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Empirical orthogonal function EOF analysis

Finnigan and Shaw [188] conducted an Empirical Orthogonal Function (EOF) analysis of an extensive wind tunnel data set obtained in a model wheat canopy. The same authors have recently performed an equivalent analysis based upon the output from the large-eddy simulation described above. [Pg.194]

EOF analysis in the context of turbulent flows was introduced by Lumley [381], It consists of finding the sequence of orthogonal eigenfunctions and associated eigenvalues that converges optimally fast when the variance of the turbulent field is represented [Pg.194]

Rij is the spatial covariance, where rx and ry are separations in the streamwise and spanwise directions. There is a denumerable infinity of solutions, / (eigenvectors), each associated with a real positive eigenvalue An. [Pg.195]

The spatial structure of the turbulent field is contained in the eigenvectors. We see that the eigenvectors are expanded as a Fourier series in the directions of flow homogeneity, x and y. The rate of convergence of the sequence of eigenvalues is a sensitive indicator of the presence and relative importance of coherent structures. EOF analysis provides not only an objective measure of the existence of dominant, spatially-extensive structure but, with minimal additional assumptions, allows us to deduce the 3-dimensional structure of the dominant eddies in their mature phase. [Pg.195]

The spatial structure derived by Finnigan and Shaw [188] matched measured time-height profiles of velocity in the xz plane and also revealed a double-roller vortex structure in the yz plane that was consistent with the mixing-layer hypothesis of canopy turbulence (Raupach et al., [530], The study was limited, however as only two velocity components were available from the wind tunnel study and the two-point measurements necessary for the EOF analysis were only performed in the y = 0 and x = 0 planes. [Pg.195]


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