Sarah Brown
Mushroom clouds are formed by large explosions, most commonly associated with nuclear explosions. They are caused by the sudden formation of a large volume of lower-density gases at high altitudes, resulting in a Rayleigh-Taylor instability. The buoyant mass of hot gas rises rapidly, cools, and interacts with the surrounding cool air, forming a temporary vortex ring that draws up a central column of smoke, debris, and condensed water vapour, resulting in the characteristic mushroom shape. The size of a mushroom cloud depends on various factors, including the yield of the bomb and atmospheric conditions such as temperature, dew point, and wind shear. The mushroom cloud produced by the Nagasaki bombing rose to a height of 45,000 feet, while some estimates place the cloud over Hiroshima at 50,000 to 60,000 feet or higher.
| Characteristics | Values |
|---|---|
| Height | 45,000 feet (Nagasaki) |
| 6-7 miles (Hiroshima) | |
| 6.58 km (yield of 15 kT bomb) | |
| Formation | Rayleigh-Taylor instability |
| Kelvin-Helmholtz instability | |
| Composition | Debris |
| Smoke | |
| Condensed water vapour | |
| Dust |
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What You'll Learn
The size of the explosion
The size of a nuclear mushroom cloud can vary depending on the size and nature of the explosion that creates it. In the case of a nuclear detonation, the bomb emits a blast of x-rays, which ionize and heat the surrounding air, creating a very hot bubble of gas known as a fireball. This fireball rises due to its buoyancy, and as it ascends, it cools and changes shape due to atmospheric friction and Rayleigh-Taylor instability. The size of the fireball and the resulting mushroom cloud depend on the yield of the bomb.
A bomb with a yield of around 15 kilotons (kt) would produce a mushroom cloud that reaches approximately 6-7 miles (about 10-11.3 km) high, according to calculations. The famous "mushroom cloud" associated with the Hiroshima bombing was reported to have reached a height of 50,000-60,000 feet, possibly even higher, which is significantly taller than the calculated height for a 15-kt bomb. This discrepancy could be due to various factors affecting the explosion and the resulting cloud's formation and expansion.
The Nagasaki bombing also produced a notable mushroom cloud. An eyewitness, William L. Laurence, described it as a "pillar of purple fire" from which emerged "a giant mushroom" that increased the total height to 45,000 feet. This description helped solidify the "mushroom" as a symbol of the atomic age, despite an earlier test explosion being described as having a "cauliflower" cloud.
It is important to note that not all large clouds associated with nuclear explosions are true mushroom clouds. For example, a photograph from Hiroshima, often identified as a mushroom cloud, was confirmed by nuclear experts to be billowing smoke from a firestorm, not a true mushroom cloud, as it lacked the characteristic shape and structure. This highlights the distinction between the visual perception of a large cloud and the specific formation of a mushroom cloud, which has distinct characteristics and is the result of specific atmospheric and physical principles.
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Atmospheric conditions
The formation of a mushroom cloud is influenced by atmospheric conditions and wind patterns. The cloud's shape is not dependent on the nuclear or thermonuclear component of the explosion, but rather the heat energy and atmospheric conditions.
A mushroom cloud is formed by a sudden, rapid, and concentrated release of heat in relatively cool surroundings. The fireball, a mass of hot, incandescent gases, rises very quickly through the air. As it rises, it experiences resistance from the air, which pushes it down sideways, leading to the flattening of the top of the cloud. This gives it the characteristic mushroom shape. The displaced gas, which is at a lower temperature than the air in the center of the column, trickles down the sides and is then sucked back in, contributing to the curling effect of the explosion's fireball. The fireball continues to rise until it reaches an area of the atmosphere where the air is no longer cool, which is quite high up, in the stratosphere.
The height reached by the 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. If there is sufficient energy remaining in the cloud, it will ascend into the more stable air of the stratosphere. The cloud attains its maximum height after about 10 minutes and is then considered stabilized". It continues to expand laterally, producing the mushroom shape. The cloud may remain visible for an hour or more before being dispersed by the wind and merging with natural clouds.
The formation of a mushroom cloud can be modelled similarly to that of a hot air balloon. The curvature of the top of the explosion causes a reduction in air pressure, leading to cooling. When the air cools past its dew point, water vapour condenses, producing water droplets that become visible as a white cloud. The appearance of these condensation clouds is influenced by the temperature and humidity of different atmospheric layers.
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Rayleigh-Taylor instability
A mushroom cloud is a distinctive mushroom-shaped cloud of debris, smoke, and condensed water vapour resulting from a large explosion. They are best known for their appearance after nuclear detonations. The atomic bomb cloud over Nagasaki, Japan, was described in The Times of London on August 13, 1945, as a "huge mushroom of smoke and dust". The cloud reached a height of 45,000 feet. Most sources indicate that a bomb with a yield of around 15 kT would produce a mushroom cloud that would go up to around 6-7 miles.
Mushroom clouds result from the sudden formation of a large volume of lower-density gases at any altitude, causing a Rayleigh-Taylor instability. This can be understood by considering a higher-density fluid like oil suspended over a lower-density fluid like water, under the influence of Earth’s gravity. The total energy of the system would be lowered if the oil moves downward, reducing its potential energy. This disturbance leads to the upward movement of the lower fluid to compensate, creating a vortex.
