Scale wind field series to theoretical standard deviation

[f.perrone2]

Hi everybody,

I have got a theoretical question regarding the turbulent wind field.
Generally the wind field stemms from a Gaussian process with 0 mean value and unitary standard deviation.

Now, because of being a random process, as well as integrating the power spectrum for only a limited range of frequency/wave numbers and because of smoothing effects due to the discretization of the space, the "rough" time series (those coming out from the fft) will not exactly match the expected standard deviations. Thus, a scaling process is usually required in order to get

std_u = 1.0;
std_v = (0.7 - 0.8)*std_u;
std_w = 0.5*std_w.

The question is: what are the implications drawn by such a scaling factor? Is it reasonable the all the u-components have exactly std = 1 (of course the same for v and w components respecting the formula above)? What do we lose in terms of correlation in time and space?

I thank you all in advance for any support.

Best regards,
Francesco Perrone

[Morten]

Hi Francesco,


I know this kind of scaling is used by load engineers to match the turbulence intensity of simulated series with prescribed values. The reason why statistics of the WEng simulated time series deviate from their target values is their limited duration. There are both systematic and random effects on the statistics, just as when you sample atmospheric turbulence with an anemometer.


If you use individual scaling for the three velocity components, you will create divergence in the simulated turbulence field. You will have to ask a load engineer, but I guess that is only a minor problem. Length scales and correlations should not be affected by scaling the variances.


I am more worried about your suggestion for the ratios of the standard deviations as they are valid for flat terrain only. It would be more correct to use the variances listed in the WEng ‘site view’ which include terrain effects. They are calculated by the smooth target spectra, not random simulations.


Regards,
Morten

[f.perrone2]

Hi Morten,

I am myself a load engineer, and at least to me "faking" time series sounds as a rather important issue: especially if I wanna benchmark the correctness of my simulated loads with those coming from measurement campaigns.

I do understand that, for WT certification needs, TI should reproduce the input and expected values, but I still have the feeling that simulations should crunch the gap with reality and not the other way around.

Besides, as you properly pointed out, in reality wind does not exactly match the theoretical spectra, but it will always be filtered in the high frequency range.

Btw, since I'm in the process of coding my own wind modeler, I will introduce kinda flag for scaling wind time series or not.

Finally, would you mind to pinpoint some conspicous bibliographic reference accounting for the terrain effects on wind components standard deviation? What I deduce from your post is that WEng embodies this effect within the theoretical spectra wind field stemms from.

I thank a lot for the poignant hints you gave me.

Kindest regards,
Francesco

[Morten]

Hi Francesco,


I recomend the following references:


- J Mann (1998) Wind field simulation, Prob. Eng. Mech. vol. 13, p. 269-282

- J Mann (2000) The spectral velocity tensor in moderately complex terrain, J. Wind Eng. Ind. Aerodyn. vol. 88, p. 581–602

- J C Kaimal and J J Finnigan (1994) Atmospheric Boundary Layer Flows, Oxford University Press.


Mann (1998) explains the WEng turbulence model for flat terrain and Mann (2000) explains extensions for terrain effects. I suggest that you start by reading Mann (2000).


Kaimal & Finnigan (1994) is my favorite text book on micrometeorology. It explains the physics, but unfortunately you will not find a simple formula for terrain effects on standard deviations of velocity perturbations.


With best regards,
Morten