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PIV Measurements in the Atmospheric Boundary Layer within and above a Mature Corn Canopy. Part II: Quadrant-Hole Analysis

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  • 1 Center for Environmental and Applied Fluid Mechanics, Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, Maryland
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Abstract

Quadrant-hole (Q-H) analysis is applied to PIV data acquired just within and above a mature corn canopy. The Reynolds shear stresses, transverse components of vorticity, as well as turbulence production and cascading part of dissipation rates are conditionally sampled in each quadrant, based on stress and vorticity magnitudes. The stresses are representative of large-scale events, while the vorticity is dominated by small-scale shear. Dissipation rates (cascading energy fluxes) are evaluated by fitting −5/3 slope lines to the conditionally sampled and averaged spatial energy spectra, while the Reynolds stresses, vorticity, and production rates are calculated directly from the spatial distributions of two velocity components. The results demonstrate that sweep (quadrant 4) and ejection (quadrant 2) events are the dominant contributors to the Reynolds shear stress, consistent with previous observations. The analysis also shows a strong correlation between magnitudes of dissipation rate and vorticity. The dissipation rates and vorticity magnitudes are higher in quadrants 1 and 4, that is, when the horizontal component of the fluctuating velocity is positive, peaking in quadrant 1. Both are weakly correlated with the Reynolds stresses except for rare quadrant 1 events. However, the more frequently occurring quadrant 4 events are the largest contributors to the dissipation rate. The production rate inherently increases with increasing stress magnitude, but lacks correlation with vorticity. Quadrants 2 and 4 contribute the most to production. However, the contribution of quadrant 1 events to negative production should not be ignored above canopy. The results show a strong disconnection between small-scale- and large-scale-dominated phenomena.

* Current affiliation: Faculty of Mechanical Engineering, Technion–IIT, Technion City, Haifa, Israel

Corresponding author address: J. Katz, Dept. of Mechanical Engineering, The Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218. Email: katz@poseidon.me.jhu.edu

Abstract

Quadrant-hole (Q-H) analysis is applied to PIV data acquired just within and above a mature corn canopy. The Reynolds shear stresses, transverse components of vorticity, as well as turbulence production and cascading part of dissipation rates are conditionally sampled in each quadrant, based on stress and vorticity magnitudes. The stresses are representative of large-scale events, while the vorticity is dominated by small-scale shear. Dissipation rates (cascading energy fluxes) are evaluated by fitting −5/3 slope lines to the conditionally sampled and averaged spatial energy spectra, while the Reynolds stresses, vorticity, and production rates are calculated directly from the spatial distributions of two velocity components. The results demonstrate that sweep (quadrant 4) and ejection (quadrant 2) events are the dominant contributors to the Reynolds shear stress, consistent with previous observations. The analysis also shows a strong correlation between magnitudes of dissipation rate and vorticity. The dissipation rates and vorticity magnitudes are higher in quadrants 1 and 4, that is, when the horizontal component of the fluctuating velocity is positive, peaking in quadrant 1. Both are weakly correlated with the Reynolds stresses except for rare quadrant 1 events. However, the more frequently occurring quadrant 4 events are the largest contributors to the dissipation rate. The production rate inherently increases with increasing stress magnitude, but lacks correlation with vorticity. Quadrants 2 and 4 contribute the most to production. However, the contribution of quadrant 1 events to negative production should not be ignored above canopy. The results show a strong disconnection between small-scale- and large-scale-dominated phenomena.

* Current affiliation: Faculty of Mechanical Engineering, Technion–IIT, Technion City, Haifa, Israel

Corresponding author address: J. Katz, Dept. of Mechanical Engineering, The Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218. Email: katz@poseidon.me.jhu.edu

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