Spatial Variability of the Flow and Turbulence Within a Model Canopy

Abstract

The spatial variability of the mean flow and turbulence in and above a model canopy is investigated using three-dimensional laser Doppler velocimetry. The mean flow and turbulence are shown to be highly variable in space within the canopy but rapidly converge above the canopy. The coherent variations in the mean flow generate dispersive fluxes contributing almost a fifth to the total flux of momentum, and a greater contribution to the divergence of the flux, within the canopy. The higher-order turbulent statistics are more variable than the mean flow and often strongly correlated in space to variations in the mean flow. The implications of this microscale spatial variability for both field experiments and other laboratory experiments into canopy flow are discussed.

Appendix: Reduced Sampling to Approximate Spatial Averaging

The experiment discussed is the first in (and the reference for) a series of experiments considering canopy flows and turbulence in complex terrain. Sampling at 20 heights and at 80 positions around every location in a complex terrain experiment is too time consuming to be practical when the flow is inhomogeneous on scales larger than the element spacing. Furthermore, the form of the spatial average needs reconsideration if the spatial scales of the complex terrain (e.g. hill length, patch size) or those of the induced perturbations in the flow are comparable to the scale of the repeating canopy unit.

To circumvent the practical aspect of these issues a reduced sampling strategy has been sought, using the detailed spatial sampling experiment as its reference. In Fig. 8 we show the vertical profiles of the spatial average of six flow statistics ($\langle \overline{u}\rangle$, $\langle \overline{w}\rangle$, $\langle \overline{u'w'}\rangle$, $\textit{TKE}$, $\langle Sk_u\rangle$ and $\langle Sk_w\rangle$) and compare these to proxies obtained through two reduced sampling methodologies. The first proxy is a six-profile average where the individual profiles are spaced equi-distantly along the centre line of the canopy repeating unit (as indicated by the locations marked by $\times$ in Fig. 1). The second proxy is a four-profile average where, again, the individual profiles spaced equi-distantly on the centre line (marked by $+$ in Fig. 1). Positions marked by are common to both reduced sampling strategies. Alternative sampling and/or weighting options are possible; however, these line averages are the simplest (whilst maintaining symmetric sampling) and most practical options available to estimate the true spatial averages over this surface.

Fig. 8

Comparison of the spatially-averaged flow statistics as quantified through three sampling strategies. The upper panels show (left to right) the streamwise component of the mean wind vector, $\overline{u}$, the vertical component of the mean wind vector, $\overline{w}$, and the turbulent vertical flux of streamwise momentum, $\overline{u'w'}$. The lower panels show (left to right) the TKE, $Sk_u$ and $\textit{Sk}_w$. On each panel the solid line (with thin solid error bars) marks the full spatial average with the error bars marking the IQR of the 80 profile spatial sample. The triangle markers show the minimum and maximum values of the 80 profile spatial sample. The dash-dotted line marks the average of the six-profile average (positions as marked by $\times$ in Fig. 1) and the dashed line the four-profile average (positions as marked by $+$ in Fig. 1)

Figure 8 illustrates that both reduced sampling strategies are able to reproduce the broad character of these and many other (not shown) turbulent statistics. Both proxies are remarkably accurate as approximations to the full spatial average, usually lying within the inter-quartile range of the 80-profile spatial sample. The six-profile average only ranges outside the spatial IQR for $\langle \overline{w}\rangle$ at three heights; the four-profile average similarly only ranges outside the IQR for $\langle \overline{w}\rangle$ and $\langle Sk_u\rangle$ at isolated heights. For most applications this agreement between the full spatial average and either the four- or six-profile averages would be sufficient. The discrepancy on $\langle \overline{w}\rangle$ is important, however, as it implies that care will be required when interpreting this important aspect of any observed response of the mean flow to complex terrain, especially when placing in the context of theory (e.g. Harman and Finnigan 2013) or mass balance calculations. A reduced sampling strategy will also be unable to fully address questions concerning any systematic variation of the degree of spatial variability with position in complex terrain (see Moltchanov et al. 2011). Finally we note that the efficacy of these reduced sampling strategies for this surface does not imply that the same strategy applies to other each experimental surfaces. Ideally, if not practically possible, such sampling strategies need to be assessed experiment by experiment.