Laura Smith
Mushroom clouds are the result of large explosions under Earth's gravity, but they are most commonly associated with the aftermath of nuclear detonations. The height of a mushroom cloud depends on the heat energy of the weapon and the atmospheric conditions. If the cloud reaches the tropopause, it tends to spread out, but if it contains sufficient energy at this height, it will ascend into the stratosphere. The size of a mushroom cloud can be calculated using equations that consider the yield of the explosion, with the distinctive shape being a result of buoyant action inside the atmosphere.
| Characteristics | Values |
|---|---|
| Formation | The sudden formation of a large volume of lower-density gases at any altitude, causing a Rayleigh-Taylor instability |
| Resulting motion | A "spherical cap bubble" |
| Shape | A mushroom cloud is formed when the mass of hot gases reaches its equilibrium level and the ascent stops, causing the cloud to flatten into the characteristic mushroom shape |
| Height | Depends on the heat energy of the weapon and atmospheric conditions; reaches maximum height after about 10 minutes |
| Color | Initially red or reddish-brown due to the presence of nitrous acid and oxides of nitrogen; changes to white due to water droplets as the fireball cools |
| NUKEMAP equation | this.cloud_bottom = function(yield) { return 1000*(1.7154976807456771E+02*Math.pow(yield/5.2402966478808509E+05,2.5445292192920910E-01)*Math.exp(yield/5.2402966478808509E+05) + -3.2665357749287349E-01) } |
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What You'll Learn
Rayleigh-Taylor instability formation
The Rayleigh-Taylor instability formation is a key process in the creation of mushroom clouds, which are typically associated with nuclear explosions. This phenomenon occurs when there is a sudden formation of a large volume of low-density gases at any altitude, resulting in a buoyant mass that rapidly rises.
The formation of a Rayleigh-Taylor instability can be understood through the concept of fluid dynamics. Imagine two layers of fluids with different densities, such as oil and water, influenced by Earth's gravity. The system seeks to minimise its total energy, so the denser fluid (in this case, water) will move downwards, while the less dense fluid (oil) moves upwards. This movement causes a disturbance, and as this disturbance grows, the denser fluid moves further down, and the less dense fluid continues to rise. This is the fundamental insight attributed to G. I. Taylor.
In the context of a mushroom cloud, the explosion creates a large volume of low-density gases that accelerate upwards against the higher-density gases above. This rapid upward movement forms turbulent vortices that curl downward, creating a temporary vortex ring—the stem of the mushroom cloud. The rising buoyant low-density air continues until it reaches an equilibrium altitude where it is no longer less dense than the surrounding atmosphere. This equilibrium is what Lord Rayleigh studied, and it is unstable to any perturbations or disturbances of the interface.
As the Rayleigh-Taylor instability develops, it transitions from a linear growth phase, where the perturbation amplitudes are small, to a non-linear growth phase. In this latter phase, the spikes and bubbles of the instability tangle and roll up into vortices, forming the characteristic mushroom shape. The final height of the mushroom cloud depends on the heat energy of the explosion and the atmospheric conditions. If the cloud reaches the tropopause, it tends to spread out, but with sufficient energy, it can ascend into the stratosphere.
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Buoyant mass of gas rises
Mushroom clouds are the result of the sudden formation of a large volume of lower-density gases, which occurs at any altitude. This causes a Rayleigh-Taylor instability, which is when a buoyant mass of gas rises rapidly, forming turbulent vortices that curl downward around its edges.
The buoyant mass of gas rises due to the same principle as a hot-air balloon. Once the hot gas has cleared the ground, it can be analysed as a "spherical cap bubble", which allows for the prediction of its rate of rise and observed diameter. As the gas rises, it cools, and the vapours condense to form a cloud. This cloud contains solid particles of weapon debris and small water droplets derived from the air sucked into the rising fireball.
The upward motion of gas creates a temporary vortex ring that draws up a central column, possibly with smoke, debris, condensed water vapour, or a combination of these elements, forming the "mushroom stem". The upward motion of gas also creates strong air currents known as "afterwinds", which can cause dirt and debris to be sucked up from the Earth's surface into the cloud. The amount of dirt and debris incorporated into the cloud depends on the height of the explosion.
The mushroom cloud reaches its maximum height after about 10 minutes, at which point it is considered stabilized. However, it continues to grow laterally, producing the characteristic mushroom shape. The final height of the cloud depends on the heat energy of the explosion and the atmospheric conditions. If the cloud reaches the tropopause, it tends to spread out. However, if there is sufficient energy remaining, a portion of the cloud will ascend into the more stable air of the stratosphere.
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Vortices and vortex ring formation
Mushroom clouds are the result of a massive energy release, creating intense heat and pressure. The physics behind their formation involves rapid expansion, rising air currents, and condensation. When a powerful explosion occurs, it releases a large amount of energy in a fraction of a second, forming a fireball that can reach temperatures hotter than the surface of the sun.
The intense heat causes the air to expand rapidly, and as the hot gases rise, they create a low-pressure area beneath, resulting in a Rayleigh-Taylor instability. This instability leads to the formation of turbulent vortices and vortex rings. The buoyant mass of gas rises rapidly, and the vortices curl downward around its edges, forming a temporary vortex ring. This vortex ring draws up a central column of smoke, debris, condensed water vapour, or a combination of these elements, forming the "mushroom stem".
