The goal of the present work is to further investigate the interaction between atmospheric boundary layer scale motions and the flow within and just above the vegetation canopy. What are the underlying mechanisms controlling the linkages between the atmospheric boundary layer scale coherent structures and those inside and just above the canopy? Focus is placed on non-linear interactions that can exist between the different scales of the organized motions as they provide a link between three or more frequencies depending on the order of the interaction.
The study uses high-resolution large eddy simulation (LES) of atmospheric flow interacting with a vegetation canopy in near-neutral conditions (Patton et al., 2012) to investigate one- and two-point analysis conducted using a spatial wavelet transform of the velocity field. Linear interactions are studied using classical auto- and cross-spectra, while bispectra and bicoherence are used to investigate the presence of non-linear coupling between scales. The auto-bispectrum of the signal u(x) (or U(k) in spectral space), an ensemble average of a product of three spectral components, indicates the statistical dependence between three scales at wave-numbers k1, k2, k3 which satisfy the condition k3 = k1+k2 (Kim & Powers, 1979). In the present work, the bispectral analysis is performed using wavelet decomposition to avoid some shortcomings of the Fourier analysis such as data windowing, periodicity, loss of localization in time and/or space of the turbulent motions under study (van Milligen et al 1995). Besides the already known linear phase relationships between velocities at two heights, the existence of non-linear interaction between large-scales and small-scales is shown. In particular, energetic large-scales of the longitudinal component present in the boundary-layer are shown to interact with the three velocity component in the canopy to generate smaller-scales inside the canopy. Finally, using the link existing between the auto-bispectrum and the skewness of a signal, the contribution of second-order scale interactions to the velocity skewness is shown.