Energy spectrum to physical domain
 

i am wondering can i get real velocity from energy spectrum function (frequency domain), which can have a form like sinusoid function?
Can i set temporal difference equal to zero in the autocorrection function?
In this way i think i can only get the mean value of u_i square. or is there any other way?
Thanks

is your spectrum derived from a temporal signal? In general, you can construct a velocity field in space with a prescribed spectrum, however you need to prescribe other condition in order to construct all the Fourier coefficients

Thanks. I havent start the experiment yet. I think i will get temporal signal instead of spatial. And can you please tell me what other conditions do I need?

since your velocity field is v(x,t) = Sum_p,q,r Cpqr(t) exp (i k .x ) you need to know the real and imaginary part of your Fourier coefficients