Mountain Waves Produced by a Stratified Shear Flow with a Boundary Layer. Part II: Form Drag, Wave Drag, and Transition from Downstream Sheltering to Upstream Blocking

Abstract

AbstractThe nonhydrostatic version of the mountain flow theory presented in Part I is detailed. In the near-neutral case, the surface pressure decreases when the flow crosses the mountain to balance an increase in surface friction along the ground. This produces a form drag that can be predicted qualitatively. When stratification increases, internal waves start to control the dynamics and the drag is due to upward-propagating mountain waves as in Part I. The reflected waves nevertheless add complexity to the transition. First, when stability increases, upward-propagating waves and reflected waves interact destructively and low-drag states occur. When stability increases further, the interaction becomes constructive and high-drag states are reached. In very stable cases, the reflected waves do not affect the drag much. Although the drag gives a reasonable estimate of the Reynolds stress, its sign and vertical profile are profoundly affected by stability. In the near-neutral case, the Reynolds stress in the flow is positive, with a maximum around the top of the inner layer, decelerating the large-scale flow in the inner layer and accelerating it above. In the more stable cases, on the contrary, the large-scale flow above the inner layer is decelerated as expected for dissipated mountain waves. The structure of the flow around the mountain is also strongly affected by stability: it is characterized by nonseparated sheltering in the near-neutral cases, by upstream blocking in the very stable case, and at intermediate stability by the presence of a strong but isolated wave crest immediately downstream of the ridge.