Surface-layer scaling for thermally-driven up-slope flows

Sloping terrain of any inclination favour the development, under daytime heating, of thermally-driven organised flows, displaying peculiar boundary layer structures, and eventually triggering the development of atmospheric convection.

The ubiquitous occurrence of variously tilted surfaces - from gently sloping plains top steep cliffs, or valley sidewalls – makes the understanding of such flows of utmost importance in view of the appropriate forecasting of the associated boundary layer transport processes. These may display quite a different structure from those, much better known, occurring over horizontal plain surfaces [1]. Also, they display a highly conceptual relevance, as the simplest, prototypal situations for many other thermally driven-flows over complex terrain [2]. Finally, with the increasing resolution of operational model runs, a more accurate parameterisation of these processes is required for a realistic simulation of their development in space and time.   

However, up-slope flows have received so far much less attention than downslope flows originating from cooling, which have been extensively investigated by means of theoretically analysis, field experiments and numerical simulations. Even the theoretical analysis on their onset and structure are rather limited (e.g. to gentle slopes: [3]). Analytical solutions, such as Prandtl’s [4], rely on severely restrictive assumptions (parallel flow, constant or slowly varying eddy viscosity and diffusivity, along-slope invariance of the ambient factors). Extensions of such solutions relaxing those restrictions are still limited [5]. Even extensive high-resolution numerical simulations are rare, and not much progress has been made after Schumann’s [6]. Further insight, especially on the conditions for flow separation, have been gained through laboratory-scale simulations [7], which however are limited to moderate flow situations.

The proposed presentation offers a comprehensive overview of our present understanding of these phenomena, ideas for scaling laws appropriate for these winds, and challenging open questions for future research.

References

1. Rotach, M. W., and D. Zardi, 2007: On the boundary layer structure over complex terrain: Key findings from MAP. Quart. J. Roy. Meteor. Soc., 133, 937-948.
2. Zardi, D. and C. D. Whiteman, 2013: Diurnal Mountain Wind Systems, Chapter 2 in “Mountain weather research and forecasting – Recent progress and current challenges” (Chow, F. K., S. F. J. De Wekker, and B. Snyder Editors), Springer Atmospheric Sciences, Springer, Berlin.
3. Hunt, J. C. R., H. J. S. Fernando, and M. Princevac, 2003: Unsteady thermally driven flows on gentle slopes. J. Atmos. Sci., 60, 2169-2182.
4. Prandtl L. 1942. Führer durch die strömungslehre, ch. V. Vieweg und Sohn [English translation: Prandtl, L., 1952: Mountain and Valley Winds in Stratified Air, in Essentials of Fluid Dynamics, Hafner Publishing Company, pp.422-425].
5. Zammett, R. J., and A. C. Fowler, 2007: Katabatic winds on ice sheets: A refinement of the Prandtl model. J. Atmos. Sci., 64, 2707–2716.
6. Schumann U. 1990. Large-eddy simulation of the up-slope boundary layer. Quart. J. Roy. Meteor. Soc. 116, 637–670.
7. Hilel Goldshmid, R.; Bardoel, S.L.; Hocut, C.M.; Zhong, Q.; Liberzon, D.; Fernando, H.J.S. Separation of Upslope Flow over a Plateau. Atmosphere 2018, 9, 165.