Predictability of Turbulent Flow in Street Canyons

Abstract

Although predictability is a subject of great importance in atmospheric modelling, there has been little research on urban boundary-layer flows. Here the predictability of street-canyon flow is examined numerically via large-eddy simulation of a unit-aspect-ratio canyon and neutrally stratified atmosphere. In spectral space there is indication of cascade-like behaviour away from the canyon at early times, but the error growth is essentially independent of scale inside the canyon; in physical space the error field is rather inhomogeneous and shows clear differences among the canyon, shear layer and inertial sublayer. The error growth is largely driven by the shear layer: errors generated above roof level are advected into the canyon while contributions from intermittent bursting and in situ development within the canyon play a relatively minor role. This work highlights differences between the predictability of urban flows and canonical turbulent flows and should be useful in developing modelling strategies for more realistic time-dependent urban flows.

Appendix

Here we compare our LES simulations with the wind-tunnel measurements of Brown et al. (2000). Their experimental set-up consisted of six identical street canyons of unit aspect ratio; data from the sixth canyon, which correspond to a fully developed turbulent flow, are used for the comparison.

The current LES shows generally good agreement with the experimental data and previous LES studies (Cui et al. 2004; Cheng and Liu 2011). Figure 11 shows vertical profiles of $\langle u\rangle$ normalized by $\langle U_\mathrm{s}\rangle$, where $\langle U_\mathrm{s}\rangle$ is the spanwise-averaged value of $u$ in the shear layer, $H\le z \le 1.5H$. The agreement is very good. Figure 12 compares second-order statistics, namely vertical profiles of TKE, $\langle q \rangle$, normalized by its average value in the shear layer. There is reasonable agreement except for the case $x=0.4H$. However, other LES simulations also show an anomalous peak in the TKE close to the roof level (Liu and Barth 2002; Cui et al. 2004).

Fig. 11

Comparison of normalized streamwise velocity profiles for the current LES (solid blue curve) and the experimental data of Brown et al. (2000) (green circles): a $x = -0.4H$, b $x = -0.25H$, c $x = 0H$, d $x = 0.25H$, e $x = 0.4H$

Fig. 12

Comparison of normalized TKE profiles for the current LES (solid blue curve) and the experimental data of Brown et al. (2000) (green circle) a $x = -0.4H$, b $x = -0.25H$, c $x = 0$, d $x = 0.25H$, e $x = 0.4H$