Observations of the dependence of the dimensionless wind speed gradient φm as a function of the Monin–Obukhov stability parameter z/Lo under strong stability diverge from results of large-eddy simulation (LES) modelling. A kinetic energy budget analysis indicates that it is likely caused by violations of the assumptions of stationarity and/or homogeneity of turbulence in the field experiments rather than in imperfections of the LES. This confirms the validity of the widely used linear approximation for φm not only at weak to moderate stability, but also under strong stability. The new interpretation of the linear approximation of φm is given in terms of turbulent scales, which gives hope for its applicability to the free atmosphere as well.