DNS of isotropic turbulence
 

Hi

I am working on to make a code to simulate isotropic turbulence with shock using DNS.

I read several papers wherein they say that the isotropic turbulence is given in the initial condition using the model given by E(k)=((k/k0)^4)*(Exp(-2*(k/k0)^2))

k0 refers to the peak value.

I tried to use this energy spectrum model and IFT to obtain the fluctuating component of velocity (as described in the book by Pope titled as Turbulent flows) but it is not working because this energy spectrum is product of velocity(k,t) and conjugate-velocity(k,t).

May I know how to set up this initial condition ?

Please help me

Thanks in advance.