Showing papers by "Giovanni Seminara published in 2003"

Bed load at low Shields stress on arbitrarily sloping beds: Alternative entrainment formulation

Abstract: [1] According to the Bagnold hypothesis for equilibrium bed load transport, a necessary constraint for the maintenance of equilibrium bed load transport is that the fluid shear stress at the bed must be reduced to the critical, or threshold, value associated with incipient motion of grains. It was shown in a companion paper [Seminara et al., 2002], however, that the Bagnold hypothesis breaks down when applied to equilibrium bed load transport on beds with transverse slopes above a relatively modest value that is well below the angle of repose. An investigation of this failure resulted in a demonstration of its lack of validity even for nearly horizontal beds. The constraint is here replaced with an entrainment formulation, according to which a dynamic equilibrium is maintained by a balance between entrainment of bed grains into the bed load layer and deposition of bed load grains onto the bed. The entrainment function is formulated so that the entrainment rate is an increasing function of the excess of the fluid shear stress at the bed over the threshold value. The formulation is implemented with the aid of a unique set of laboratory data that characterizes equilibrium bed load transport at relatively low shear stresses for streamwise angles of bed inclination varying from nearly 0° to 22°. The formulation is shown to provide a description of bed load transport on nearly horizontal beds that fits the data as well as that resulting from the Bagnold constraint. The entrainment formulation has the added advantage of not requiring the unrealistically high dynamic coefficient of Coulomb friction resulting from the Bagnold constraint. Finally, the entrainment formulation provides reasonable and consistent results on finite streamwise and transverse bed slopes, even those at which the Bagnold formulation breaks down completely.

On the convective nature of bar instability

Abstract: Bar instability is recognized as the fundamental mechanism underlying the formation of large-scale forms of rivers. We show that the nature of such instability is convective rather than absolute. Such a result is obtained by revisiting the linear stability analysis of open-channel uniform flow over a cohesionless channel of Colombini et al. (1987) and using the Briggs (1964) criterion to distinguish between the convectively and absolutely unstable temporally asymptotic response to an initial boundary-value perturbation of bed topography. Examining the branch-point singularities of the dispersion relation, which can be determined in closed form, we show that all the existing branch-point singularities characterized by positive bar growth rate ω i , involve spatial branches of the dispersion relation which, for large positive values of ω i , lie in the same half λ-plane, λ denoting the complex bar wavenumber. Hence, the nature of instability is convective and remains so for any value of the aspect ratio, the controlling parameter of the basic instability, as well as for any lateral mode investigated. The latter analytical findings are confirmed by numerical solutions of the fully nonlinear problem. In fact, starting from either a randomly distributed or a localized spatial perturbation of bed topography, groups of bars are found to grow and migrate downstream leaving the source area undisturbed. The actual bars observed in laboratory experiments arise from the spatial-temporal growth of some persistent initial perturbation. The nonlinear development of such perturbations is shown to lead to a periodic pattern with amplitude independent of the amplitude of the initial perturbation. Bars are also found to lengthen and slow down as they grow from the linear into the nonlinear regime, in agreement with experimental observations. The distance from the initial cross-section at which equilibrium is achieved depends on the initial amplitude of the perturbation, a finding which calls for a revisitation of classical laboratory observations reported in the literature.

Depth‐integrated modeling of suspended sediment transport

Abstract: [1] We derive a depth-averaged model of suspended sediment transport. The development of the analysis leads us to revisit the asymptotic approach originally developed by Galappatti [1983], more recently generalized by >Wang [1992] and widely employed in commercial codes. We show that Galappatti's approach is formally incorrect as it differs from the formal asymptotic expansion of the exact solution. Moreover, the correct approach rather than leading to a differential equation for the depth-averaged concentration actually provides higher order corrections for the leading order equilibrium approximation of the depth-averaged concentration. Such corrections can be expressed in terms of spatial and temporal derivatives of the leading order solution. The latter picture is demonstrated on a model problem which is easily amenable to analytical treatment. On the basis of the formal asymptotic expansion of the exact solution we are then able to derive an analytical form for the flux of suspended sediment in slowly varying flows, which is suitable to applications to a variety of morphodynamic contexts including tidal and fluvial environments. An example of potential applications of the present approach is provided by examining the problem of suspended sediment transport due to a flood wave.