Katabatic winds are very frequent but poorly understood or simulated over steep slopes. This study focuses on a katabatic jet above a steep alpine slope. We assess the buoyancy terms in both the turbulence kinetic energy (TKE) and the Reynolds shear-stress budget equations. We specifically focus on the contribution of the slope-normal and along-slope turbulent sensible heat fluxes to these terms. Four levels of measurements below and above the maximum wind-speed height enable analysis of the buoyancy effect along the vertical profile as follow: (i) buoyancy tends to destroy TKE, as expected in stable conditions, and the turbulent momentum flux in the inner-layer region of the jet below the maximum wind-speed height $$z_j$$ ; (ii) results also suggest buoyancy contributes to the production of TKE in the outer-layer shear region of the jet (well above $$z_j$$ ) while consumption of the turbulent momentum flux is observed in the same region; (iii) In the region around the maximum wind speed where mechanical shear production is marginal, buoyancy tends to destroy TKE and our results suggest it tends to increase the momentum flux. The present study also provides an analytical condition for the limit between production and consumption of the turbulent momentum flux due to buoyancy as a function of the slope angle, similar to the condition already proposed for TKE. We reintroduce the stress Richardson number, which is the equivalent of the flux Richardson number for the Reynolds shear-stress budget. We point out that the flux Richardson number and the stress Richardson number are complementary stability parameters for characterizing the katabatic flow apart from the region around the maximum wind-speed height.