Stratification effects on flow and bed topography in straight and curved erodible streams

Abstract

[1] In this paper, I investigate flow and suspended sediment transport in fluvial channels and develop an analytical theory to account for the effects of stratification on the flow field and on sediment concentration. The turbulence closure needed to account for density stratification is adapted from the model of Mellor and Yamada (1982). Solutions are found for both straight and constant curvature channels. In the latter case, in order to evaluate the secondary flow induced by curvature, I take advantage of the fact that the ratio of flow depth to radius of curvature is typically small in the field, which leads to a solution of the governing equations through an appropriate asymptotic expansion. Steady fully developed flow conditions in a bend of constant width are considered. Results show that buoyancy, besides affecting the vertical profiles of longitudinal velocity and concentration through a reduction of eddy viscosity and eddy diffusivity, enhances significantly the vertical distribution of lateral velocity. I then speculate that this stronger helical flow in river bends should lead to steeper lateral bed profiles with respect to the unstratified case. Such hypothesis is supported by an application of the Exner equation to the ideal case of a uniform and steady flow in constant curvature channels. It also appears that particle size crucially affects bed morphology as it affects the flux of suspended sediment under stratified conditions. The analytical model is validated by comparing predictions with laboratory investigations showing excellent agreement. It is shown that sediment‐laden flows experience an additional friction with respect to clear water flows. This can be accounted for by simply increasing the effective bed roughness. A relation for this additional contribution in terms of the near bed Richardson number is derived by fitting the results of the stratified model to experimental observations. The potential use of the present approach and further developments are finally discussed.