Large Eddy Simulation Study of Atmospheric Boundary Layer Flow over an Abrupt Rough-to-Smooth Surface Roughness Transition

Abstract

The atmospheric boundary layer flow downstream of an abrupt rough-to-smooth surface roughness transition is studied using large eddy simulations (LES) for a range of surface roughness ratios. Standard wall models assume horizontal homogeneity and are inapplicable for heterogeneous surfaces. Two heterogeneous-surface wall models are evaluated, one based on a local application of similarity theory using a twice-filtered velocity field (BZ model) and another based on a local friction-velocity obtained by blending the upstream and downstream profiles (APA model). The wall shear stress and the turbulence intensity (TI) are sensitive to the wall model while the mean streamwise velocity and the total shear stress (TSS) are less sensitive. The APA model is more accurate than the BZ model on comparison to previous experiments. The wall shear stress obtained using the APA wall model is sensitive to the ratio of the equilibrium and the internal boundary layer (IBL) heights, while other statistics are not. The IBL height is insensitive to the turbulent quantity (TSS or TI) on which it is based. Several analytical relations for the IBL height are evaluated using the LES data. Two models are found to be accurate for different roughness ratios while one model is reasonable over the full range investigated. A phenomenological model is developed for the TI downstream of the roughness jump using a weighted average of the upstream and far-downstream profiles. The model yields reasonable predictions for all roughness ratios investigated.

Appendix 1: Grid Convergence

Sensitivity of different statistics of the ABL flow to the grid resolution used in the LES are studied first. Besides using two wall models and three different grids, the results are also compared with experimental data of Chamorro and Porté-Agel (2009) wherever available. The surface roughness values are $z_{01}=0.5$ mm and $z_{02}=z_{01}/83.3$. The APA model is utilized with $\alpha =0.027$.

Fig. 20

Streamwise evolution of wall shear stress after the abrupt surface roughness transition for different grid sizes for $m=83.3$ and $z_{01}=0.5$ mm using a BZ and b APA wall models. Experimental results are from Chamorro and Porté-Agel (2009)

Fig. 21

Vertical profiles of the mean streamwise velocity at different downstream locations after the abrupt surface roughness transition for different grid sizes for $m=83.3$ and $z_{01}=0.5$ mm using a BZ and b APA wall models; Log Law for streamwise velocity corresponding to the upstream region is ${\overline{u}}=(u_{*1}/ \kappa ) \log {(z/z_{01})}$

Fig. 22

Vertical profiles of a TSS and b TI at different downstream locations after the roughness jump using different grid sizes and the APA wall model for $m=83.3$ and $z_{01}=0.5$ mm

Figure 20 shows the surface shear stress after the change in surface roughness for different grid sizes using the BZ and APA wall models for $m=83.3$. Here, the shear stress at the bottom wall downstream of the surface roughness jump ($\tau$) is normalized by the surface shear stress upstream of the jump ($\tau _0$). The LES data show appreciable change in magnitude when compared between the $128\times 32\times 32$ and $192\times 64\times 64$ grid cases. An additional simulation for grid size of $240\times 80\times 80$ is also compared and it is observed that there is little change in magnitude when compared with the $192\times 64\times 64$ grid.

The temporally and spanwise averaged streamwise velocities at two downstream locations ($x/\delta =0.5,\;1.0$) after the roughness jump are presented in Fig. 21. These profiles are almost insensitive to the grid resolution for both models. Small differences are seen close to the top of the domain, where the velocity profiles are seen to agree better with the upstream logarithmic law, Eq. (1), with increasing grid resolution. Closer to the bottom boundary, the velocity accelerates due to the reduced surface roughness. This acceleration is the same for all grids for the BZ as well as APA wall models.

The total shear stress (TSS) and the streamwise turbulence intensity (TI) are shown at two downstream locations for the APA wall model in Fig. 22. The TI increases when going from the coarsest to the intermediate grid, but is unchanged over the two finest grids employed here. This indicates that a computational grid with $240\times 80\times 80$ points is sufficient to obtain grid-independent results. Consequently, all simulations reported in Sect. 3 utilize these many grid points.