Wind-tunnel study of the interaction between coherent structures in the flow over an urban-like terrain

During the past few years, large-scale motions (LSM) in turbulent boundary layers over smooth-walls have received renewed attention from the research community. Common features of the LSMs found in wall-bounded flows are that they consist in elongated low- and high-speed regions, the length of which scale with the boundary-layer depth (d) and can reach several times d, they populate the log- and outer layer, they are animated by a meandering motion in the horizontal plane (Hutchins & Marusic, JFM, 2007) and interact with near-wall turbulence through an amplitude-modulation mechanism (Mathis et al, JFM, 2009). The finding of this last characteristics relies on the clear spectral separation between large-scale motions and the near-wall turbulence found in high Reynolds number flows. At the same time, attention has been devoted to the structure of boundary layer flows developing over rough walls, at laboratory scales or in the framework of atmospheric flows over urban or vegetation canopies, demonstrating similarities between flows over smooth and rough wall. In particular, the presence of streaky patterns of low- and high-speed regions, of ejection and sweep motions associated to the hairpin model and the organization of hairpin vortices in packets have been evidenced (Jimenez, Ann Rev Fluid Mech, 2004; Finnigan et al, JFM, 2009; Inagaki & Kanda, BLM, 2010; Takimoto et al, BLM, 2011). The results obtained in flows over rough-walls suggest that, in spite of the strong disturbance of the flow at the wall, LSMs exist and interact with the canopy flow in a similar manner as in smooth wall boundary layers. However, in configurations representative of flows over urban canopies, it is likely that the clear spectral separation between large-scale motions and the near-wall turbulence found in high Reynolds number canonical boundary layers may not exist, the obstacles generating structures of scales much larger than the typical length-scales observed in near-smooth-wall turbulence. Building upon these recent results, the aim of the present work is to investigate the dynamical link between the large-scale structures existing in the turbulent boundary layer developing over a cubical roughness array and the roughness sublayer above the canopy. This study, conducted in an atmospheric wind tunnel, is based on non-time resolved stereoscopic PIV measurements performed in a vertical plane (3h wide, 5h high, h being the cube height) aligned with the longitudinal axis in a flow configuration representative of the atmospheric boundary layer (ABL) developing over an urban canopy. The rough wall is composed of a staggered array of cubes of height of h = 50 mm distributed on the wind tunnel floor over a total length of 22 m and a width of 2 m, with a plan area density of 25%. The experiments have been performed with three free-stream velocity Uref = 2.9, 5.8 and 9.1 m/s (h+ = h.u*/ν = 650, 1300, 2000). 4000 three-component velocity fields have been recorded in each case at a frequency of 5Hz. The proper orthogonal decomposition (POD) of the velocity is used to perform the extraction of the coherent structures in the logarithmic region. The previous analysis conducted by Perret & Rivet (8th Turbulent Shear Flow Phenomena Symp, 2013) by using standard POD of the PIV snapshot dataset found that the first POD mode corresponded to the occurrence above the canopy of a large-scale high-speed downward (or low-speed upward) motion, being a major contributor to the velocity variance and the shear-stress in that region. This first POD mode was found to leave a strong imprint in the temporal correlation with an integral time scale of several d/Uref, confirming that this mode corresponds to large-scale coherent structures of the flow developing above the canopy. However, due to the limited longitudinal extent of the measurement region, the POD decomposition was not able to capture the complete the full dynamics of the large-scale structures and its interaction with the near-canopy flow. In the present study, a modification of the POD kernel is introduced to include time-delayed information and thereby capture the streamwise elongated character of the large-scale structures existing in the log-region. The obtained set of modes is then used via the extended POD procedure (Borée, Exp Fluids, 2003) to extract the part of the canopy flow that is the most correlated with the identified large-scale eddies. The velocity field in the canopy region is therefore separated into two distinct components: a component correlated with the large-scale and an uncorrelated component, e.g into a large- and a small-scale component. Using this decomposition of the canopy flow, the influence of the ABL flow onto the roughness sublayer is analyzed via the computation of spatio-temporal second- and third-order correlations between the contribution of the large-scale structures of the ABL and the smaller-scale flow in the canopy region. It is shown that, in agreement with the literature, the near-canopy flow is directly influenced by passing inclined large-scales of low- or high-momentum from the log-layer, mechanism that leaves an imprint into the classical two-point temporal correlation. Analysis of third-order correlations shows that the roughness sublayer flow is under the influence of the ABL structure through a mechanism resembling an amplitude-modulation type phenomena. The ultimate goal of this ongoing study is to identify the mechanisms of interaction between the ABL and the canopy flow and to contribute to the development of wall or canopy model.