Mathematical modelling of bedload transport over partially dry areas

The paper describes the derivation of a depth-averaged, two-dimensional form of the sediment balance equation, suitable to study the morphodynamics of movable sediment beds even when the flow depth attains values comparable to bed irregularities. This equation is derived by double-averaging in time and in space the instantaneous three-dimensional sediment balance equation. For this, a proper phase function is introduced, which depends on the statistics of bed topography. The structure of the macroscopic volumetric sediment discharge vector resulting from the averaging procedure is discussed for the case of dominant bedload transport. The theoretical framework developed within the paper sets the stage for a proper parametrization of the physical processes acting at spatial scales smaller than those usually resolved by depthaveraged numerical models.