Amplitude modulation of the roughness sub-layer in an atmospheric surface layer
Résumé
Atmospheric surface layers developing above urban areas in windy conditions are of high interest since the high roughnessof the urban canopy primarily impacts the flow interactions with the ground (friction, heat exchange, pollutant dispersion).The wide range of scales at play and the fully non-linear dynamics of such a high Reynolds turbulence make its inves-tigation challenging at best. With access to increasing Reynolds numbers in direct numerical simulations, some studies[3] have brought more insight into the organisation of the flow within canopies modelled as distributions of aligned orstaggered cubes, but the findings remain fragmentary and largely geometry-dependent. Another more generalisable focusconcerns the outer part of the flow and how it interacts with the canopy dynamics. Recent experiments [7, 6] have high-lighted large-scale meandering "super-structures", shown to correlate well with the small scale dynamics directly abovethe canopy [2]. Such features could be similar to those occurring over smooth walls. Indeed, over the past ten years theworks of Marusic and co-workers [4, 5] conducted with smooth and sand-grain rough walls have shed light on the natureof the coupling between near-wall turbulence and the outer region. They have demonstrated that when the outer andinner layers are well separated in scales (for high enough Reynolds numbers), small scale turbulence intensity is stronglymodulated in amplitude and frequency by large-scale events, described as elongated Low- or High- Momentum Regions(labelled LMRs & HMRs) encompassing most of the boundary layer thickness. A predictive model making use of thatmechanism was developed [4]. To the authors’ knowledge, this approach has only been transposed once to the case ofhigh-roughness elements: last year by Anderson [1] in a channel flow using large-eddy simulations.The present contribution endeavours to identify amplitude modulations of the turbulent small scales in the roughnesssub-layer by LMRs and HMRs, based on high Reynolds number experiments (Reδ=u∗δ/ν= 25000) carried out in theLHEEA atmospheric wind-tunnel: the boundary layer of thicknessδ'1m develops over a 20m-long canopy of staggeredcubes (h= 50mm high). It is worth noting that while this amplitude modulation process has been extensively studiedthrough time-series – mostly hot-wire measurements – we here propose to make use of spatially extended data to evidencethe spatial signature of such an amplitude modulation. To that aim, wide-range Stereo Particle Image Velocimetry (SPIV)was performed in two horizontal planes, both in the roughness sub-layer and in the logarithmic region. SPIV fields canbe concatenated streamwise using Taylor’s hypothesis, hence making possible low-pass filtering both streamwise andspanwise. One obtains the triple decompositionu=u+uL+us, withuLthe large scale velocity andusthe remainingsmall scale velocity. This notably gives access to spatial maps of modulation parameter. LMRs & HMRs will alsobe pinpointed and delimited using thresholds in streamwise velocityuLso as to obtain probability density functions ofvarious quantities (e.g.swirling strength) in the frame of reference of every large scale event. Results will show the salientslightly phase-forward amplitude modulation of the small scales by the HMRs (Figure 1).