We have already investigated stably stratified flows over a two-dimensional hill in a channel of finite depth by using a two-dimensional direct numerical simulation (DNS). Through these numerical studies, many findings about flows around the hill are clarified. In the present study, to investigate the flow around the hill under real atmospheric situations, we have performed a three-dimensional DNS. In these calculations, to avoid a troublesome boundary layer effect on the flow around the hill, a free-slip condition was imposed on the ground upstream of the hill and a no-slip condition was imposed on the hill surface and downstream of the hill, much as in the previous numerical studies. Attention is focused on the effect of stable stratifications on the three-dimensionality of unsteady separated and reattaching flow behind the hill for 0≤K≤1.3. The numerical results were compared with those obtained from two-dimensional calculations. For K=0 and 0.8, the flows around the hill between two-and three-dimensional calculations exhibit different behavior. This is mainly due to the appearance of the three-dimensionality in the spanwise direction. For K=1 and 1.3, the fully-developed flow fields between two-and three-dimensional calculations exhibit an almost same behavior near the hill, because a stationary lee wave with long wavelength appears downstream of the hill. In other words, for K=1 and 1.3, the flow variation in the spanwise direction is strongly suppressed by the stable stratification effect so that the flows around the hill become an almost two-dimensional flow in the x-and z-directions.

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