Principal Length Scales in Second-Order Closure Models for Canopy Turbulence

Abstract

Triaxial sonic anemometer velocity measurements vertically arrayed at six levels within and above a pine forest were used to examine the performance of two second-order closure models put forth by Wilson and Shaw and by Wilson. Based on these measurements, it was demonstrated that Wilson?s model reproduced the longitudinal velocity standard deviation σu better than did Wilson and Shaw?s model. However, Wilson and Shaw?s model reproduced the measured mean velocity ?u? near the forest?atmosphere interface better than Wilson?s model did. The primary mechanisms responsible for discrepancies between modeled and measured ?u? and σu profiles were investigated. The conceptual formulations of these two closure models differ in the characteristic length scales and timescales used in the closure parameterizations of the mean turbulent kinetic energy dissipation rate term, the pressure?strain rate term, and the flux-transport term. These characteristic length scales were computed and compared with measured integral length scales inside the canopy. A discussion on how these length scales compare with the mixing layer analogy also is presented.