Numerical Estimations of Horizontal Advection inside Canopies

Abstract

Local advection of scalar quantities such as heat, moisture, or carbon dioxide occurs not only above inhomogeneous surfaces but also within roughness elements on these surfaces. A two-dimensional advection?diffusion equation is applied to examine the fractionation of scalar exchange into horizontal advection within a canopy and vertical turbulent eddy transport at the canopy top. Simulations were executed with combinations of various wind speeds, eddy diffusivities, canopy heights, and source strengths. The results show that the vertical turbulent fluxes at the canopy top increase along the fetch and approach a limit at some downstream distance. The horizontal advection in the canopy is maximum at the edge of canopy and decreases exponentially along the fetch. All cases have the same features, except the absolute quantities depend on the environmental conditions. When the horizontal axis is normalized by using the dimensionless variable xK/uh2, horizontal diffusion is negligible, and the upwind concentration profile is constant, the curves of horizontal advection and vertical flux collapse into single, unique lines, respectively (x is the horizontal distance from the canopy edge, K is the eddy diffusivity, u is the wind speed, and h is the canopy height). The ratios of horizontal advection to the vertical turbulent flux also collapse into one universal curve when plotted against the dimensionless variable xK/uh2, irrespective of source strength. The ratio R shows a power-law relation to the dimensionless distance [R = a(xK/uh2)?b, where a and b are constant].