The mass balance of mountain glaciers is of interest for several applications (e.g., local hydrology or climate projections), and turbulent fluxes can be an important contributor to glacier surface mass balance during strong melting events. The underlying complex terrain leads to spatial heterogeneity and non-stationarity of turbulent fluxes. Owing to the contribution of thermally induced flows and gravity waves, exchange mechanisms are fully three-dimensional, instead of only vertical. Additionally, glaciers have their own distinct microclimate, governed by a down-glacier katabatic wind, which protects the glacier ice and interacts with the surrounding flows on multiple scales. In this study, we perform large-eddy simulations with the Weather Research and Forecasting model at a horizontal grid spacing of 48 m to gain insight into the boundary-layer processes over an Alpine valley glacier, the Hintereisferner. We choose two case studies from the Hintereisferner experiment measurement campaign with different synoptic wind directions (southwest and northwest). Model evaluation with an array of eddy-covariance stations on the glacier tongue and surroundings reveals that the Weather Research and Forecasting model is able to simulate the general glacier boundary-layer structure. Under a southwesterly airflow, the down-glacier wind is supported by the synoptic wind parallel to the glacier axis, a stable boundary layer is present over the ice surface, and local processes govern the turbulence kinetic energy production. Under northwesterly airflow, a cross-glacier valley flow and a breaking gravity wave lead to strong turbulent mixing and to the subsequent erosion of the glacier boundary layer. Stationarity analysis of the sensible heat flux suggests non-stationary behaviour for both case study days, whereas non-stationarity is highest on the northwesterly day during the gravity-wave event. These results suggest that the synoptic wind direction Ivana Stiperski, Lindsey Nicholson, and Tobias Sauter contributed equally to this work.