Application of the Karhunen-Loeve expansion to the analysis of large-scaleturbulent motions in the atmospheric boundary layer

The method of empirical orthogonal functions as applied to the analysis of turbulence, namely, simultaneous time series of fluctuations of meteorologi cal parameters measured at different heights is discussed. The capabilities of the method are illustrated by the example of time series of wind speed and direction fluctuations measured in the lower 300-m layer from a high-ri se meteorological tower in Obninsk. It is shown that the first eigenvector corresponds to general accelerations-decelerations and rotations of the ent ire flow, and the second eigenvector, to longitudinal or transverse eddies with their centers lying in the middle of the layer. The projections of the process onto these eigenvectors are principal in the low-frequency variabi lity of the flow. Cross-spectral analysis and wavelet transforms are employ ed to find the relations between the elements of the processes and to ident ify some features of the realizations in question.