The scalar field over a canopy covered hill

3 The scalar field over a canopy covered hill 

The mean scalar concentration c and its eddy flux / are divided into background and hill-induced perturbations as follows, 

The background scalar field in the canopy CB(z) is the solution of the one-dimensional mass conservation equation, 

We parameterize the background scalar flux FB(z) using the same mixing length model that we used for momentum, 

As was the case for momentum also, the use of a mixing length is merely a convenient heuristic in the mean flow but is physically correct when used to model the scalar perturbations caused by the hill. Using (5.5), (5.20) and (5.21), the mean canopy mass conservation equation (5.19) becomes, 

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THE SCALAR FIELD OVER A CANOPY COVERED HILL... 

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