Estimating the friction velocity in stable boundary layers

A new method is proposed for the calculation of friction velocity in stable turbulent boundary layer flows, where gravity waves propagation is possible. The method is used in the upstream mean velocity profile proposed by Weng (1997a), that allows for the propagation of gravity waves, in substitution of the log-linear profile, based on the Monin-Obukhov similarity theory. Theoretical predictions are obtained with the theoretical linear model of Hunt et al. (1988a), using the Weng's velocity profile and a modification suggested by Hunt et al. (1988b) to include stability effects in the calculation of flows over hills. Numerical simulations are carried out with a non-hydrostatic micro-mesoscale two-dimensional numerical model (FLEX), developed by Argain et al. (2008). The theoretical results are compared with the numerical predictions and with observations made by Coppin et al. (1994). The comparisons of the theoretical with numerical and experimental results show a considerable improvement in the behaviour of the theoretical model when the friction velocity is calculated using the method proposed here.