Two-Point Correlation Analysis Of Neutrally Stratified Flow Within And Above A Forest From Large-Eddy Simulation

Abstract

Two-point space-time correlations of velocities, a passive scalar and static pressure are calculated using the resolvable flow fields computed by large-eddy simulation (LES) of neutrally stratified flow within and above a sparse forest. Zero-time-lag spatial auto-correlation contours in the streamwise-vertical cross-section for longitudinal and lateral velocities and for a scalar are tilted from the vertical in the downstream direction, as is typical in near-wall sheared flow. On the other hand, auto-correlations of vertical velocity and of static pressure are vertically coherent. Zero-time-lag spatial auto-correlations in the spanwise-vertical cross-section show no distinct tilt, and those for both longitudinal and vertical velocities demonstrate distinct negative side lobes in the middle forest and above, while longitudinal velocity in the subcrown trunk space is laterally in-phase. Static pressure perturbations appear to be spatially coherent in the spanwise direction at all heights, especially inside the forest. Near the forest floor, longitudinal velocity is found to be in-phase with static pressure perturbation and to be closely linked to the instantaneous streamwise pressure gradient, supporting a previous proposal that longitudinal velocity in this region is dominantly modulated by the pressure patterns associated with the coherent sweep/ejection events. Near treetop height, a lack of linkage between the pressure gradient and the local time derivative of the longitudinal velocity supports the hypothesis of advection dominating turbulent flow. The major phase characteristics of the two-point correlations essentially remained the same from four LES runs with different domain size and/or grid resolution. A larger LES domain yielded better agreement with field observations in a real forest on both the magnitudes of the correlations and the single-point integral time scales. A finer grid resolution in the LES led to a faster rate of decrease of correlation with increasing separation in space or time, as did the higher frequency fluctuations in the turbulent records from field measurements. Convective velocities estimated from the lagged two- point auto-correlations of the calculated flow fields were compared with similar calculations from wind-tunnel studies. At the canopy top, estimates from the correlation analyses agree with the trans- lation velocity estimated from instantaneous snapshots of a scalar microfront using both LES and field data. This translation velocity is somewhat higher than the local mean wind speed. Convective velocities estimated from lagged correlations increase with height above the canopy. It is suggested that an appropriate filtering procedure may be necessary to reduce the effects of small-scale random turbulence, as was reported in a study over an orchard canopy. The mean longitudinal velocity near the treetops is found to be more appropriate than the local mean longitudinal velocity at each height to link single-point integral time scales with directly calculated spatial integral streamwise length scales.