The atmospheric dynamics in an alpine valley under stable conditions (e.g. either at night or in winter) is mainly dominated by down-slope flows. These flows are triggered by horizontal temperature gradients due to the radiative cooling of the slopes on the mountain sides. Internal gravity waves must be generated by these down-slope flows if the atmosphere of the valley is stably-stratified. The waves may be trapped and possibly break, thereby inducing mixing within the valley despite the stable conditions. These points are addressed here, using numerical simulations with the ARPS code. Both an idealized version of the Chamonix valley and the actual topography of that valley are considered in order to investigate the features of the emitted internal gravity waves and to evaluate the potential of the wave dynamics in fluid mixing. We found that the wave characteristics are controlled by the valley dimensions and that the waves are therefore trapped. Ubiquitous wave breaking is observed in the atmosphere of the valley, implying that mixing should be quantified to evaluate its importance.