Application of Time Series Models to the Spectral Analysis of Irregular Turbulence Data

Most existing algorithms for the spectral analysis of irregularly sampled random processes can estimate the spectral density until frequencies up to the mean data rate or somewhat higher. A new time series method extended that frequency range with a factor thousand or more, for certain processes. Two requirements have been found for the new algorithm to give useful results. Firstly, at least about ten closest pairs of neighboring irregular observations should have a distance that is less than the minimum resampling distance that has to be used for the discrete-time frequency range. Secondly, a rather low order time series model should be appropriate to describe the character of the data. The consequences and importance of this second demand are studied for irregular turbulence observations with narrow spectral details. Low order models are estimated from equidistant hot-wire observations and from irregularly sampled LDA (Laser Doppler Anemometer) data, obtained from the same turbulence process. The irregular data are resampled with the nearest neighbor method, both with and without slotting. Apart from the usual bias contributions of resampling irregular data, LDA data can give an additional spectral bias if the instantaneous sampling rate is correlated to the actual magnitude of the turbulent velocity.