About Methods of Generating Inflow Turbulence!

Adonis

Hello, everyone:

Recently, I read a paper "Simulation of spatially evolving turbulence and the applicability of Talor's hypothesis in compressible flow" by Sangsan Lee, Sanjiva K. Lele, and Parviz Moin published in Phys. Fluids 4(7), July 1992. In this paper, the authors proposed a method to generate inflow turbulence. After perusing it for some time, I still don't understand this method. It is called a "random fluctuation" method. I have several questions to ask: 1. From physical space to spectral space, what kind of fourier transform did the authors make? Continuous time FT? Or Discrete Time FT? Or discrete FT?It seems that the authors assumes the x2 and x3 directions are periodical, thus k2 and k3 are just discrete numbers which are the multiples of 2*pi/L1 and 2*pi/L2 respectively where L2 and L3 are the lengths in x2 and x3 directions.

2.What's the base to assume k1=omega/U1, while omega is frequency and U1 is the inlet mean flow velocity.

3.What's the procedure to get fourier coefficients f(k2,k3,omega,t)=Sqrt(Eff(k2,k3,omega))*exp(i*phi( k2,k3,omega,t))? is f==0 when t<0?

4.If what I mentioned above is the case ,then It seems that just a limited number of terms were left to be inversely transformed to the physical space.

5.As I know the perturbation is in every direction, so u',v',w' coexist. But in this paper just a f'(x2,x3,t) is obtained at last. I wonder whether I should do some mente carlo sampling in the theta-phi space and then f'*cos(theta) to get u', f'*sin(theta)*sin(phi) to get v' and f'*sin(theta)*cos(phi) to get w'. In this way to get a isotropic turbulence.

6.I know there are some newly developed methods to generate inflow turbulence. However, is there a method which could be used to generate inflow random velocities when given the energy spectrum of these velocities in forms of wave number?