Stable Stratified Flows over Isolated Obstacles: Results from MATERHORN Experiments

The distortion of stable density stratified flow by mountains is a key topic in mountain meteorology, since flow structures in the proximity of mountains determine the weather extremes, such as shear layer instabilities, vortex shedding and lee/internal wave breaking as well as accretion/dispersion of pollutants. With regard to the latter, the prediction of streamline that separates flow moving over the mountain summit from that goes around the mountain, which is called the dividing streamline, is of great practical interest. This work deals with quantification of the dividing streamline height.

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 H_S and verifying the existing and alternative formulae to estimate H_S. In particular, this work revisits the analytical solution H_S = 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 H_S in terms of Lambert-W functions, with alternative scaling for H_S. This explicit solution predicts L_b = u_* ⁄ N κ as the scaling variable for H_S, where L_b 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