An analytical model for daily-periodic slope winds. Part 2: Solutions

This article presents an analytical model for the diurnal cycle of slope-normal profiles of potential temperature and wind speed characterizing thermally driven slope winds, generated by a daily-periodic surface energy budget. The model extends the solution proposed by Zardi and Serafin, originally formulated for a pure sinusoidal surface forcing temperature. To account for the asymmetric features characterizing the daytime and nighttime phases, a full Fourier series expansion is derived, the coefficients and phases of which are prescribed from the surface energy budget driven by the daily-periodic radiation model described in Part 1 of the present work. The model is applicable for any slope angle (0(degrees) <= alpha <= 90(degrees)) and orientation, at any latitude and elevation (up to 2500 m), and for all seasons. Despite some inherent limitations, the most remarkable being the absence of moist processes and latent heat fluxes, the model captures most key features of daily-periodic slope wind systems, in particular the asymmetry between daytime and nighttime phases. Moreover, it allows exploration of the sensitivity of these flows to the various factors concurring in their development, and offers a basis for more realistic analytical solutions for slope winds.