Talk:Taylor–Green vortex

Boundary conditions?

Does the article assume periodic boundary conditions (i.e. are we on a torus)? If so, could this please be stated explicitly? Penguian (talk) 07:05, 6 July 2010 (UTC)

Either time-dependent Dirichlet or periodic boundary conditions would work. Italo Tasso (talk) 15:55, 22 May 2014 (UTC)

Inconsistency

In the "Original work" section we have u = A cos(ax) sin(by) sin(cz). In the "Taylor–Green vortex solution" section we have u = sin(x) cos(y). This is not consistent with A = a = b = 1. Same for v. Italo Tasso (talk) 16:02, 22 May 2014 (UTC)

Sorry, see what you mean, (sin and cos are interchanged, and also for "v" there is a negative sign. This should be made consistent. The notation in the "Original work" is actually that of Taylor--Green, so probably best to keep to that way. 155.198.167.28 (talk) 16:36, 22 May 2014 (UTC)

Exact or approximate solution?

In the "Taylor–Green vortex solution" it says "gives agreement with this exact solution, if the exponential is expanded as a Taylor series". Does it mean it is an approximate solution? It is a bit confusing. Is it an exact solution or an approximate solution for small t? Italo Tasso (talk) 16:10, 22 May 2014 (UTC)

The 3D solution, as written, is known only for small time. The 2D solution is exact. However, to map the 2D exact solution, to the 3D solution (which is only for small time), the Taylor series expansion of F(t) is required. 155.198.167.28 (talk) 16:20, 22 May 2014 (UTC)

Coefficient in the exponential

I am not completely sure, but it seems to me that -2 should be replaced by -4 in e^{-2 nu t} coefficient in order to solve N.S. Analogously, in the article about 3D Taylor-Green, there should be -6 instead of -3, I think. 185.140.246.81 (talk) 16:41, 12 January 2024 (UTC)