I came across difficulty in setting an initial 2D homogeneous
turbulence. I referred to all the literatures I can reach but they
all just say that 'we set an initial velocity field with following
energy spectrum ...' and no further details are available. I think
the key point is to randomly generate a field in the Fourier space which
satisfy the complex conjuate condition, but how to manage this?
Some one did mention that they generate a random field with half of the
Fourier modes and the other half can be determined by the symmetry
condtion. This is definitely ture for 1D cases. But for 2D cases,
following this procedure one essentially first generate 1/4 of the
entire Fourier modes and there is other 3/4 modes need to be determined.
If you have some treasure experience on this topic please contact me.
I need your kind help !!!
With best regards
Department of Computational Science
National University of Singapore