Evaluation of the Turbulent Kinetic Energy Dissipation Rate Inside Canopies by Zero- and Level-Crossing Density Methods

Abstract

Inferring the vertical variation of the mean turbulent kinetic energy dissipation rate (ε) inside dense canopies remains a basic research problem to be confronted. Using detailed laser Doppler anemometry (LDA) measurements collected within a densely arrayed rod canopy, traditional and newly proposed methods to infer ε profiles are compared. The traditional methods for estimating ε at a given layer include isotropic relationships applied to the viscous dissipation scales that are resolved by LDA measurements, higher order structure function methods, and residuals of the turbulent kinetic energy budget in which production and transport terms are all independently inferred. The newly proposed method extends earlier approaches based on zero-crossing statistics, which were shown to be promising in a number of laboratory flows. The extension to account for an arbitrary threshold (hereafter referred to as the level-crossing method) instead of zero-crossing minimizes the effects of instrument noise on the inferred ε. While none of the ε methods employed here can be titled as ‘measured’, these methods differ in their underlying assumptions and simplifications. Above the canopy, where a balance between production and dissipation rate of turbulent kinetic energy is expected, the agreement among all the methods is reasonably good. In the lower-to-middle layers of the canopy, all the methods agree except for those based on a structure-function inference of ε. This departure can be attributed to the lack of a well-defined inertial subrange in these layers. In the upper canopy layers, the disagreements between the methods are largest. Even the higher order structure-function methods disagree with each other when ε is inferred from third- and fifth-order moments. However, for all layers within the canopy, the proposed zero- and threshold-crossing methods agree well with estimates of ε derived from the isotropic relationship applied to the viscous dissipation range. Finally, the advantages of introducing thresholds to minimize two types of instrument noises, additive and multiplicative, are briefly discussed.