3 ms·
Yes, numerical error breaks the symmetry. It could be as small as the rounding error due to finite precision, but most likely a few orders of magnitude bigger t
by semi-extrinsic 9y ago
Yes, numerical error breaks the symmetry. It could be as small as the rounding error due to finite precision, but most likely a few orders of magnitude bigger thanks to errors in the numerical method.
In reality, even if you can manage perfectly symmetric initial and boundary conditions, thermal noise would still cause this symmetry breaking.
Since these systems are physically unstable, the source of initial perturbation is unimportant as long as it is small.
- btrettel 9y agoAs an addition to my other comment, I've read and heard some fluid dynamics researchers/engineers rely on numerical error to break symmetries and lead to turbulence, etc., but it would be hard to call this physical. I think a better approach would be as I said in my other comment, adding noise to the initial condition. This is particularly problematic for studies of the transition to turbulence, as presumably such a phenomena would be strongly dependent on the details of the accumulation of errors/noise, and relying on numerical errors would essentially be like adding noise without quantifying it. To be clear, it absolutely is correct to say that this would lead to symmetry breaking. Depending on the numerical method and the computer, it might take a long time, if I recall correctly.