Neutral Buoyancy and Lateral Spreading of the Plume

When the plume reaches a height of neutral buoyancy does it stop going up? Somewhat surprisingly, the answer is no.

The reason is that the plume does not enter the buoyant region with a vertical velocity equal to zero. As the cartoon to the right shows, all that the buoyant interface (the dotted line in the figure) really indicates is that the particle is no longer being accelerated upward. At the buoyant interface, the upward force, Fb, is equal to the particles weight, thus there is no acceleration. Above this level, the particle is acclerated in the downward direction.

The plume will rise above height Hb to the total plume height Ht

Ht is generally approximately 1.3 times Hb. This height can be approximated with several techniques.

Carey and Bursik (2000) use the equation:

Ht = Q ^0.259, where Q is the volumetric flux in (m^3)/s.

A different method is described by Sparks (1986).

Sparks (1986) model for plume height

Using numerical modeling, Sparks related plume height to mass flux. Additionally, his model accounts for the affects of the tropopause -- the level in the atmosphere where the vertical temeprature gradient is no longer decreasing.

The plot to the right shows the total plume height, Ht as a function of mass flux for the tropical regions (stippled) and temperate regions. For both fields, the left curve represents magma erupted at 1000C, and the right curve shows magma erupted at 600C. Note the marked effects of the tropopaus on column height, and the effects of temperature.

Additional attention should be given to how plumes spread between heights Hb and Ht.

The plumes spread as density currents, or gravity flows -- both terms indicating that flow occurs due to a density contrast between the material in the plume and the surrounding atmosphere. It is this spreading that gives rise to the "mushroom clou" appearance of Plinian eruptions. Of course, prior to the nuclear era, "mushroom cloud" was not in the globe's vocabulary, and instead the plumes were described as shaped like giant trees. The figure to the right shows the eruption plume from the 1991 Pinatubo eruption.

Plumes can spread laterally at very high rates, and not surprisingly, the wind can affect these rates. The cartoons below contrast a plume spreading with no wind, and one spreading with a wind coming from the left. Note that both plumes have mushroom

From the USGS.

The Pinatubo eruption cloud spread to a diameter of 400 km in just 5 hours.