Space-Time correlation wind
 

I am trying to comprehend a problem about atmospheric turbulence to which some of you may share some opinions. I have implemented a divergence-free algorithm for synthetic inlent turbulence for LES and I obtain good results for anisiotropic fluctuating time histories in Eulerian description (Huang 2010). Now I want to somehow transfer these in Lagrangian coordinates for one time instance to have the time-history basically spread out along one line of x+dx (dx=Udt with Taylor's approximation, U beeing free stream velocity) which will give me as many points in longitudinal direction as number of time steps and U'(t) would be U'(x). Now I know Taylor's approximation works only for certain frequencies only and my question is - is this right to do? And if it is, do I have a constrain on the frequency spectrum that I am simulating? I hope it is not nonsense. Thanks!

To tell the truth, I am not sure of what you want to do ....could you better explain?

Thanks for your answer.
What I mean is: say you generate a signal U((x0,y0),t), t=i*dt with i=1:NSteps at one point with coordinates (x0,y0) with U_mean along x direction. Is it correct to say that the signal can be represented as U(x,(y0,t0)) having
at one time instance (t0) instantaneous velocity at points (x0,y0),(x1,y0),(x2,y0),(x3,y0).. (xi,y)as xi=i*U_mean*dt? In 2D this would mean a plane of a velocity field (ofc for Ux and Uy) along the mean wind direction for one time instance.

And one additional question: is anyone aware of a method computing divergence free velocity field including points along the mean velocity? Instead of points on a plane, you generate signals for points in a cube lets say. I guess
this would mean including a phase in the random signal generation.

I come from different background than CFD, and I know you can compute these type of stochastic multivariate multidimensional ergodic time histories but it does not satisfy the divergence free condition. Again, what I am asking it might be nonsense, but hopefully there is an answer.
Thanks :).

Therefore, what you are asking is if at any point x0,y0 in an inflow plane z=constant is generated a problem like:

du/dt + U du/dx=0

which has the 1D solution u(x,t)=u(x-Ut,0) where U is an average velocity in streamwise direction. Right?

I doubt you can use the frozen-turbulence Taylor hypothesis ...but it is not clear to me the case you are working on... if you have an inflow plane with velocity data for the LES simulation why do you need to assume arbitrarily the values along x?

Yep, it is the problem you described in 1D. So I guess you don't think its right to use the Taylor's hypothesis?

I am working with another method, not with FV - LES and trying to figure it out something which could be used for synthetic turbulence generation. Say how to compute random instantaneous turbulence field in a cube with certain statistical characteristics, rather than inflow conditions. Or even a 2D (x,y) plane in which
U_mean is along x.

I'll check it out using Lagrangian statistics, but I am quite new in here so I am not aware if the method works.

Thanks anyway!

I strongly suggest to follow the assessed technique presented in the literature. For example in this review

http://www.annualreviews.org/doi/abs...rnalCode=fluid