Why does a nuclear explosion have directionality?

It just occurred to me that almost all images I've seen of the (in)famous mushroom cloud show a vertical column rising perpendicular to the ground and a horizontal planar ring parallel to the ground.

Not that I'm an expert (that's why this question) but I have rarely seen anything go in the 45 degree angle. Or for that matter anything other than the 'special' 0 degree horizontal plane and 90 degree vertical column. Shouldn't there be radial vectors at all angles between 0 and 90 degrees giving rise to a hemispherical explosion envelope? Why is it a vertical cylinder?

PS: I understand the top expands eventually on cooling and lowered air pressure giving the mushroom look but my questions is for the previous stage - the vertical column.

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The horizontal planar ring "parallel" to the ground is an illusion. In reality, the shock wave is spherical but also invisible. The half going down goes into the ground and cannot be seen because it is blocked by the earth. The half going up is invisible, because there's nothing in the air to show its passing. Only the small part that radiates at 0 degrees appears to be visible, because that's the only place where there's consistently something visible to reflect it's passing (grass, water surface, ground dust, etc.). – RBarryYoung Apr 18 '14 at 17:41
Note that in tests, you often see lots of small rocket smoke trails. They are to witness the passage of the shock wave through the air. – Phil Perry Apr 18 '14 at 21:37
@RBarryYoung - the horizontal planar ring is not an illusion. This is Mach stem, generated at the intersection of the incident and reflected waves. – Deer Hunter Apr 19 '14 at 13:05
I want to emphasize @DeerHunter's point here, that ring is a real effect, but it is not a property of the explosion itself; instead it is a property of the geometric relationship and interaction between the explosion and the ground. – dmckee Apr 19 '14 at 19:26
@DeerHunter Ah, I was unaware of that. This might be worth adding as an answer. – RBarryYoung Apr 21 '14 at 11:20

The explosion certainly is hemispherical, see, for instance, this explosion caused by the Trinity bomb:

The gas cloud that you posted, and what many would consider is synonymous to the nuclear weapons, comes after the explosion.

Nuclear bombs are actually usually ignited above ground for "maximum destruction." Since the nuclear reaction is immensely hot (about 4000 K whereas the surface of earth is sitting pretty around 300 K), the gas rises much the same way a hot-air balloon rises.

At some point, the cold air from around the explosion gets sucked under the mushroom cap and causes the thin column you see:

Thus, for the most part, it is the extreme temperatures that cause the explosion "bubble" to rise in the first place. And it is the convective air currents under the bubble that cause the column to form.

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I had thought that the height was to minimize fallout by avoiding dirt bonding to radioactive material. A little research seems to show that "maximum destruction" is the goal: blog.nuclearsecrecy.com/2012/08/08/the-height-of-the-bomb – Phil Apr 18 '14 at 21:09
Yeah, it's not so productive to spend the bomb's energy digging a huge crater, unless your target is an underground complex. Exploding at altitude exposes a larger area to destruction from blast, heat, and radiation; which is usually the intent of whoever exploded the bomb -- secondary effects of reducing neutron activated radioactive fallout (from surface material) are not the primary purpose. – Phil Perry Apr 18 '14 at 21:35
There are actual a large number of bomb designs each for a particular effect/target. Most nuclear weapons are targeted at other nuclear weapons and are therefor some sort of "bunker buster" designed to produced a focused blast against the ground. They usually detonate by proximity fuse a few dozen feet from the ground. Close enough for most of the sphere of the fireball to hit the ground but far enough to avoid crashing before detonating. Of all the designs, only the "city killers" were configured for maximum blast and altitude in order to devastate a wide area. – TechZen Apr 19 '14 at 4:31

Exotic designs of atomic devices have directionality because of interaction with the material surrounding the core. This was documented by George Dyson in his book PROJECT ORION, when he revealed the 'pusher capsule' bombs would have had a filler which turned into plasma and 'pushed' on the plate on the bottom of the spacecraft.

However, as seen in the Operation Starfish exoatmospheric explosions, detonations in space are spherical unless the device is specially designed for directionality, and most devices (as per my reading of Chuck Hansen) are not designed for directionality.

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