|Di Silvio, Giampaolo|
Submitted to: Journal of Hydraulic Engineering
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 6/11/2010
Publication Date: 2/1/2011
Citation: Fasolato, G., Ronco, P., Langendoen, E.J., Di Silvio, G. 2011. Validity of uniform flow hypothesis in one-dimensional morphodynamic models. Journal of Hydraulic Engineering. 137(2):183-195. Interpretive Summary: Computer models of the adjustment of channel bed profile and bed-material composition that are based on the complete set of one-dimensional flow and sediment transport equations require a large computational effort and detail of channel geometry and bed materials. Simplified models can be derived by omitting certain terms from the equations. Guidelines under which flow and sediment transport conditions these simplified models can be used, are however not available. A widely used simplification is uniform flow, where it is assumed that bed slope and water surface slope are parallel. This simplification significantly reduces computational effort and required data on channel geometry. Through rigorous mathematical and numerical analysis criteria have been established that determine the spatial and temporal scales that can be studied when using the uniform-flow assumption. The analysis shows that spatial and temporal detail that can be resolved increases when flow velocity and sediment concentration increase. The uniform-flow assumption is therefore best applied to small mountain rivers. Applications for large watersheds are possible, but are limited to simulations over larger spatial and temporal intervals.
Technical Abstract: The local-uniform-flow (LUF) hypothesis is a simplification of the governing equations describing river morphodynamics, which is needed to determine the evolution of the bed profile and bed-material composition in the case of large time and space scales. This paper presents a rigorous analysis of the full one-dimensional river hydrodynamic and morphodynamic mathematical model and its LUF approximation. The analysis establishes two criteria to assess the validity of the LUF hypothesis: (1) a criterion for rivers in equilibrium and (2) a criterion for evolving rivers (i.e., in non-equilibrium). The first criterion is based on the concept of the morphological box. Variations of the river bed longer than the box length are adequately reproduced by the LUF hypothesis, whereas only spatially averaged values are resolved within the box. The second criterion is based on the concept of an evolution window. Temporal variations represented by sinusoidal waves with wave periods larger than the evolution window can be adequately reproduced by the LUF hypothesis, whereas variations with shorter periods are averaged within this window. To limit the error introduced by the LUF hypothesis the minimum size of the morphological box and the evolution window increases when the Froude number decreases. Further, the minimum size of the evolution window increases for decreasing sediment concentration and increasing mixing layer thickness (i.e., for larger bed forms). The LUF hypothesis is therefore best applied to small mountain rivers for which both the minimum size of the morphological box and the evolution window is relatively small, so that spatial and temporal variations can be resolved in more detail. Applications using the LUF hypothesis for large watersheds (including the lowland portion of the fluvial network) are possible, but are limited to simulations over larger spatial and temporal intervals.