The mass balance of mountain glaciers is of interest for several applications (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. Due 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 WRF model with dx=48 m to gain insight on the boundary-layer processes over an Alpine valley glacier, the Hintereisferner (HEF). We choose two case studies from a measurement campaign (August 2018) with different synoptic wind directions (South-West and North-West). Model evaluation with an array of eddy-covariance stations on the glacier tongue and surroundings reveals that WRF is able to simulate the general glacier boundary-layer structure. Under southwesterly airflow, the down-glacier wind is supported by the South-Western synoptic wind direction, 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 strong turbulent mixing and to the subsequent erosion of the glacier boundary layer. Stationarity analyses of the sensible heat flux suggest non-stationary behaviour for both case study days, while non-stationarity is highest on the NW day during the gravity-wave event. These results suggest that the synoptic wind direction has, in addition to upstream topography and the atmospheric stability, a strong impact on whether a local glacier boundary layer can form or not, influencing whether a glacier is able to maintain its own microclimate.