The flow over wind turbines immersed in a half-channel configuration is studied using large-eddy simulation with the aim of determining the sensitivity of the results to the vertical domain height (which is equal to the boundary layer height). For the same surface roughness, differences in the vertical domain height lead to differences in the turbulence intensity and the vertical shear stress incident on the turbine. This affects the turbulence fluctuations in the wake, the height of the internal boundary layer, and the wake expansion coefficient. The differences in the wake expansion coefficient lead to non-negligible differences in the mean velocity beyond five diameters downstream of the turbine. The sensitivity to the vertical domain size is larger for a boundary layer over a rougher surface. We propose guidelines for selecting the vertical domain size, depending on the quantity of interest and on the aim of the numerical study. © 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.