Wind Velocity Profile within Plant Communities

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Observed wind velocity profiles within crops are explained by using data on corn field by STOLLER and LEMON and on wheat field by PENMAN and LONG. An inter-relation of variation of turbulent diffusivity with height and wind velocity is obtained.Normalized velocity profiles in corn field are shown for several wind velocities at a crop surface in Fig. 1-1. From the evidence that these profiles are in good agreement with each other, we can see that wind velocity gradient is proportional to wind velocity. We havedu/dz=p(z)⋅u (1)p(z) is a function depending only on height, which results from the observed wind profiles within crop. If u=uH at crop surface z=H, u=uHe-∫HZpdZ (2)Normalized wind profiles in wheat field are also shown for moderate wind and for calm wind at crop surface in Fig. 2-1. On the figuer it is clear that the profile distinctively depends upon the surface wind velocity. If the relation between wind velocity gradient and wind velocity is expressed by the following equation for wheat field, du/dz=p(z, u)⋅u (3)p(z, u) is a function depending not only on height, but also on wind velocity. The values of p(z, u) at z=45cm are plotted against wind velocity in Fig. 2-2. If the difference of wind velocity between the two normalized profiles in Fig. 2-1 is neglected, the wind profile in wheat field can be also expressed as eq. (2) roughly.Eqs. (1) and (3) may be deduced from the following consideration. Momentum flux is expressed asτ=ρ⋅(1-F')⋅w'⋅u' (4)where F' is the horizontal per cent area of leaves and stalks per unit volume. Ifw'∝u and (u'2)1/2∝u (5)then τ=ρ⋅(1-F')⋅a⋅u2 (6)a is proportionality factor, assumed to be a function only of height. Kate of change in momentum flux is equal to the drag force offered by plants, that is, dτ/dz=ρ⋅C⋅F⋅u2 (7)whers F is total area of leaves and longitudial section of stalks per unit volume, a function of height, and C is drag coefficient of plant, depending on height. From eqs. (7) and (8).du/dz=1/2a(1-F')[C⋅F-d/dz{a⋅(1-F')}]⋅u (8)Putting 1/2a(1-F')[C⋅F-d/dZ{a⋅(1-F')}]=p (9)then du/dz=p⋅u (10)If C is assumed to be a function only of z, p is also a function only of z. Then we can obtain the expression (1). In order to explain the relation between p and u for wheat field as shown in Fig. 2-2, we assume C is to increase in phase with wind velocity. Then we can also, explaine the expression (3) for wheat field.If turbulent diffusivity K is defined byτ=ρ⋅(1-F')⋅K⋅du/dz (11)then K=a/pu (12)It is seen that the K-profile is decided by three profiles of a, p and u. If a is assumed to be a constant through layer, K-profile is roughly estimated with observed profiles of p and u by use of KH at a crop surface, where KH can be computed from a well-known formula of turbulent diffusivity above a crop field, that is K=k⋅u*⋅(z-d). Fig. 4 shows the K-profiles within a corn field by rough estimation.