Page 159 - Fundamentals of Physical Volcanology

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136 CHAPTER 9

turbulent, and some low-viscosity basaltic flows, reaching it must have flowed even further from the
especially when flowing down very steep slopes or vent and so the wave of cooling will have advanced
over cliffs, are locally turbulent. Also, there is every further into it causing a larger fraction of it to have
reason to think that many of the extremely low- cooled. This means that the yield strength of the
viscosity komatiite flows that were much more levée material will increase with distance from the
common in the Earth’s early history flowed in a very vent and the flow will get thicker. Meanwhile
turbulent fashion, and we see evidence for tur- the continuing penetration of the cooling effects
bulent lava motion on the Moon and Mars, as means that, even though the core of the flow is still
described in Chapter 13. very hot, less of its thickness is hot enough to
Now that we can relate the speed of a flow to its deform easily, and so its advance speed slows
depth, we are in a position to establish the final down. The width of the channel is thus forced to
relationship that determines the geometry of a lava change, usually in the direction of getting wider, so
flow. This is the requirement that, as long as the that the flux of lava from the vent is still accommo-
mass of lava being erupted from the vent every dated by the flow. Finally all of this process must go
second, M , does not change, the same flux of lava on even though the flow may be advancing down
f
must be flowing at every point in the flow. The flux the flank of a volcano, on which the ground slope
is the product of the cross-sectional area of the varies with distance from the vent. And further-
flow and the flow speed, and the area is the depth more, it is quite possible that there are changing
of lava in the channel multiplied by the channel conditions in the magma reservoir supplying the
width, w . Thus we have vent which mean that the erupted mass flux also
c
changes with time.
M = ρ w d U (9.8)
f c c
and although all three of w , d , and U may be 9.7 Lengths of lava flows
c c
changing (and even ρ may change a little if some of
the gas bubbles in the flow burst and collapse), they It will be clear from the above description that ana-
must do so in such a way that the product of all four lyzing the motion of lava flows, and predicting how
quantities remains constant. they will evolve as they advance down the slopes of
The implication of these equations can be sum- a volcano, is not easy. One important property of
marized as follows. Lava is erupted from a vent flows does seem to be fairly predictable, however,

with a given viscosity and a negligible (or at least and this is the maximum distance to which a single
very small) yield strength. It flows downslope, and cooling-limited flow unit can travel. Recall eqn 9.1
immediately begins to cool at its upper and lower that described the depth to which cooling can
edges. The cool material on the top surface of the penetrate a flow. It might be expected that when
flow is carried to the front, falls onto the ground most of the thickness of a flow was cooled it would
and is pushed sideways to form a levée on either stop moving. To investigate this we take the ratio
side of the central channel. The partly solidified between the cooling depth and some characteristic
levée material behaves as a Bingham plastic with a thickness scale of the flow. The number that is used
yield strength that determines the levée width and is called the equivalent diameter of the flow, d ,
e
thickness. The core of hot material in the central and it is defined as four times the cross-sectional
channel behaves as a Newtonian fluid and pushes area of the flowing lava divided by its wetted
the levées aside until the combination of the width perimeter. The reason for this definition can be
of the channel, the flow speed of the lava, and the explained as follows.
depth of the lava can just accommodate the flux Imagine lava flowing in a lava tube that has a
coming from the vent. The simplest situation is one circular cross-section with radius r. Then its cross-
2
in which the depth of lava in the channel is just sectional area is πr and, if the lava completely fills
equal to the depth of the inner edge of the levées. it, all of the perimeter is wetted by the lava, so the
As the front of the flow advances, the material wetted perimeter is 2πr. Then d is equal to four
e