Stratified Flow Past a Hill: Dividing Streamline Concept Revisited

The Sheppard formula (Q J R Meteorol Soc 82:528–529, 1956) for the dividing streamline height Hs assumes a uniform velocity U∞ and a constant buoyancy frequency N for the approach flow towards a mountain of height h, and takes the form Hs/ h= (1 - F) , where F= U∞/ Nh. We extend this solution to a logarithmic approach-velocity profile with constant N. An analytical solution is obtained for Hs/ h in terms of Lambert-W functions, which also suggests alternative scaling for Hs/ h. A ‘modified’ logarithmic velocity profile is proposed for stably stratified atmospheric boundary-layer flows. A field experiment designed to observe Hs is described, which utilized instrumentation from the spring field campaign of the Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) Program. Multiple releases of smoke at F≈ 0.3 –0.4 support the new formulation, notwithstanding the limited success of experiments due to logistical constraints. No dividing streamline is discerned for F≈ 10 , since, if present, it is too close to the foothill. Flow separation and vortex shedding is observed in this case. The proposed modified logarithmic profile is in reasonable agreement with experimental observations.