Experimental Investigation of Turbulent Momentum Transfer in a Neutral Boundary Layer over a Rough Surface

Abstract

The turbulent characteristics of the neutral boundary layer developing over rough surfaces are not well predicted with operational weather-forecasting models. The problem is attributed to inadequate mixing-length models, to the anisotropy of the flow and to a lack of controlled experimental data against which to validate numerical studies. Therefore, in order to address directly the modelling difficulties for the development of a neutral boundary layer over rough surfaces, and to investigate the turbulent momentum transfer of such a layer, a set of hydraulic flume experiments were carried out. In the experiments, the mean and turbulent quantities were measured by a particle image velocimetry (PIV) technique. The measured velocity variances and fluxes $${(\overline{{u_{i}^{\prime}}{u_{j}^{\prime}}})}$$ in longitudinal vertical planes allowed the vertical and longitudinal gradients (∂/∂z and ∂/∂x) of the mean and turbulent quantities (fluxes, variances and third-order moments) to be evaluated and the terms of the evolution equations for ∂e/∂t, $${\partial \overline{u^{\prime 2}}/\partial t}$$ , $${\partial \overline{w^{\prime 2}}/\partial t}$$ and $${\partial \overline{{u^{\prime}}{w^{\prime}}}/\partial t}$$ to be quantified, where e is the turbulent kinetic energy. The results show that the pressure-correlation terms allow the turbulent energy to be transferred equitably from $${\overline{{u^{\prime}}^{2}}}$$ to $${\overline{{w^{\prime}}^{2}}}$$ . It appears that the repartition between the constitutive terms of the budget of e, $${\overline{{u^{\prime}}^{2}}}$$ , $${\overline{{w^{\prime}}^{2}}}$$ and $${\overline{{u^{\prime}}{w^{\prime}}}}$$ is not significantly affected by the development of the rough neutral boundary layer. For the whole evolution, the transfers of energy are governed by the same terms that are also very similar to the smooth-wall case. The PIV measurements also allowed the spatial integral scales to be computed directly and to be compared with the dissipative and mixing length scales, which were also computed from the data.