Subelement Form-Drag Parameterization in Rough-Bed Flows

Abstract

Spatial averaging of the Reynolds-averaged Navier–Stokes equations gives the double-averaged Navier–Stokes equations, for which boundary drag appears naturally and explicitly in momentum conservation equations. Increasing use of the double-averaged equations, e.g., for relating flows to three-dimensional bed roughness, for evaluation of profiles of flow stresses and velocities in ecologically significant regions below roughness tops, and for modeling purposes, requires parameterization of boundary drag at subelement scales. Based on seven flows over repeated square-rib roughness and ten flows over repeated fixed simulated sand waves, with measured velocities and bed pressures, expressions for form-drag coefficient CD =f (elevation below roughness top, relative roughness submergence, roughness steepness) are obtained for each of the two-dimensional roughness types. Using these equations, form drag variation with elevation below roughness tops can be calculated using either the double average of the square ...