flow length: 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 t s 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  s = (T s -T a )/(T e -T e ), where T a is temperature of the atmosphere; T s, solidification temperature; T e, 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

 is a measure of the cohesive strength of the volcano and its underlying plate Olympus Mons