Quadrant Analysis of the Reynolds Shear Stress in a Two-Height Canopy

• Published in: Flow, turbulence and combustion turbulence and combustion, 2023-06, Vol.111 (1), p.35-57
• Main Authors: Shig, Lior, Babin, Valery, Shnapp, Ron, Fattal, Eyal, Liberzon, Alex, Bohbot-Raviv, Yardena
• Format: Article
• Language: English
• Subjects: Automotive Engineering; Canopies; Engineering; Engineering Fluid Dynamics; Engineering Thermodynamics; Fluid- and Aerodynamics; Heat and Mass Transfer; Particle image velocimetry; Quadrants; Roughness; Shear stress; Velocity distribution
• ISSN: 1386-6184; 1573-1987
• DOI: 10.1007/s10494-023-00421-6

We study experimental data from a two-height roughness bed forming a top and bottom canopy sublayer of heights h and h /2, respectively. We focus on the double-averaged profiles of Reynolds stresses and the difference in contributions from sweep and ejection events, Δ S 0 . The two-height roughness adds to the typical canopy–air interface at height h another, previously unexplored, inner-canopy interface at height h /2. We apply particle image velocimetry within and above the two-height canopy and obtain the flow statistics over a representative repeating cell area. A quadrant analysis of the turbulent velocity fields is used to explore Δ S 0 . Our results show that, like in homogeneous dense canopies, ejections dominate the contribution to the measured shear stress ( Δ S 0 < 0 ) above 1.5 h , while sweeps dominate below ( Δ S 0 > 0 ). In the two-height canopy roughness, Δ S 0 peaks twice, right below the top and the bottom sublayer heights. We test how well the measured Δ S 0 can be reproduced by the complete and incomplete cumulant expansion methods (CEM and ICEM), and further test a simplified gradient diffusion approach to the third-order velocity moments in the ICEM (ICEM-GD). We demonstrate that CEM and ICEM reproduce the measured Δ S 0 fairly well above the canopy but over-estimate its values inside the canopy. It is also found that ICEM-GD captures the general shape of Δ S 0 at heights dominated by ejections and reproduces the two peaks inside the canopy. But it fails above the canopy in the range h < z < 1.5 h . This failure uncovers the counter-gradient nature of the turbulent energy and shear stress flux associated with dense canopy flows.