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STEADY EXPLOSIVE ERUPTIONS 81

ascent are reduced, and so more of the energy jet engine, and the flared shape is called a de
released can be used in acceleration. Lavalle nozzle.
There is no guarantee that a dike will have the
correct shape to allow the supersonic transition to
6.4.2 Dike shape, vent geometry and
occur. The dike width, t, is controlled by the distri-
exit velocity
bution of stresses that caused the dike to propagate;
There is another factor which exerts a control on in the early stages of the opening of a vent, the
the speed at which fragmented magma erupts chances are that the dike will get narrower toward
through vents, and also influences what happens the surface, not wider. If the supersonic transition
just above the vent, and that is the pressure in the cannot occur, the best that the magma can do is
magma in the vent. Magma rising from a high- to reach the surface traveling exactly at the local
pressure source region beneath the surface must speed of sound. This condition is described as
eventually reach a pressure equal to that of the choked flow, and when the flow is choked the
atmosphere after it leaves the vent. In the sim- pressure in the magma in the vent can be much
plest case, the pressure in the magma decreases greater than the atmospheric pressure, and the
smoothly as it rises and exactly equals atmospheric eruption speed will then be much less than if the
pressure at the vent. But this does not always hap- transition had occurred. There will be a violent
pen. The reason is that every fluid (i.e., gas or liquid) expansion, both upward and sideways, of the mag-
has associated with it a natural speed at which matic gas just above the vent, with the pressure
pressure changes propagate through it. Pressure adjusting to atmospheric and the gas and pyroclasts
changes in air are what we experience as sound, accelerating to speeds similar to, but somewhat less
and so this natural speed is called the speed of than, those that they would have had if the whole
sound in the fluid. The speed of sound in magma acceleration had been a smooth process.
is quite small, much less than in a pure gas or pure It is possible for quite complicated situations
liquid. The exact value depends on the pressure to develop if rocks break off from the wall of the
and the gas/liquid volume ratio, but it is generally dike as the eruption progresses. If the magma
−1
within a factor of two of 100 m s . This is true both encounters a series of increases and decreases in
before and after fragmentation; in each case it is the width along the dike, a corresponding series of
interaction between the two components, one liq- subsonic-to-supersonic-back-to-subsonic transitions
uid and one gas, that causes the low speed. Before can occur, and it is in these situations that, at least

fragmentation the gas bubbles have to be deformed for a short vertical distance, the temperature of the
as the pressure in them changes when the sound magma can increase a little in contrast to its general
wave goes by. After fragmentation magma clots are decrease.
suspended in the gas, and these have to be pushed However, in most eruptions, significant erosion
and pulled by the gas as the sound wave travels. of the dike walls occurs mainly near the surface
It was shown above that it is quite common for where the wall rocks tend to be weakest. Also,
the expansion of the gas exsolved by magmas to pyroclasts are deposited around the vent, building
provide enough energy to accelerate the magma up a deposit which effectively increases the length
−1
to speeds well in excess of 100 m s . Thus, these of the dike to a small extent. In both cases, the
magmas should erupt at speeds which, as far as stresses acting will preferentially cause the walls of
the magma itself is concerned, are supersonic. the dike to adjust toward the de Lavalle nozzle
However, it is well-established in fluid mechanics shape which allows the supersonic transition to
that a fluid flowing through a pipe can only become occur. Thus, what begins as a choked eruption
internally supersonic if, in the region where the can quite quickly evolve into a pressure-balanced
transition occurs, the pipe first constricts slightly eruption. Figure 6.3a shows a number of different
and then flares outward by a sufficiently great dike shapes, and the effects of these differing
amount. The need to have this happen is what gives shapes on the exit velocity of the gas–pyroclast
rise to the characteristic shape of the back end of a mixture are illustrated in Fig. 6.3b. Note that model