Global stability of concentration profiles in uniform sediment-laden channel flow

Abstract

A famous quote of Landau and Lifschitz reads: "Yet not every solution of the equations of motion, even if it is exact, can actually occur in nature. The flows that occur in nature must not only obey the equations of fluid dynamics, but must also be stable". In this paper we examine the global stability of concentration profiles of fine sediment in uniform channel flow. We integrate the fully transient equations with a conservative numerical scheme to obtain the asymptotic states for a wide range of initial conditions. It is found that the steady state solutions are stable and are therefore likely to develop under experimental conditions. The decay rate of the disturbances is in line with the hydraulic time scale defined by the ratio of the channel height and the friction length. In combination with the averaged flow velocity it is possible to assess the adaptation length of the concentration profile along the channel slope. This information is important for the interpretation of measured concentration profiles that are assumed to represent a steady-state solution for benchmark purposes. In addition the role of the added mass force on the stability is studied. The role of this force seems limited for the experimental conditions studied in this paper.