Eulerian and Lagrangian time scales of the turbulence above staggered arrays of cubical obstacles

Abstract

We present results from water-channel experiments on neutrally-stable turbulent flows over staggered arrays of cubical obstacles modelling idealised urban canopies. Attention is concentrated on the vertical profiles of the Eulerian (TE) and Lagrangian (TL) time scales of the turbulence above three canopies with different plan area fractions (λP = 0.1, 0.25 and 0.4). The results show that both the streamwise and vertical components of TL increase approximately linearly with height above the obstacles, supporting Raupach’s linear law. The comparisons with the Lagrangian time scales over canyon-type canopies in the skimming flow and wake interference regimes show that the staggered configuration of cubical obstacles increases the streamwise TL, while decreasing its vertical counterpart. A good agreement has also been found between the eddy viscosities (KT) estimated by applying Taylor’s theory and the classical first order closure relating the momentum flux to the velocity gradient. The results show that KT obeys Prandtl’s theory, particularly for λP = 0.25 and 0.4