Modelling atmospheric flows over isolated orography: stable stratification and separation effects

Physical processes that underpin thermally-stratified flows in complex terrain still remain not completely understood. Atmospheric flow prediction models heavily rely on sub-grid parameterisation schemes for closure, and their performance for complex terrain remains inferior to that of flat terrain, especially under conditions of strong stratification close to the surface. Motivated by this and a number of other applications ranging from air quality to wind energy, in this paper we discuss an extension of an analytical, physics-based model of flow over hills with low slope to include significant interactions between external flow and up- and down-slope buoyancy driven flows. Starting from an approach flow and by considering how the relation between the surface stress and the pressure perturbation depends on the eddy viscosity profile (Hunt & Richards 1984), it is shown how the variation of near-surface winds over the slopes depend on stable stratification, and how this may lead to separation and stagnant conditions. The model is also extended to include buoyancy forces in the surface layers directed up and down the slopes that are comparable with inertial forces as well as buoyancy forces in the outer layers. In this case the flow displays intriguing dynamics that differs for the cases of heated and cooled mountain surfaces. The convergence and divergence of these near surface flows induce vertical motions in the stratified outer layer, which also affect the overall flow structure, notably the tendency for and the locations of flow separation. In the case of isolated mountains with moderate slope with an incident flow and stronger stable stratification (with Froude number less than 1), the theory developed predicts criteria for flow separation and stagnation. The flow below the dividing streamline height zd (below the top of the hill) passes round the hill and separates downwind, while above zd the flow passes over the 'cut-off' mountain as if it only exists above zd (Hunt et al. 2006). Extensive datasets based on multiple instrumentation deployed around an isolated mountain (Granite Peak) in Utah were obtained during the recent field campaigns of the MATERHORN project (www.nd.edu/~dynamics/materhorn), which are used here to validate the new theory developed. It is shown that the presented modelling approach is capable of predicting the effects of buoyancy driven flows above and below the dividing stream line as well as the effects of local flow variations over protrusions and valleys on the sides of realistic mountains.

References

Hunt, J.C.R. and Richards, K.J., 1984. “Stratified airflow over one or two hills” . Boundary Layer Meteorology 30, 223-259.

Hunt, J.C.R., Vilenski, G.G. and Johnson, E.R., 2006. “Stratified separated flow around a mountain with an inversion layer below the mountain top”. J. Fluid Mechanics.556, 105-119.