  Large-eddy simulations of the atmospheric boundary layer are often performed
using pseudo-spectral methods, which adopt a fringe-region approach to
introduce inflow boundary conditions. However, we notice that a standard
fringe-region technique excites spurious gravity waves when stratified
atmospheres are considered, therefore enhancing the amount of energy reflected
from the top of the domain and perturbing the velocity and pressure fields
downstream. In this work, we develop a new fringe-region method that imposes
the inflow conditions while limiting spurious effects on the surrounding flow.
This is achieved by locally damping the convective term in the vertical
momentum equation. We first apply the standard and wave-free fringe-region
techniques to two-dimensional inviscid-flow simulations subjected to 169
different atmospheric states. A similar study is performed on a
three-dimensional domain using a couple of atmospheric states. In all cases,
the new fringe-region technique outperforms the standard method, imposing the
inflow conditions with a minimal impact on the surrounding flow. Moreover, we
also investigate the performance of two already existing non-reflective upper
boundary conditions, that is a Rayleigh damping layer (RDL) and a radiation
condition (RC). Results highlight the importance of carefully tuning the RDL to
limit the distortion of the numerical solution. Also, we find that the tuned
RDL outperforms the RC in all cases. Finally, the tuned RDL together with the
wave-free fringe-region method are applied to an LES of a wind farm operating
in a conventionally neutral boundary layer, for which we measure a reflectivity
of only 0.75%.
