M. Bolla Pittaluga

A simple model for vertical profiles of velocity and suspended sediment concentration in straight and curved submarine channels

We develop a simple model to describe vertical profiles of velocity and suspended sediment concentration in submarine channels. We consider a conservative turbidity current flowing in a confined channel under steady and uniform flow conditions. The turbulence closure for density stratification is adapted from the model of Mellor and Yamada (1982). Solutions are obtained for both straight and constant curvature channels. In the latter case, in order to evaluate the secondary flow induced by curvature, we 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. Comparison of results on longitudinal velocity profiles in straight channels with experimental and field observations shows an excellent agreement and allows for the prediction of concentration profiles and suspended sediment size from known bed slope, current thickness, and normalized velocity at the turbidity current-ambient water interface. The model is able to capture the presence of multiple circulation cells on the vertical and the sense of rotation of the near-bottom secondary flow that can be either reversed (directed outward) or normal oriented (directed inward) with respect to the classical fluvial orientation. The parameters controlling the orientation of secondary flow in submarine channels are identified, and the implications on the bed morphology are discussed. The potential use and future developments of the present approach are also discussed.

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

[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.

Estuarine Patterns: An Introduction to Their Morphology and Mechanics

The aim of the present review is to expose the average reader (assumed to have little previous knowledge of morphodynamics) to an overview of some aspects of estuarine morphodynamics tackled from a mechanical perspective. It will appear that the tidal analogue of several phenomena which are extensivelydiscussed and fairlyw ell understood in the fluvial literature, still await to be fully explored. When writing reviews of this kind, authors are usuallyconfron ted with a dilemma: either treating superficiallya large number of aspects of the problem or discussing fewer topics in greater depth. In the present case we have chosen the former alternative, which seems appropriate to the non specialistic audience assumed above, though space limitation will not allow a systematic treatment of the subject. The reader interested in achieving a more advanced understanding is referred to the extensive literature quoted in the paper.

Reply to comment by Z. B. Wang and H. J. De Vriend on “Depth integrated modeling of suspended sediment transport”

[1] Let us first thankWang and De Vriend [2004] for their attention and their careful scrutiny of our paper. Let us also clarify that the motivation of our work was not to show that Galappatti’s [1983] model (hereinafter referred to as G83) was incorrect, but rather to develop a depth-averaged formulation of suspended sediment transport suitable for long-term morphological predictions, able to take into account weak non equilibrium effects of the kind often encountered in tidal as well as fluvial environments. Unfortunately, the mathematical framework appropriate to perform such investigation is precisely that proposed in G83, which forced us to revisit critically the latter work. [2] Let us come to the points raised by the Wang and De Vriend, which do concern G83’s approach rather than our formulation, whose validity does not seem to be questioned. The issue underlined in the discussion is whether or not G83’s perturbation scheme is correct and the basis for the Wang and De Vriend’s defense are the works of Wang [1992] and Wang and Ribberink [1986] (hereinafter referred to as W92 and WR86, respectively). We then also need to revisit the latter works.