Turbulence intensity values at individual wind grid points are lower than the value set in the interface.
Every so often, users of the Mann turbulence model notice a discrepancy between the TI value they have entered in the user interface, and the TI value found from analysing a wind time series at a grid point in the wind field. Such a discrepancy is to be expected when using the Mann model. This article explains why.
Mann turbulence
The Mann model is a self-consistent model of the entire three dimensional wind field. All three turbulence components are generated simultaneously and the method accounts for correlation between components (in particular the correlation between vertical and longitudinal turbulence caused by Reynolds stress is captured – which the Kaimal model does not do).
Within the Mann model there is no requirement for the spectral distribution or TI values from the time series at an individual grid point to match that of the whole wind field. This means that variance plotted for an individual grid point will not necessarily lead to the same TI as the whole wind field. However, when averaged over many grid points, the variance will approach a constant value. This will be a slightly lower value than the Kaimal value due to the loss of high frequency variance by the Mann model.
If we compare the Mann model with the Kaimal model, we find that for Kaimal wind files the spectral statistics of the turbulence are satisfied at each individual grid point. This means that for Kaimal wind files, consistent variance numbers for time series from each individual grid point are seen and the TI value for each grid point will match the overall TI value for the whole wind field.
The loss of high frequency variance in the Mann model arises from the limitation on the number of Fast Fourier Transform (FFT) points underlying the turbulence generation. The number of FFT points determines the minimum wavelength in a given direction. Restriction on the maximum number of FFT points limits resolution and results in deficiencies in the high frequency turbulence generation. Mann argued that this is realistic, because it represents averaging of the turbulence over finite volumes of space which is appropriate for practical engineering applications.
It should always be noted that with any turbulence model, using hub wind speed statistics may result in a mismatch in turbulence statistics compared to the specified conditions if there is no wind file grid point at the exact hub location. In this situation the wind data at the hub location is generated by interpolating between the surrounding points.