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Initial conditions in physical space from energy spectrum

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Old   February 19, 2016, 01:51
Default Initial conditions in physical space from energy spectrum
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Aru
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Hi,
For validation purpose, I want to simulate homogeneous isotropic turbulence using my code. Following literature, my initial conditions have a known one dimensional energy spectrum E(k). I need to give initial conditions in physical space, with N^3 grid points.
I have learnt that I have to proceed as follows.
  1. Generate a random velocity field (u_1,u_2,u_3) in the physical domain.
  2. Transform to wavenumber space.
  3. Impose incompressibility condition \hat{u}.\vec{k}=0, by projecting velocity vectors on plane normal to \vec{k}.
  4. Scale to the given spectrum \hat{u}\rightarrow\frac{\hat{u}}{|\hat{u}|}E(k).
  5. Transform back to physical space
I am using Matlab to generate the initial conditions, and steps 1 and 2 looks traightforward to me.
However in step 3, how will I do the orthogonalization process \hat{u}=\hat{u}-(\hat{u}.\vec{k})\vec{k}/k^2 with my FFT data? What is the wavenumber vector \vec{k}, when FFT data has wavenumbers in the range [1,N/2] in all 3 directions?
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Old   February 19, 2016, 05:06
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Filippo Maria Denaro
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have a look here

http://users.ictp.it/~krs/pdf/1993_008.pdf
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Old   February 19, 2016, 06:58
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Thank you for the response.
However, the document does not have any additional information than what I understand now. My problem is specific. I have the amplitude-wavenumber information (data) after transformation to Fourier space. With my limited knowledge, I don't know how to get \hat{u}.\vec{k} from this available data.
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Old   February 19, 2016, 16:32
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Filippo Maria Denaro
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using search function, you can find many posts in this forum about the initial conditions, for example:

http://www.cfd-online.com/Forums/mai...procedure.html
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energy spectrum, fourier transform, matlab

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