An EOF Analysis of the Structure of the Large-Eddy Motion in a Plant Canopy

Almost all objective statistical analyses of turbulence structure in plant canopies have been confined to time series measured at a point. These have furnished detailed information on the temporal structure of canopy turbulence but its spatial structure has been inferred largely from the much more subjective process of compositing time-height cross sections of variables measured on single towers. Here we describe an Empirical Orthogonal Function analysis (EOF) of a three dimensional, 2-point velocity covariance field, measured in a wind tunnel. The rate of convergence of the EOF eigenvalue spectrum has been used as an objective test for the presence of distinct large turbulent structures.

We found that in the roughness sublayer (2h>z>0), where h is the canopy height, the sequence converged much more rapidly than in the lower surface layer (6h>z>0), 75% of the total velocity variance being captured by the first three of 42 eigenmodes. The analysis was extended to three dimensions, where over 50% of the variance and most of the spatial structure of the covariance fields were captured by an even smaller fraction of the total number of eigenmodes.

With some relatively weak additional assumptions we were able to construct the velocity field of a 'characteristic eddy' a typical member of the ensemble of large coherent structures. It consisted of a pair of counter-rotating streamwise vortices centred above the canopy. The sense of rotation of the vortex pair was opposite to that found in the wall region of boundary layers but matched that found in plane mixing layers, lending some support to the proposition of Raupach et al (1996) that the turbulent structure of the roughness sub-layer is modeled on the plane mixing layer rather than the boundary layer.

A strong gust or sweep motion generated between the vortices was responsible for most of the shear stress carried by the large eddies. The region of significant transport of momentum by the characteristic eddy is much smaller than the region of coherence of the eddy's velocity field and the characteristic eddy is responsible for between 50% and 75% of the total momentum flux in the canopy. The velocity field of the eddy on the x-z plane between the two vortices closely matches velocity fields other workers have deduced from composited time-height cross sections of the velocity field.

References . Raupach, M.R., Finnigan, J.J., Brunet, Y. 1996. Coherent eddies and turbulence in vegetation canopies: the mixing layer analogy. Boundary-Layer Meteorol., 78, 351-382.