Non-linear interaction between the lower-atmosphere and vegetation canopy flows

The importance of coherent eddies in the turbulence structure of flows over and in vegetation canopies is now well-admitted (Finnigan, 2000; Finnigan et al., 2009). These eddies have been shown to play an important role in turbulence production and in the transfer of momentum and scalars between the canopy layers and aloft. Through ejection (upward transport of slow moving air) and sweeps (downward transport of fast moving air), these coherent structures leave their imprint on both the skewness of the longitudinal velocity (Su) and the skewness of the vertical velocity (Sw). In near-neutral conditions, negative values of Sw (and positive values of Su) correspond to vigorous shear-induced sweeps of short duration (Finnigan 1979; Shaw et al., 1983; Leclerc et al., 1991). As pointed out by Watanabe (2004), these canopy-eddies are always under the influence of the atmospheric boundary layer scale coherent structures, which are of larger scales (in time and space). In the near-surface region of the neutral atmospheric boundary-layer, such large-scales have been found to consist in elongated regions of low- or high- speed streamwise velocity (see for instance Lin et al. 1996; Drobinski et al. 2004). The influence of the large-scales on the canopy turbulence can consist of a simple superimposition of large-wavenumber turbulence over smaller-scale (canopy related) turbulence. This type of mechanism is similar to that found by Chougule et al. (2012) who showed that, at given spectral frequencies, a phase relationship can exist between velocity components measured at different heights in the atmospheric boundary-layer. The existence of this linear relationship can be viewed as the effect of a large-scale eddy detected at two different height but with a time-lag depending on how it has been stretched and deformed by the wind shear.

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.