EDDY VISCOSITY FOR MULTILAYER FOLIAGE (M = 1)

Introduction

In Chapter 4 we derived the vertical distribution of atmospheric eddy viscosity within the crown of leafy plants for closed canopies (i.e., M =1) of homogeneous circular cylinders (Eq. 4.40, m = 1/2), and for a nearly conical spruce (Eq. 4.102, m = 1/2, Ψ = 1). These crowns were assumed to have homogeneous foliage density which is high areally and low volumetrically. Using the terminology of Horn (1971), such crowns are often referred to as being multilayer. To compare the effect of multilayer crown geometry on the turbulent mixing we first derive the equations for a hemispherical crown and for a pure conical crown, both again at M = 1.

Keeping in mind the requirement for compensation light intensity at the lowest leaf level at all radii, any crown which does not fill its circumscribing cylinder must be non-homogeneous in leaf area density, that is at = at (ξ, r). We will deal with this variation in an approximate fashion by first averaging radially. In other words, we assume at(ξ) to be homogeneous and isotropic in the radial direction and deal with slices, Δξ of the circumscribing cylinder which are each homogeneous over the full cylindrical crossection (cf. Fig. A.1b).