All this is on the edge of my knowledge, so I could well be wrong. Insert “I thinks” and “from what I remembers” as appropriate throughout what follows.
If we start with non-interacting air molecules then the standing waves of pressure are the normal modes of the container. With non-interacting molecules the movement of a single molecule is not necessarily chaotic, whether it is or not depends on the shape of the container.
Assuming no loss (Q factor of infinity) then, knowing that the motion contains some contribution from a particular normal mode allows us to plot that normal mode (sine wave say) out to infinite future (and past) times. However, in a chaotic system it is required that the frequencies of the normal modes are approximately equally spaced. Their are no big gaps in the frequencies. I think the relevance of this to this question is that if all we know is that normal mode number 27 has some amplitude that sine wave we can infer out is added to all the other modes, which add white noise. (The mode spacing argument ensuring the noise is in fact white, and not colored noise that we could exploit to actually know something). So, assuming that mode 27 only has a typical amplitude we learn very little.
When we add collisions between the air molecules back in, then I believe it is chaotic for any shape of container. Here the true normal modes of the total system include molecule bumping, but the standing waves we know about from the non-interacting case are probably reasonably long-lived states.
All this is on the edge of my knowledge, so I could well be wrong. Insert “I thinks” and “from what I remembers” as appropriate throughout what follows.
If we start with non-interacting air molecules then the standing waves of pressure are the normal modes of the container. With non-interacting molecules the movement of a single molecule is not necessarily chaotic, whether it is or not depends on the shape of the container.
Assuming no loss (Q factor of infinity) then, knowing that the motion contains some contribution from a particular normal mode allows us to plot that normal mode (sine wave say) out to infinite future (and past) times. However, in a chaotic system it is required that the frequencies of the normal modes are approximately equally spaced. Their are no big gaps in the frequencies. I think the relevance of this to this question is that if all we know is that normal mode number 27 has some amplitude that sine wave we can infer out is added to all the other modes, which add white noise. (The mode spacing argument ensuring the noise is in fact white, and not colored noise that we could exploit to actually know something). So, assuming that mode 27 only has a typical amplitude we learn very little.
When we add collisions between the air molecules back in, then I believe it is chaotic for any shape of container. Here the true normal modes of the total system include molecule bumping, but the standing waves we know about from the non-interacting case are probably reasonably long-lived states.