A streamfunction-vorticity formulation is used to explore the extent to which turbulent and turbulently inviscid solutions to the mean momentum balance explain the mean flow across forest edges and within cavities situated inside dense forested canopies. The turbulent solution is based on the mean momentum balance where first-order closure principles are used to model turbulent stresses. The turbulently inviscid solution retains all the key terms in the mean momentum balance but for the turbulent stress gradients. Both exit and entry versions of the forest edge problem are explored. The turbulent solution is found to describe sufficiently the bulk spatial patterns of the mean flow near the edge including signatures of different length scales reported in canopy transition studies. Next, the ‘clearing inside canopy’ or the so-called ‘cavity’ problem is solved for the inviscid and turbulent solutions and then compared against flume experiments. The inviscid solution describes the bulk flow dynamics in much of the zones within the cavity. In particular, the solution can capture the correct position of the bulk recirculation zone within the cavity, although with a weaker magnitude. The inviscid solution cannot capture the large vertical heterogeneity in the mean velocity above the canopy, as expected. These features are better captured via the first-order closure representation of the turbulent solution. Given the ability of this vorticity formulation to capture the mean pressure variations and the mean advective acceleration terms, it is ideal for exploring the distributions of scalars and roughness-induced flow adjustments on complex topography.