### Abstract:

The momentum flux by orographic gravity waves and the turbulent heat flux in wave-breaking regions are estimated from aircraft data from ALPEX. The fluxes on 6 March 1982 are controlled by low-level directional shear of the mean flow and associated critical level with wave stress decreasing toward the critical level. On 25 March 1982 a critical level does not occur and wave stress is approximately constant with height within the observational domain. The calculation of these fluxes appears to be the first direct comparison between simple models of gravity-wave momentum flux and observed atmospheric fluxes.
To develop a simple formulation of gravity wave drag for large-scale models, the gravity-wave stress super-saturation theory by Lindzen is generalized for the application to vertically varying mean flows. The wave momentum flux estimated from the generalized model agrees well with the observations for the two ALPEX days. For the 6 March case, the vertical divergence of wave momentum flux below the critical level is comparable to the Coriolis term in the momentum equation. The effective height of the surface topography required for the formulation of the wave momentum flux at the ground surface is estimated from the data and found to agree with the formulation of Stern and Pierrehumbert.
Wave breaking below the critical level leads to a convectively unstable region 10–20 km wide where well-organized turbulent-scale convection occurs. The magnitude of the observed upward turbulent heat flux can be approximated by using the flux gradient relationship in which the mixing length and modified shear are derived from the generalized wave-stress supersaturation condition. However, the net turbulent heat flux across the entire width of the mountain waves appears to be small due to cancellation between the upward heat flux in the convectively unstable region and the downward heat flux at the back of the wave. The spatially averaged wave-scale heat flux is also small for the data analyzed here.