Averaging procedures for flow within vegetation canopies

Abstract

Most one-dimensions models of Now within vegetation canopies are based on horizontaiIy averaged flow variables. This paper formalizes the horizontal averaging operation. Two averaging schemes are considered: pure horizontal averaging at a single instant, and time averaging followed by horizontal averaging. These schemes produce different forms for the mean and turbulent kinetic energy balances, and especially for the 'wake production' term describing the transfer of energy from large-scale motion to wake turbulence by form drag. The.differences are primarily due to the appearance, in the covariances produced by the second scheme, of dispersive components arising from the spatial correlation of time-averaged flow variables. The two schemes are shown to coincide if these dispersive fluxes vanish.

Turbulence in an almond orchard: Vertical variations in turbulent statistics

“…Verification of the existence of a dispersive term is important in modelling subcanopy horizontally-averaged flow and exchanges (see Raupach and Shaw, 1982). Presently, the dispersive term inside a plant canopy is assumed to equal zero, based on measurements made above a model canopy (Raupach etal., 1980(Raupach etal., , 1986.…”

“…Presently, the dispersive term inside a plant canopy is assumed to equal zero, based on measurements made above a model canopy (Raupach etal., 1980(Raupach etal., , 1986. The dispersive term arises from the temporal and spatial averaging of a turbulent flux (Raupach and Shaw, 1982):…”

“…Under steady-state conditions, these equations contain terms for advection, the source or sink strength of the entity of interest and the divergence of the turbulent transfer of the entity (e.g., Raupach and Shaw, 1982;Finnigan, 1985). Early theoretical representations of turbulent transfer in plant canopies relied on first-order closure or 'K-theory' models, where a flux is defined as the product of the vertical gradient of the entity and the eddy dfiusivity of that entity (K) (e.g., Brown and Covey, 1966).…”

Turbulence structure in a deciduous forest

“…In the past decade, many theoretical advances have been made, regarding the description of turbulence transfer in plant canopies, using higher-order closure and Lagrangian models (e.g., Shaw, 1976;Wilson and Shaw, 1977;Wilson et& 1981;Raupach and Shaw, 1982;Finnigan, 1985;Meyers and Paw U, 1986;Raupach, 1987). Unfortunately, little of the available within-canopy wind data is adequate to test and improve these models since much of these data consists only of measurements of mean scalar wind speed (e.g., Landsberg and James, 1971;Kalma and Stanhill, 1972).…”

Quantifying net ecosystem exchange by multilevel ecophysiological and turbulent transport models

“…The overbar and hÁi denote time and horizontal averaging respectively [34] and primes denote fluctuations from time averages; c is the scalar concentration, w is the vertical velocity and F c ¼ hw 0 c 0 i is the vertical turbulent flux.…”