Stratified Flows over and around Long Dynamically Tall Mountain Ridges

Uniformly stratified flows approaching long and dynamically tall ridges develop two distinct flow components over disparate time scales. The fluid upstream and below a “blocking level” is stagnant in the limit of an infinite ridge and flows around the sides when the ridge extent is finite. The streamwise half-width of the obstacle at the blocking level arises as a natural inner length scale for the flow, while the excursion time over this half-width is an associated short time scale for the streamwise flow evolution. Over a longer time scale, low-level horizontal flow splitting leads to the establishment of an upstream layerwise potential flow beneath the blocking level. We demonstrate through numerical experiments that for sufficiently long ridges, crest control and streamwise asymmetry are seen on both the short and long time scales. On the short time scale, upstream blocking is established quickly and the flow is well described as a purely infinite-ridge overflow. Over the long time scale associated with flow splitting, low-level flow escapes around the sides, but the overflow continues to be hydraulically controlled and streamwise asymmetric in the neighborhood of the crest. We quantify this late-time overflow by estimating its volumetric transport and then briefly demonstrate how this approach can be extended to predict the overflow across nonuniform ridge shapes.