Modelling the dispersion of a passive tracer from a continuous poit source in a steady thermally-driven slope wind

Thermally-driven slope winds regularly occur over simple inclines and mountain valley sidewalls under clear-sky, calm-wind synoptic situations. As typical features of mountainous terrains these flows contribute to the transport of momentum, heat, and mass, including pollutants and other passive tracers.

A simple model for the dispersion of a passive tracer in a thermally driven wind over a slope is presented. The source of the tracer is pointwise and the emission continuous. Dispersion results from the combination of along-slope advection by a pure anabatic/katabatic flow and slope-normal turbulent diffusion. The mean wind is modeled following Prandtl’s (1942) steady state solution assuming a K-closure for momentum and heat fluxes, where the eddy viscosity and diffusivity are constant. The advection-diffusion equation for the passive tracer is solved with a constant eddy diffusivity as well. Results are compared with those that are obtained neglecting the dynamical structure of the wind, i. e.  adopting a classical Gaussian model with uniform wind velocity. A sensitivity analysis of resulting concentrations on the height of the source above ground and on the wind strenght is proposed. Two different regimes are identified, depending on the relative position of the source and the velocity maximum. Moreover, mathematical relationships between the position and the intensity of the ground concentration field, and their dependence on environmental parameters are outlined.

Reference

Prandtl L. 1942. Führer durch die Strömungslehre, Chapter 5. Vieweg und Sohn: Braunschweig, Germany. [English translation: Prandtl L. 1952. Mountain and valley winds in stratified air, in Essentials of Fluid Dynamics: 422–425. Hafner Publishing Company: New York, NY]