In the context of a nuclear explosion, the Rayleigh-Taylor instability occurs when a less dense fluid is 'accelerated' into a more dense fluid. The sudden explosion near the surface leads to the formation of a large volume of low-density gases, which start accelerating upwards rapidly against the higher-density gas above it. This rapid upward movement forms a temporary 'vortex ring', which forms the stem of the mushroom cloud. The rising buoyant low-density air will eventually reach an equilibrium altitude, where it is no longer of lower density than the surrounding atmosphere, and it disperses downwards, causing the mushroom shape.
The evolution of the Rayleigh-Taylor instability can be divided into four main stages. In the first stage, the perturbation amplitudes are small, and the equations of motion can be linearized, resulting in exponential instability growth. In the early portion of this stage, a sinusoidal initial perturbation retains its sinusoidal shape. In the second stage, non-linear effects begin to appear, and the ubiquitous mushroom-shaped spikes and bubbles of the instability start to form. In the third stage, the instability growth becomes non-linear as the spikes and bubbles tangle and roll up into vortices. In the final stage, the Rayleigh-Taylor instability reaches its nonlinear stage, with its "fingers" constituting a large flow of material that is sheared relative to the higher-density fluid.
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Height of the cloud
The height of a nuclear mushroom cloud can vary depending on the size and nature of the explosion. A nuclear explosion creates a fireball, a very hot, roughly spherical mass of incandescent gases and x-rays. This fireball rises due to its buoyancy, and as it does so, it draws in more air, creating strong air currents called "afterwinds". The rising cloud of gas and entrained moist air eventually reaches an altitude where it is no longer of lower density than the surrounding air, and it disperses, drifting back down in the form of fallout.
The height the cloud reaches depends on various factors, including the temperature, dew point, and wind shear profiles of the surrounding air. The size of the explosion also plays a role, as a larger explosion will create a more massive cloud that can rise to greater altitudes. For example, the atomic bomb that detonated over Nagasaki, Japan, in 1945 produced a mushroom cloud that increased the height of the pillar of the explosion to a total of 45,000 feet, according to an eyewitness account by William L. Laurence.
Most sources indicate that a bomb with a yield of around 15 kilotons would produce a mushroom cloud that reaches a height of around 6-7 miles (approximately 10-11.3 km). However, there are discrepancies in these estimates, as some sources claim that the mushroom cloud over Hiroshima rose to a height of 50,000-60,000 feet (approximately 9.1-11.1 km), which is higher than the calculated range for a bomb of that yield.
It's important to note that the stabilization altitude of the cloud, or the point at which it stops rising and begins to flatten into the characteristic mushroom shape, is a critical factor in determining its height. This stabilization altitude is influenced by the temperature, dew point, and wind conditions in the atmosphere, and it can vary significantly depending on these factors.
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Mushroom clouds from non-nuclear explosions
Mushroom clouds are most commonly associated with nuclear explosions. However, they can also occur as a result of non-nuclear explosions, volcanic eruptions, and impact events. The formation of a mushroom cloud is due to the sudden creation of a large volume of lower-density gases at any altitude, resulting in a Rayleigh-Taylor instability. The buoyant mass of gas rises rapidly, forming turbulent vortices that curl downward, creating a temporary vortex ring with a central column of smoke, debris, condensed water vapour, or a combination thereof, resulting in the iconic "mushroom stem".
The size of the explosion determines the size of the mushroom cloud. For instance, the atomic bomb detonated over Nagasaki, Japan, produced a mushroom cloud that rose to a height of 45,000 feet. In comparison, the bomb tested during Operation Crossroads in 1946 formed a "cauliflower" cloud, but a reporter also described it as "the mushroom, now the common symbol of the atomic age".
Even smaller explosions can produce mushroom clouds. As little as 10 kg of explosives may be enough to create a small mushroom cloud, and as few as 150-200 kg can spark rumours of nuclear testing. Mushroom clouds were also observed prior to the Atomic Age, such as during the 1782 Franco-Spanish attack on Gibraltar, where a floating battery exploded with a mushroom cloud after being set ablaze.
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Frequently asked questions
The cloud produced by the bomb that fell on Nagasaki, Japan, was described as a "giant mushroom" that increased the height of the pillar of purple fire to a total of 45,000 feet.
The mushroom cloud over Hiroshima, Japan, rose to a height of 50,000-60,000 feet, according to some sources. However, nuclear experts claim that the commonly identified image of the Hiroshima mushroom cloud is actually billowing smoke from a firestorm.
The height of a mushroom cloud depends on various factors, including the temperature, dew point, and wind shear profiles. A bomb with a yield of 15 kT would likely produce a mushroom cloud about 6-7 miles high.
A mushroom cloud forms when an explosion creates a hot bubble of gas that rises and expands, creating a powerful updraft that draws in dust and debris, forming the stem of the mushroom. The ascent stops when the hot gases reach equilibrium, and the cloud begins to flatten and spread out.
No, mushroom clouds can be formed by any sufficiently large explosion or detonation, including conventional weapons such as thermobaric bombs. Natural events like volcanic eruptions can also produce mushroom clouds. However, the term is most commonly associated with nuclear explosions due to their distinctive appearance.
