[Fangcheng Shi]

Hi, guys!
I am carrying out a DNS on isotropic turbulence. I divide the process for setting the initial condition into two parts as followed:

Part 1: Non-dimensional variables. I use a specified spectrum for velocity which is divergence free:

By using this spectrum, I can get the velocities in wave-number domain, u(k), v(k) and w(k). Based on Fourier transform, the velocities in spatial domain, u(x), v(x) and w(x), are calculated. The non-dimensional pressure and density are set to be 1.

Part 2: Dimensional variables. The turbulent Mach number, Mat, and the Reynolds number based on Taylor length, Reλ, are given in this case. The reference values are calculated as followed:
1. I set 288.15K and 1m as reference temperature, T0, and reference length, L, respectively. The reference sound speed, c0, and reference viscosity coefficient, miu0, can be calculated.
2. Combining u(x), v(x), w(x) and Mat, I can get the Mach number , Ma. Then, the reference velocity, V0, is equal to Ma times c0.
3. Combining u(x), v(x), w(x) and Reλ, I can get the Reynolds number based on reference length, ReL. Then, the reference density can be calculated, based on ReL.
Using the above reference values, the dimensional velocities, pressure and density can be calculated.

I am not sure the above method is right or not?