Reliability of third-order moment parameterization for models of turbulent boundary layer over gentle topography

An analysis is made of the transport equation of Reynolds shear stress, written in a streamline coordinate system, starting from the fields of first-and second-order moments of wind velocity, measured in a terrain-following system over gentle topography, in order to verify the usual parameterizations of third-order moments. The equation is split into two parts: the first contains the terms which can be calculated directly from measurements, the second involves the pressure-velocity correlation considering the terms of rapid distortion, curvature and return to isotropy and the transport of triple velocity-correlation modelled assuming a flux-gradient approximation. Moreover, the error estimates associated with both parts have been computed using a Monte Carlo technique which takes into account the experimental errors. This analysis is performed on mind tunnel data over a gently shaped two-dimensional valley and hill. The comparison between the measured and modelled parts is good near the surface, whereas, at higher levels, where the pertubations induced by the topography are significant, there ape large zones generally characterized by streamlines with concave curvature in which the flux-gradient approximation used to compute the triple product correlation cannot be applied.