Momentum absorption by vegetation

Abstract

Measurements were made in a wind‐tunnel of the drag on elements of a simply‐structured artificial crop, and of the wind profiles above and within the crop. Analysis demonstrates that the drag force on an element of such an array can be calculated from the profile of the turbulent shear flow within the array, using the known (and unmodified), wind‐tunnel value of the drag coefficient of the individual element; that the zero‐plane displacement (d) of an aerodynamically rough surface can be identified with the level of action of the drag on its elements; and that von Kármán's constant = 0.41 ± 0.03. The relation z0 = 0.36 (h – d) is suggested for the roughness parameter of vegetation of height h. Calculated values of the drag force, f, on unit column of a real stand of beans in the field, using individual‐element drag coefficients (Cd) and measured wind speeds, give f = 3.5 τ 0 where τ 0 is the downward momentum flux derived from the shape of the wind profile above. On the evidence of conclusion (i) and the dense and complex nature of the bean canopy, the factor 3.5 is attributed to mutual sheltering of neighbouring canopy elements rather than as evidence that the Cd – values are modified by turbulent shear flow. For the artificial crop, and for the real crop, recognition of the wind‐speed dependence of the individual‐element drag coefficients gives values of eddy viscosity, KM, almost constant in the height range h/3 < z ⩽ h and significantly larger than those found when constant drag coefficients are assumed. Constant KM within a crop canopy is consistent with the wind profile u(z)/u(h) = {1 + α(1 – z/h)}−2: an explicit expression is given for the parameter α.