In the 2D case, there’s no escaping exponential decay of the autocorrelation function for any observable satisfying certain regularity properties. (I’m not sure if this is known to be true in higher dimensions. If it’s not, then there could conceivably be traps with sub-exponential escape times or even attractors, but I’d be surprised if that’s relevant here—I think it’s just hard to prove.) Sticking to 2D, the question is just how the time constant in that exponent for the observable in question compares to 20 seconds.
The presence of persistent collective behavior is a decent intuition but I’m not sure it saves you. I’d start by noting that for any analysis of large-scale structure—like a spectral analysis where you’re looking at superpositions of harmonic sound waves—the perturbation to a single particle’s initial position is a perturbation to the initial condition for every component in the spectral basis, all of which perturbations will then see exponential growth.
In this case you can effectively decompose the system into “Lyapunov modes” each with their own exponent for the growth rate of perturbations, and, in fact, because the system is close to linear in the harmonic basis, the modes with the smallest exponents will look like the low-wave-vector harmonic modes. One of these, conveniently, looks like a “left-right density” mode. So the lifetime (or Q factor) of that first harmonic is somewhat relevant, but the actual left-right density difference still involves the sum of many harmonics (for example, with more nodes in the up-down dimension) that have larger exponents. These individually contribute less (given equipartition of initial energy, these modes spend relatively more of their energy in up-down motion and so affect left-right density less), but collectively it should be enough to scramble the left-right density observable in 20 seconds even with a long-lived first harmonic.
On the other hand, 1 mol in 1 m^3 is not very dense, which should tend to make modes longer-lived in general. So I’m not totally confident on this one without doing any calculations. Edit: Wait, no, I think it’s the other way around. Speed of sound and viscosity are roughly constant with gas density and attenuation otherwise scales inversely with density. But I think it’s still plausible that you have a 300 Hz mode with Q in the thousands.
In the 2D case, there’s no escaping exponential decay of the autocorrelation function for any observable satisfying certain regularity properties. (I’m not sure if this is known to be true in higher dimensions. If it’s not, then there could conceivably be traps with sub-exponential escape times or even attractors, but I’d be surprised if that’s relevant here—I think it’s just hard to prove.) Sticking to 2D, the question is just how the time constant in that exponent for the observable in question compares to 20 seconds.
The presence of persistent collective behavior is a decent intuition but I’m not sure it saves you. I’d start by noting that for any analysis of large-scale structure—like a spectral analysis where you’re looking at superpositions of harmonic sound waves—the perturbation to a single particle’s initial position is a perturbation to the initial condition for every component in the spectral basis, all of which perturbations will then see exponential growth.
In this case you can effectively decompose the system into “Lyapunov modes” each with their own exponent for the growth rate of perturbations, and, in fact, because the system is close to linear in the harmonic basis, the modes with the smallest exponents will look like the low-wave-vector harmonic modes. One of these, conveniently, looks like a “left-right density” mode. So the lifetime (or Q factor) of that first harmonic is somewhat relevant, but the actual left-right density difference still involves the sum of many harmonics (for example, with more nodes in the up-down dimension) that have larger exponents. These individually contribute less (given equipartition of initial energy, these modes spend relatively more of their energy in up-down motion and so affect left-right density less), but collectively it should be enough to scramble the left-right density observable in 20 seconds even with a long-lived first harmonic.
On the other hand, 1 mol in 1 m^3 is not very dense, which should tend to make modes longer-lived in general. So I’m not totally confident on this one without doing any calculations. Edit: Wait, no, I think it’s the other way around. Speed of sound and viscosity are roughly constant with gas density and attenuation otherwise scales inversely with density. But I think it’s still plausible that you have a 300 Hz mode with Q in the thousands.