Origin of the "underpressure" or "negative phase" in a blast wave

[Gruxg]

In the blast wave generated by an explosion, after a first violent increase in the air pressure, there is a "negative phase" in which the pressure drops below the initial atmospheric pressure (see e.g. https://en.wikipedia.org/wiki/Blast_wave ). According to wikipedia, this underpressure is the cause of the so called Wilson cloud that forms when the explosion takes place in humid air ( https://en.wikipedia.org/wiki/Condensation_cloud ) -

But what is the cause of this negative phase? Would it occur too if the initial increase in pressure, instead of being caused by a fast heating of the air at the point of the explosion, were caused by an expansion by pure machanical means?

At first I thought about a possible explanation but now I think it is not convincing or at least not complete: shortly after the explosion the hot air bubble in the center starts to move upwards by convection, because it is less dense than the cooler air around it. I understand this produces a wind towards the explosion and maybe a "negative pressure" near the ground and possibly some seconds after the explosion. However, the Wilson cloud seems to develop much faster and in a spherical way, so there must be another mechanism that operates in a shorter time scale responsible for the spherical underpressure wave. Maybe the central bubble that expands violenty due to heating contracts again a little in a very short time causing a vacuum?

 

[A.T.]

But what is the cause of this negative phase?

Causation is tricky in fluid mechanics. One aspect is the inertia of the air: The air moving outwards doesn't stop immediately once the propelling over-pressure is gone. Another way to look at it: If you have increased density at the front, you must have decreased density somewhere.

 

[Gruxg]

One aspect is the inertia of the air: The air moving outwards doesn't stop immediately once the propelling over-pressure is gone

But is the propelling over-pressure gone so quickly? Let's think in a similar but simpler system: a cylinder with air, open in one end, and with a piston in the other. The piston suddenly moves and stops, producing a pressure wave in the air inside the tube. Would we have a negative pressure too following the overpresure?

Another way to look at it: If you have increased density at the front, you must have decreased density somewhere.

Yes, but one thing is density and another thing is pressure. One volume of air can have lower density but higer pressure than other, and vice versa (because pressure depends also on the temperature.

 

[256bits]

But is the propelling over-pressure gone so quickly? Let's think in a similar but simpler system: a cylinder with air, open in one end, and with a piston in the other. The piston suddenly moves and stops, producing a pressure wave in the air inside the tube. Would we have a negative pressure too following the overpresure

Like a sound wave.
http://physics.bu.edu/~duffy/semester1/c20_disp_pressure.html

 

[nettleton]

A blast wave describes the situation in which a decaying front traveling above sound speed heats the gas behind it leaving a falling temperature gradient. To attain equilibrium a negative pressure is necessary.

 

[Gruxg]

Like a sound wave.

But in a sound wave we have a periodic oscillation or vibration: the source of the sound moves back and forth. In an explosion and in my example of the tube with the piston is not obvious that the same happens. The piston does not move back and forth, only moves in one direction for a short time and then stops. It is clear that the air pressure will increase and then decrease...but it is not so clear for me if it reaches a pressure lower than the initial one before the equilibrium is restored.

This could be related also with another matter: how an initial shock wave becomes at some distance a conventional sound wave.

 

[Gruxg]

A blast wave describes the situation in which a decaying front traveling above sound speed heats the gas behind it leaving a falling temperature gradient. To attain equilibrium a negative pressure is necessary.

Interesting, but I do not understand it. Could you elaborate a little or give any link to a more elaborated explanation? Thanks!

 

[nettleton]

Assuming a point source the intensity of the lead front decays eventually to a sound wave as it expands spherically.

 

[nettleton]

Like a sound wave.
http://physics.bu.edu/~duffy/semester1/c20_disp_pressure.html

 

[nettleton]

yes,

 

[Gruxg]

The link you quote explains what a sound wave is, not how the lead front decays to a sound wave.

 

[nettleton]

As the leading front of the blast wave expands and encompasses more of the media it deays to form a sound wave which, as it expands drops in intensity. A further way to envisage the process, is that the blast front is formed from a given amount of energy and its propagation means a steadily decreasing energy density.