Shockwave of mushroom cloud rising at supersonic speed

[darkdave3000]

I'm modelling the Hiroshima nuclear explosion on a real time real scale physics simulator.

My initial simulations based on data accumulated from wikipedia such as temperature of the fireball the radius of it and using air pressure and air density data based on the detonation height of 600m has yielded a surprising result of the mushroom cloud reaching supersonic speeds as it rises like a balloon upward and creating a shockwave of its own that might have been the shockwave the pilots of the "Enolagay" felt 11 miles away.

I also simulated drag and the change of drag coefficient of a sphere shaped object namely the fireball.

Can you guys confirm if mushroom clouds reach supersonic speeds rising up? And if they make a shockwave of their own after the initial explosion that would have caused the first shockwave?

Image Description:

The screenshots of my simulation software shows a simplified model of the Earth with the tallest building of the world and mount Everest in view to allow players to have a sense of scale, the atmosphere also changes shades every 1km upward . The red circles are soundwaves that travel at the speed of sound based on the height they were spawned. The fireball changes color as it cools from 6,000 C and becomes invisible at 15degC. The fireball has a diameter of about 370m and expands gradually.

 

[boneh3ad]

I'm sorry but I don't fully understand what your images are showing. The circle is the fire ball and it is moving upward?

 

[darkdave3000]

I'm sorry but I don't fully understand what your images are showing. The circle is the fire ball and it is moving upward?

Yes , the yellow circle is the "Littleboy" fireball, it's 6,000 deg C and has a diameter of about 370m (and increasing gradually). Red circles are 1 second interval sound pings from the fireball. So you can actually see shockwaves form as a result of the fireball gradually exceeding mach 1 as some portions of those red circles converge in certain directions. For example in the zoomed out picture you can see that at that point the fireball is speeding upward at roughly mach 1.

 

[256bits]

Yes , the yellow circle is the "Littleboy" fireball, it's 6,000 deg C and has a diameter of about 370m

Certainly possible for a large fireball. The one in question might be a little small.
From Wiki it seems that the atmospheric density scale height is a determining factor for the size of the heated region of lower density than surrounding air.

If the size of the fireball is comparable to the atmospheric density scale height, the whole cloud rise will be ballistic, overshooting a large volume of overdense air to greater altitudes than the final stabilization altitude. Significantly smaller fireballs produce clouds with buoyancy-governed ascent

https://en.wikipedia.org/wiki/Mushroom_cloud

Additional
http://astro.unl.edu/naap/scaleheight/sh_bg1.html
https://en.wikipedia.org/wiki/Scale_height

You might have to do some more research on the subject to determine if the fireball actually does go ballistic

 

[darkdave3000]

Certainly possible for a large fireball. The one in question might be a little small.
From Wiki it seems that the atmospheric density scale height is a determining factor for the size of the heated region of lower density than surrounding air.https://en.wikipedia.org/wiki/Mushroom_cloud

Additional
http://astro.unl.edu/naap/scaleheight/sh_bg1.html
https://en.wikipedia.org/wiki/Scale_height

You might have to do some more research on the subject to determine if the fireball actually does go ballistic

The fireball rises due to buoyancy of hotter less dense gasses in it compared to air outside of it. It's basically rising like an over sized balloon.
That's what the simulation shows anyways. In fact the fireball goes all the way into space(100km) but at that point the temperature of the fireball gas is roughly 15 degrees C so its harmless by then. The size of the fireball is also larger by then about 1.2km in diameter, but again at that point its cooler.

 

[256bits]

The fireball rises due to buoyancy of hotter less dense gasses in it compared to air outside of it. It's basically rising like an over sized balloon.
That's what the simulation shows anyways. In fact the fireball goes all the way into space(100km) but at that point the temperature of the fireball gas is roughly 15 degrees C so its harmless by then. The size of the fireball is also larger by then about 1.2km in diameter, but again at that point its cooler.

Another site I found from investigating your modeling brought this site up.
It is an interesting description of what goes on in the explosion.
Your post has made me learn something new about nuclear explosions, which otherwise I would never have thought of researching.
Curious to know what got you started in this if you don't mind.

the site is,
http://www.abomb1.org/nukeffct/enw77b3.html
A relevant section regarding the fireball going ballistic says the following, with some more description than that given by Wiki,

2.129 Other aspects of fireball size are determined by the conditions under which the fireball rises. If the fireball is small compared with an atmospheric scale height, which is about 4.3 miles at altitudes of interest (¤ 10.123), the late fireball rise is caused by buoyant forces similar to those acting on a bubble rising in shallow water. This is called "buoyant" rise. The fireball is then essentially in pressure equilibrium with the surrounding air as it rises. If the initial fireball radius is comparable to or greater than a scale height, the atmospheric pressure on the bottom of the fireball is much larger than the pressure on the top. This causes a very rapid acceleration of the fireball, referred to as "ballistic" rise. The rise velocity becomes so great compared to the expansion rate that the fireball ascends almost like a solid projectile. "Overshoot" then occurs, in which a parcel of dense air is carried to high altitudes where the ambient air has a lower density. The dense "bubble" will subsequently expand, thereby decreasing its density, and will fall back until it is in a region of comparable density.

 

[darkdave3000]

Another site I found from investigating your modeling brought this site up.
It is an interesting description of what goes on in the explosion.
Your post has made me learn something new about nuclear explosions, which otherwise I would never have thought of researching.
Curious to know what got you started in this if you don't mind.

the site is,
http://www.abomb1.org/nukeffct/enw77b3.html
A relevant section regarding the fireball going ballistic says the following, with some more description than that given by Wiki,

I'm a solo simulations programmer working for my self and am trying to secure a job in a Chinese university that wants me to teach computer games development so I've been trying to impress them with my specialty of making realistic physics models of the Earth and Space in both 2D and 3D visualizations. Simulti.tech is my website which I am hoping will be a real company eventually. At the moment I am just using it as a CV. I want to develop simulation engines compatible with VR and Augmented tech to help improve understanding of science and developing technology by allowing people to experiment with "what if" scenarios. At the moment I am trying to develop a rocket to orbit sim that will allow reenacting Apollo missions in real time with the 3D version compatible with Occulus Rift VR tech.

 

[darkdave3000]

Hi all, I am making a retraction to the supersonic mushroom cloud. I missed a square root sign for the drag equation thus allowing the cloud to rise faster than normal. You can visit my website to view a retraction I made in the video on this topic.

After fixing the drag algorithm the mushroom cloud rises at subsonic speeds in my simulation.

David