A flow visualization experiment was conducted around a semi-isolated axisymmetric hill at the Granite Mountain Atmospheric Sciences Test Bed (GMAST) located at the US Army's Dugway Proving Ground (DPG). Multiple releases of smoke were made at F ≈ 0.3 – 0.4, where F = U / N h, U is the approach flow velocity, N the buoyancy frequency and h the height of the obstacle. The experiment, which capitalized on a suite of instrumentation used in the spring field campaign of the Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) Program, was aimed at observing the dividing streamline height HS and verifying the existing and alternative formulae to estimate HS. In particular, this work revisits the analytical solution HS = h (1 – F) of Sheppard (1956) and relaxes the assumption of uniform approach velocity assumed in deriving the above. A modified logarithmic velocity profile for stably stratified flows is proposed, and an expression is derived to predict the corresponding dividing streamline height. An analytical solution is thus obtained for HS in terms of Lambert-W functions, with alternative scaling for HS. This explicit solution predicts Lb = u* ⁄ N κ as the scaling variable for HS, where Lb being the canonical buoyancy length scale.
A laboratory experiment conducted in a stratified water channel is used to investigate the balance of kinetic and potential energy of fluid parcels along streamlines surrounding the obstacle, flow stagnation, energy dissipation and wave breaking.
This research was funded by Office of Naval Research Award # N00014-11-1-0709, Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) Program