[Geysers] Regular vs. Irregular Geysers

[Jeffrey Cross]

Here is a little item that might explain why some geysers are regular and
others are irregular.  Although this is probably very over-simplified, I
thought the results were interesting.

If two objects (the water in the geyser and the temperature of the
geyser's surroundings at depth) are of different temperatures, the rate of
heat exchange is assumed to be proportional to the temperature difference.

The formula for the temperature at time t is:

Temp (t) = (T surroundings) + (T initial - T surroundings) x e^(-rt).

If you say that the geyser will erupt when its temperature is very close
to the T surroundings, then if the T surroundings decreases only a little
bit, the eruption will be very late.

But if you say that the geyser will erupt when its temperature is far
below the T surroundings, then for the same change in T surroundings the
geyser will be only a little bit late.

For example, if you set r = 0.1, T initial = 373K (100C), T surroundings =
458K (185C), then it will take 16 minutes to heat the geyser to 440K
(arbitrarily chosen as the temperature which will cause an eruption).
Decrease T surroundings to 453K (cooled by 5 degrees) and the geyser will
erupt after 18 minutes.  It is 2 minutes late out of a 16-minute interval.

With the same values but setting the temperature at which the eruption
will start at 450K (10 degrees higher than before), then the geyser will
erupt after 24 minutes.  And if you decrease T surroundings by 5 degrees
as before, now the geyser will erupt after 32 minutes.  It will be 8
minutes late out of a 24-minute interval.

You can see from the above that the closer the initiation temperature and
the surrounding temperature are, the more sensitive the geyser will be to
slight changes in its energy supply.

For geysers like Old Faithful, I would guess that the energy content is
increasing rapidly when the eruption starts, and that is why it is quite
regular.

Jeff Cross
jacross at lamar.colostate.edu