Flows over Isolated Mountains at Low Froude Numbers Driven by the Approach Wind and by Downslope Buoyancy Forces

Stably stratified flow winds over topography can be classified into two broad classes, flows dominated by the cooling of the mountain slope surface (e.g., downslope flows) and those under significant synoptic influence. While an extensive literature exists on both, few studies deal with the interaction between the two types of flows, which is indeed the common case found in nature and the topic of this study.

A scaling analysis is presented here, aimed at extending current approximated models of stratified flows around isolated mountains at low Froude numbers, so that they can also be valid when both types of flows exist.

Contributions of the approach flow and downslope flows are first characterized individually by means of local Froude numbers, F_H and F_S respectively, and their individual dynamics below and above the dividing streamline height is discussed and mathematically modelled. Thereafter, a simple criterion is proposed, based on the ratio R between the magnitudes U_a and U_s of the approach flow and downslope flow respectively.

It is shown that R ≈ U_a /(0.01 g H)^1/2. Thus, for typical low wind speed conditions over low mountains, R > 1 and the approach-flow dynamics dominates the flow, viz. downslope flows are generally less significant. In this case, the proposed model predicts the classical behavior described in several theoretical and experimental studies, with the flow going around the mountain in horizontal planes, except those streamlines sufficiently close to the summit that may rise and pass over. In the mid region of the mountain, stagnation points are generated at the leading face while a separated wake-flow region is found on the leeward side.

Instead, for large mountains (typically greater than 1000 m) R tends to be small, and the slope on the upper part of the mountain exceeds about 0.1, whence the buoyancy driven downslope flow undergoes a hydraulic-jump transition. It forms an accelerating flow above, and becomes a quasi-steady state gravity current flow down at the lower slope. In this situation the approach flow is weak compared to the downslope flow, but it is affected by horizontal entrainment into the downslope layer, which leads to a reduction in the size of the separated wake region.

As part of the Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) Program, an stand-alone atmospheric field study with smoke flow visualization was conducted at the US Army's Dugway Proving Ground (DPG), in Utah (USA). The study dealt with a small mountain {M1} with height H₁ of 80 m and width of about 1 km (where visualization was conducted), adjacent to the higher Granite Mountain {M2} with height H₂ ~ 800 m and 10 km long (with a sharply peaked ridge-line). For the flow over { M1}, where F_H ~ 0.5, the estimated value of R is about 2 and the observed usual dividing streamline behavior characteristic of low Froude number flow is consistent with the scaling. For {M2}, buoyancy-driven slope flows with velocity of 2-3 m/s exceeded the approach velocity, consistent with the calculated value of R of about 1/3. >