Mushroom Cloud & Rayleigh-Taylor Instability
The ‘Mushroom Cloud’, is often what comes to mind when we think about surface nuclear detonations, large volcanic eruptions. Most recently, we saw it’s appearance in a unfortunate blast that occurred in an coastal city in Western Asia.
But, what exactly causes this characteristic cloud to form?
A mushroom cloud is actually a ‘flammagenitus cloud’ or a ‘fire cloud’. As the name suggests, this type of cloud forms usual as a product of a fires (Ex — Wildfires) or volcanic eruptions. One of it’s characteristic feature is the occurrence of ‘dry-lighting’ or simply, lighting without rain. The image below shows this type of cloud over the horizon.
When we come to a mushroom cloud, the cloud here is composed of debris, smoke, condensed water vapour, and sometimes like in the case of a nuclear detonation, radio-active isotopes. But, not all fire-clouds become mushroom clouds and that’s because of the Rayleigh-Taylor Instability.
The Rayleigh-Taylor instability can be simply explained with the help of an example. Consider a case wherein a higher density fluid like oil is suspended over a lower density fluid like water, under the influence of Earth’s gravity. We know that any system tends to achieve a state where it’s overall total energy is the lowest. So, in this case, the total energy of the oil-water system would be lowered if the oil moves down below the water, so as to reduce it’s potential energy. This downward movement of oil, a disturbance, would lead to the upward movement of water to compensate. This disturbance keeps growing in favour reducing the potential energy, as shown in the figure below. Note the initial position of the fluid interface at 0. This set-up was studied by Lord Rayleigh.
Taylor then came up with the insight that a similar situation would arise when a less dense fluid is ‘accelerated’ into a more dense fluid, which is exactly what happens in the case of a mushroom cloud. The sudden explosion near the surface leads to the formulation of a large volume of low density gases which start accelerating upwards rapidly against the higher density gas above it. This rapid upward movement leads to formation of downward directed turbulent vortices, forming a temporary ‘vortex ring’, which forms the stem of the mushroom cloud.
Thereafter, the rising buoyant low density air will finally reach an equilibrium altitude, the altitude at which this air is no longer at lower density than the surrounding atmosphere. At this point, it stops rising and disperses downwards, causing the mushroom shape. Thus, a combination of Rayleigh-Taylor instability along with the sudden upward acceleration caused by the explosion leads to the formation of the mushroom cloud. The below image shows the mushroom cloud formed by the explosion of Fat Man.
