Derivation of canopy resistance in turbulent flow from first-order closure models

Abstract

Quantification of roughness effects on free surface flows is unquestionably necessary when describing water and material transport within ecosystems. The conventional hydrodynamic resistance formula empirically shows that the Darcy-Weisbach friction factor f~(r/hw)1/3 describes the energy loss of flowing water caused by small-scale roughness elements characterized by size r ( < < hw), where hw is the water depth. When the roughness obstacle size becomes large (but