Momentum transfer to plant canopies: Influence of structure and variable drag

Abstract

Theory is developed to assess momentum transfer to vegetation canopies displaying a ‘dynamic’ response to variations in the level of mean wind-speed. For a broad range of conditions it is demonstrated that αku h(h−d)/(u ∗h) = 1.11 ± 0.17 (95 % confidence interval) with: α, as the wind-speed extinction coefficient in the upper canopy; k, von Karman's constant; u h , the wind-speed at h, the canopy height; u ∗ , the friction velocity and d, the zero plane displacement. The above relationship together with background discussion lends support to the assumption that τ = K(d u ̄ /dz) can be a reasonable approximation in the upper canopy with: τ as the shear stress, K, the momentum diffusivity and (d u ̄ /dz) the velocity gradient. With the assumption of an exponential variation of wind-speed with height in the upper layers of a plant canopy and the use of a wind-speed dependent drag coefficient C d , theory is developed to describe the profiles of shear-stress and momentum diffusivity within canopies of contrasting vertical structure. In a uniform canopy it is shown that the wind-speed and diffusivity profiles are dissimilar except for the case of C d independent of wind-speed. For canopies with a vertical structure of Gaussian form, the momentum diffusivity in the upper layers may exceed the interface value, but decreases in lower layers. From analysis of wind profiles measured within and above a cotton canopy, it is shown that the effective drag coefficient of foliage elements increases with wind-speed. The diffusivity profiles within the canopy depend to first order upon the profiles of effective foliage area participating in momentum exchange. There are contrasting views as to how this may be determined for the actual foliage area profile.