Turbulent kinetic energy budget in the boundary layer developing over an urban-like rough wall using PIV

Abstract

In the present work, a boundary layer developing over a rough-wall consisting of staggered cubes with a plan area packing density λp = 25% is studied within the wind tunnel using Particle Image Velocimetry (PIV) to investigate the Turbulent Kinetic Energy (TKE) budget. To access the full TKE budget, an estimation of the dissipation (ε) using both the transport equation of the resolved-scale kinetic energy and Large-Eddy (LE) PIV models based on the use of a subgrid-scale model following the methodology used in large-eddy simulations is employed. A low-pass filter, larger than the Taylor microscale, is applied to the data prior to the computation of the velocity gradients ensuring a clear cutoff in the inertial range where the models are valid. The presence of the cube roughness elements has a significant influence on the TKE budget due to the region of strong shear that develops over the cubes. The shear layer is shown to produce and dissipate energy, as well as transport energy through advection, turbulent transport, and pressure transport. The recirculation region that forms through the interaction of the shear layer and the canopy layer, which is the region below the height of the cube roughness, creates rapid longitudinal evolution of the mean flow thereby inducing weak production. Finally, through stochastic estimation of the conditional average, it is shown that localized regions of backscatter (energy transfer from unresolved to resolved scales) and forward scatter (energy transfer from resolved to unresolved scales) occur as a result of coherent vortical structures.