AbstractNumerical simulations are performed to assess the influence of horizontal and vertical model resolution on the turbulent erosion of a cold‐air pool (CAP) by foehn winds in an Alpine valley near Innsbruck, Austria. Strong wind shear in the transition zone from the CAP to the overlying foehn generates turbulence by shear‐flow instability and contributes to the CAP erosion. The sensitivity of this process to grid resolution in the “grey zone” of turbulence is studied with the Weather Research and Forecasting model in large‐eddy simulation (LES) mode with a horizontal grid spacing of 200, 40, and 13.33 m and in mesoscale mode with a grid spacing of 1 km. Moreover, two different vertical resolutions are tested. The mesoscale simulation exhibits deficiencies in the CAP development and is neither able to resolve nor parametrize the effect of Kelvin–Helmholtz (K–H) instability. In contrast, the LES with the coarsest horizontal grid spacing begins to explicitly permit K–H instability, albeit individual K–H waves are not completely resolved, and thereby greatly improves the stability and wind profile of the foehn. Refining the LES grid spacing leads to a more explicit and realistic representation of turbulence, but surprisingly has little impact on mean quantities. An increase in the vertical resolution shows the greatest benefit in the turbulent upper part of the foehn jet, whereas an increase in the horizontal resolution improves the turbulence characteristics, especially at the foehn–CAP interface. However, spectral analysis indicates that even a horizontal grid spacing of 40 m does not fully capture the energy cascade in the inertial subrange. Eddies remain too large and foehn–CAP interaction is too vigorous compared with the simulation with 13.33 m grid spacing. Nevertheless, results illustrate the potential benefit of an𝒪(100 m) model resolution for improving numerical weather predictions in complex terrain.