Dear all,

I am coding the 2D decay turbulence and coming across a difficult in set the initial homogeneous turbulent field. There is always a large difference between the desired energy spectrum and my numerical spectrum. I also find that the main point is how to randomly generate velocity ( streamfunction or anything else) in the wavenumber space which SHOULD satisfies the condition of complex conjugate. I did refer to the book `Fluid Flow Phenomena' by P. Orlandi and the old paper by S. A. Orszag but still can not get some idea for my codes. If anyone has some experience, please kindly give me some hints.

PS. the procedure described in the `Fluid Flow Phenomena' seems not correct scince one can not get a real function from the RANDOMLY generated streamfuntion which does not satisfies the complex conjugate condition.

Thank you very much!

It should not be so difficult. I have done the following for 3D turbulence. First give the velocity in spectral space a random complex number, for instance the real and imaginary part have a random value between -1 and 1 (make sure that it is random value between -1 and 1 and not between 0 and 1). Then set the modes U(0,0) U(n/2,0) U(0,n/2) U(n/2,n/2) to zero. Make the velocity field divergence free! Then I calculate the spectrum and modify the amplitudes of the waves so that I get the desired spectrum.

Good luck.