DYNAMICS OF A TURBULENT BOUNDARY LAYER OVER CUBICAL ROUGHNESS ELEMENTS: INSIGHT FROM PIV MEASUREMENTS AND POD ANALYSIS

Abstract

The dynamics of the turbulent boundary layer developing over a cube array is analysed using stereoscopic PIV measurements performed in an atmospheric wind tunnel. The longitudinal component u of the velocity is analysed via the snapshot POD. It is first demonstrated that the first POD mode of u corresponds to large-scale elongated coherent structures of lowor high-speed which are non-negligible contributors to the shear-stress and the turbulent kinetic energy. Their relationship with the smaller scales of the flow is investigated via the computation of oneor two-point third order statistics and is shown to be of non-linear nature. INTRODUCTION During the past few years, very-large-scale motions (VLSMs) in turbulent boundary layers over smooth-walls have received renewed attention from the research community. Both numerical and experimental studies have highlighted their influence on the near-wall turbulence and their contribution to the kinetic energy and Reynolds shear-stress in different type of wall-bounded flows such as pipe flows (Monty et al., 2007), channel flows (del Alamo & Jimenez, 2003), laboratory boundary layers (Marusic & Hutchins, 2008) and atmospheric boundary layers (Guala et al., 2011). Common features of the VLSMs found in wall-bounded flows are that they consist in elongated lowand high-speed regions (Hutchins & Marusic, 2007), the length of which scales with outer-length variable (δ ) and can reach several times δ (Guala et al., 2011), they populate the log and outer layer, they are animated by a meandering motion in the horizontal plane (Hutchins & Marusic, 2007) and interact with near-wall turbulence through an amplitudemodulation mechanism (Mathis et al., 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 (Guala et al., 2011; Mathis et al., 2009). At the same time, attention has been devoted to the structure of boundary layer flows developing over rough walls, at laboratory scales (see Jimenez 2004 for a review) or in the framework of atmospheric flows over urban or vegetation canopies (Finnigan et al., 2009; Inagaki & Kanda, 2010; Takimoto et al., 2011), demonstrating similarities between flows over smooth and rough wall. In particular, the presence of streaky patterns of lowand high-speed regions, of ejection and sweep motions associated to the hairpin model and the organization of hairpin vortices in packets have been evidenced. Recently, Inagaki & Kanda (2010) showed the presence in the atmospheric flow developing over an array of cubes of very-large-scale elongated lowspeed regions, with some sub-structures included in these streaks. These structures, educed by filtering in the spanwise direction the time-series from a spanwise array of 15 sonic anemometers, share some common features with the above mentionned VLSMs evidenced in smooth wall flows and support the observations of Drobinski et al. (2004) revealing streaky structures within the atmospheric surface layer. In their study of the atmospheric turbulence over a cubical array arranged in a square pattern, Takimoto et al. (2011) showed the intermittent presence of large-scale upward motions across the whole vertical cross-section of the gap between two cubes correlated with the presence of lowspeed streaks in the boundary layer. The same correlation between the boundary layer and flow penetrations and ejections inside and from the canopy has been found by Perret & Savory (2013) in their wind tunnel study of the flow over a street canyon model. From their particle image velocimetry (PIV) measurements performed over a cube array, Rivet et al. (2012) evidenced the presence of vortex clusters intermittently shed off the roughness elements and convected in the boundary layer. They also showed that the dynamics of the associated shear-layers developing from the top of the obstacles is correlated with the occurence of lowand high-speed events in the log-region. The results obtained in flows over rough-walls suggest that, in spite of