The formation of vortex rings has fascinated scientists for over a century. Vortex rings can be observed in nature, such as in volcanic eruptions or the behaviour of certain animals. They are also created by human activities, like artillery fire or the tricks of fire-eaters. Vortex rings were first mathematically analysed by German physicist Hermann von Helmholtz in 1858, and they play a significant role in understanding various natural and man-made phenomena.
The size and duration of a mushroom cloud depend on the heat energy of the explosion and atmospheric conditions. If the cloud reaches the tropopause, it tends to spread out. However, if it still retains sufficient energy, it can ascend into the stratosphere, reaching its maximum height in about 10 minutes. The cloud may remain visible for an hour or more, eventually dispersing into the surrounding atmosphere.
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Fallout and blast wave
The blast wave and fallout from a nuclear explosion are two of its most destructive effects. The blast wave refers to the shock wave of air radiating outward from the explosion, causing sudden changes in air pressure and high winds that can crush and knock down objects. The blast wave travels faster than the speed of sound and moves outward spherically from the centre of the explosion. The shock wave is initially inside the surface of the developing fireball, which is created by the explosion's "soft" X-rays. Within a fraction of a second, the dense shock front moves past the fireball, causing a reduction in the light emanating from the explosion. This interaction between the shock wave and fireball produces a characteristic double flash, which is used to verify that an atmospheric nuclear explosion has occurred.
For air bursts at or near sea level, 50-60% of the explosion's energy goes into the blast wave, and the amount depends on the size and yield of the bomb. The blast wave is more destructive when the explosion occurs in denser media, such as water, as it creates more powerful shock waves while limiting the area of its effect. In contrast, when the explosion is surrounded only by air, the lethal blast and thermal effects scale more rapidly than lethal radiation effects as the explosive yield increases.
The fallout from a nuclear explosion refers to the radioactive contamination released into the environment. This contamination is composed of radioactive material from the bomb and surrounding matter that has been rendered radioactive by neutron radiation. The amount of fallout is greater when the explosion occurs on or near the Earth's surface, allowing the fireball to touch the ground. Fallout can also occur from explosions at higher altitudes if there is sufficient radioactive material to descend and circulate in a huge circular area.
The delayed effects of radioactive fallout can inflict damage over an extended period, ranging from hours to years. The impact of fallout depends on factors such as whether one is indoors or outdoors, the size and proximity to the explosion, and the direction of the wind carrying the fallout. Radiation poisoning is almost certain for individuals caught in the open within a radius of 0-3 kilometres from a 1-megaton airburst. However, individuals in reinforced concrete buildings may be protected from the lethal effects of the radiation and blast zone, as observed in Hiroshima.
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Atmospheric conditions
The formation of a mushroom cloud is dependent on atmospheric conditions. The phenomenon occurs due to buoyant action inside the atmosphere, which is only possible up to a certain height. The height reached by the radioactive cloud depends on the heat energy of the weapon and the atmospheric conditions. If the cloud reaches the tropopause, around 6-8 miles above the Earth's surface, it tends to spread out. However, if the cloud retains sufficient energy at this height, a portion of it may ascend into the more stable air of the stratosphere.
The stabilization altitude, or the height at which the cloud stops ascending and begins to flatten into the characteristic mushroom shape, is strongly influenced by the temperature, dew point, and wind shear in the air at and above the starting altitude. The temperature and dew point can impact the formation of the cloud, with vapors condensing to form a cloud containing solid particles of weapon debris and water droplets. Additionally, wind shear can affect the spread and dispersion of the cloud.
The density of the atmosphere also plays a crucial role in the formation of mushroom clouds. The buoyant mass of gas rises rapidly, forming turbulent vortices that curl downward, creating a temporary vortex ring that draws up a central column of smoke, debris, condensed water vapor, or a combination of these elements to form the "mushroom stem." This process is influenced by the density gradients within the atmosphere, which can vary with altitude.
Furthermore, the presence of inflowing winds or "afterwinds" can impact the amount of dirt and debris sucked up from the Earth's surface into the cloud. In an air burst, only a small proportion of the dirt and debris become contaminated with radioactivity, while a burst near the ground can result in larger amounts of contaminated material being drawn into the cloud. The afterwinds are influenced by the height of the burst, with stronger updrafts occurring at higher altitudes.
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Frequently asked questions
Mushroom clouds are formed by large explosions under Earth's gravity and are best known to appear after nuclear detonations. They are caused by buoyant action inside the atmosphere, which only occurs up to a certain height.
The size of a mushroom cloud depends on the heat energy of the weapon and the atmospheric conditions. The cloud may reach the tropopause, about 6-8 miles above the Earth's surface, and spread out. If there is sufficient energy remaining, a portion of the cloud will enter the stratosphere.
After a nuclear explosion, a fireball is formed. As it rises, a Rayleigh-Taylor instability is created, causing air to be drawn upwards and into the cloud. This forms strong air currents called "afterwinds", which can carry dirt and debris upwards, forming the stem of the mushroom cloud.
A mushroom cloud reaches its maximum height after about 10 minutes, at which point it is considered stabilized. It continues to expand laterally, producing the characteristic mushroom shape. The cloud can remain visible for about an hour or more before being dispersed by the wind.
The height of a mushroom cloud can be calculated using the NUKEMAP tool, which uses yield as the input variable. The equations provided by NUKEMAP are curve fits from a graph that goes up to 30 megatons. The height of the cloud depends on the density of the atmosphere, which affects how the clouds form and their size.
