We extend the micropolar fluid theory of Hayakawa and Mitarai, et al. [PRL 88, 174301 (2002)] to dense, relatively shallow flows of spherical grains down an inclined plane on which spherical bumps have been affixed. We update the model of Louge [PRE 67, 061303 (2003)], and show the role played by couple stresses in establishing the solid volume fraction in the core of the flow.