Setting Up a Large-Eddy Simulation to Focus on the Atmospheric Surface Layer

Abstract

Large-eddy simulations (LES) above forests and cities typically constrain the simulation domain to the first 10–20% of the Atmospheric Boundary Layer (ABL), aiming to represent the finer details of the roughness elements and sublayer. These simulations are also commonly driven by a constant pressure gradient term in the streamwise direction and zero stress at the top, resulting in an unrealistic fast decay of the total stress profile. In this study, we investigate five LES setups, including pressure and/or top-shear driven flows with and without the Coriolis force, with the aim of identifying which option best represents turbulence profiles in the atmospheric surface layer (ASL). We show that flows driven solely by pressure not only result in a fast-decaying stress profile, but also in lower velocity variances and higher velocity skewnesses. Top-shear driven flows, on the other hand, better replicate ASL statistics. Overall, we recommend, and provide setup guidance for, simulation designs that include both a large scale pressure forcing and a non-zero stress and scalar flux at the top of the domain, and that also represent the Coriolis force. Such setups retain all the forces used in typical full ABL cases and result in the best match of the profiles of various statistical moments.

Appendices

Appendix 1: Grid Convergence of the Full ABL Simulation

Below we compare profiles of up to third-order statistics in the ABL obtained using a low resolution (LR) and a high-resolution (HR) domain. The respective number of grid points are $144\times 144\times 108$ (LR) and $288\times 288\times 216$ (HR), while the remaining characteristics of the simulation are identical.

Appendix 2

For reference, this section compares cases 2 and 6 from Table 1 with the inclusion of a canopy. The same details described in Sect. 2 are used, where now an additional drag term $D_i$ is added to the momentum Eq. (2) to represent a sink of momentum imposed by the trees,

$$\begin{aligned} D_i = - C_D a(z) {\widetilde{u}}_{i} |{\widetilde{u}}_{i}|. \end{aligned}$$

(6)

$C_D$ is the drag coefficient ($=0.25$ in the present paper) and a(z) is the leaf-area density profile, where the leaf-area index LAI =$\int _{0}^{h} a(z) dz=2$ in the present study. A source term $S_c(z)$, representing scalar q emitted by the canopy, is additionally included in Eq. (3). The same leaf-area density and scalar source profiles from Su et al. (1998) were used in our simulations, and were represented by the lowest 10 grid points of the domain. With $N_z=108$, we thus have $L_z/h=$10.8 and $h\approx$13 m.

Fig. 6

Same as Fig. 1, where two canopy flows are considered. Simulation S + U$^G$ + C + F contains top stress, pressure gradient (geostrophic forcing), Coriolis and constant flux at the top, while the second case is solely driven by a streamwise pressure term. The same resolution was used for both simulations ($144\times 144\times 108$ grid points). Continuous black line represents the canopy top, while dashed black line represents the height above which a sharp gradient is observed when a top stress drives the flow

Fig. 7

Same as Fig. 2, where two canopy flows are considered. Simulation S + U$^G$ + C + F contains top stress, pressure gradient (geostrophic forcing), Coriolis and constant flux at the top, while the second case is solely driven by a streamwise pressure term. The same resolution was used for both simulations ($144\times 144\times 108$ grid points). Continuous black line represents the canopy top, while dashed black line represents the height above which a sharp gradient is observed when a top stress drives the flow

To ensure a constant scalar flux in the case S + $U^G$ + C + F, the subgrid scale flux component at the top includes both surface and canopy flux contributions, i.e.,

$$\begin{aligned} \pi _\textrm{top} = \pi _\textrm{bottom} + \sum _{z=0}^{z=h} S_c. \end{aligned}$$

(7)

Finally, the turbulent scales $u_*$ and $q_*$ are computed above the canopy. Comparison of both simulations is shown in Figs. 6 and 7. As with the simulations over flat terrain in the body of the paper, significant differences can be noted with the S + $U^G$ + C + F case displaying more realistic vertical patterns.