4 results
Nearly pure sorting waves and formation of bedload sheets
- Giovanni Seminara, Marco Colombini, Gary Parker
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- Journal:
- Journal of Fluid Mechanics / Volume 312 / 10 April 1996
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- 26 April 2006, pp. 253-278
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Bedload sheets are coherent migrating patterns of bed material recently observed both in flume studies and in field streams with beds of coarse sand and fine gravel. This newly recognized feature is inherently associated with the heterogeneous character of the sediment and consists of sorting waves with distinct coarse fronts only one or two coarse grains high.
The question of the formation of bedload sheets poses an interesting and peculiar stability problem for the grain size distribution. Sorting waves are essentially two-dimensional migrating perturbations associated with variations of this distribution. We show that their growth is strictly associated with grain sorting. In fact the latter gives rise to perturbations of bedload transport which drive small perturbations of bottom elevation the amplitude of which scales with grain size. The sorting wave also induces spatial variations of bottom roughness, and consequently alters the fluid motion, which conversely exerts a spatially varying stress on the bed. The feature of bedload sheets which allows them to be distinguished from dunes over beds with coarse sand or fine gravel is then the fact that sorting is the dominant effect controlling their growth, rather than being a relatively small perturbation of the mechanism which gives rise to dunes in the case of uniform sediment.
The requirement that perturbations should not alter the sediment budget leads to an integral condition which gives rise to an integro-differential mathematical problem. With the help of recently developed bedload relationships suitable for mixtures, as well as appropriate modelling of turbulent channel flow over a bed with spatially periodic perturbations of bottom elevation and roughness we are able to derive a general dispersion relation which can be readily solved in terms of undisturbed size densities in the form of sums of Dirac distributions.
Perturbations are found to be unstable within a range of wavenumbers depending on the relative roughness and Froude number. We show that when the effects of perturbations of bottom elevation are neglected the unstable region corresponds to the range of conditions where the bottom stress leads bottom roughness, a range distinct from that which characterizes the formation of dunes. This result is given a physical explanation which depends crucially on the deviation from equal mobility of different grain sizes in the surface layer. The effect of perturbations of bottom elevation is however not negligible when the bottom roughness is fairly large compared to depth. In the latter case perturbations of bottom elevation and of bottom roughness are equally important, and gravel sheets are not easily distinguished from small-amplitude dunes.
Comparison with the field observations of Whiting et al. (1985, 1988) is satisfactory insofar as the bedload sheet mode is unstable under the conditions of the experiments, and the predicted wavelengths fall within the experimental range. The laboratory observations of Kuhnle & Southard (1988), on the other hand, appear to fall within a range of bottom roughness where the observed bedforms do not exhibit features unambiguously distinct from those of small-amplitude dunes.
Meanders
- GIOVANNI SEMINARA
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- Journal:
- Journal of Fluid Mechanics / Volume 554 / 10 May 2006
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- 24 April 2006, pp. 271-297
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In the last few decades cooperation among fluid dynamicists and geomorphologists has allowed the construction of a rational framework for the quantitative understanding of several geomorphologic processes involved in the shaping of the Earth's surface. Particular emphasis has been given to the dynamics of sedimentary patterns, features arising from the continuous dynamic interaction between the motion of a sediment-carrying fluid and an erodible boundary. It is this interaction which ultimately gives rise to the variety of natural forms, often displaying a high degree of regularity, observed in rivers, estuaries, coasts, as well as in the deep submarine environment. Theoretical analyses and laboratory experiments have shown that the nature of most of the observed patterns is related to fundamental instability mechanisms whose particular character lies in the fact that it is the mobile interface between the fluid and the erodible boundary, rather than the flow itself, that is unstable. Developments have been general enough to reach the status of a distinct branch of fluid mechanics, geomorphological fluid mechanics. This paper concentrates on the mechanics of fluvial meandering. Our aim is to provide the reader with a systematic overview of the fundamental aspects of the subject, assessing, with the help of recent and novel results, settled as well as unsettled issues.
On Rayleigh's criterion for slowly varying flows
- Giovanni Seminara
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- Journal of Fluid Mechanics / Volume 91 / Issue 3 / 11 April 1979
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- 19 April 2006, pp. 547-562
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The inviscid centrifugal instability of slowly varying flows is shown to be asymptotically associated with the lowest-order spatial dependence of the basic flow satisfying Rayleigh's criterion. This result requires special attention for basic flows which reverse their direction. At the instant of reversal the growth rate of the disturbance bifurcates and the choice of the proper branch requires that viscous effects be taken into account within a conveniently small neighbourhood of the branch point. Previous results by Rosenblat (1968) are shown to be incorrect. Such results were based on overlooking the need for viscous effects to be accounted for within a neighbourhood of the bifurcation point. This led to a wrong choice of the path to be followed at bifurcation.
Experimental observations of upstream overdeepening
- GUIDO ZOLEZZI, MICHELE GUALA, DONATELLA TERMINI, GIOVANNI SEMINARA
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- Journal of Fluid Mechanics / Volume 531 / 25 May 2005
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- 18 May 2005, pp. 191-219
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The issue of morphodynamic influence in meandering streams is investigated through a series of laboratory experiments on curved and straight flumes. Both qualitative and quantitative observations confirm the suitability of the recent theoretical developments (Zolezzi & Seminara 2001) that indicate the occurrence of two distinct regimes of morphodynamic influence, depending on the value of the width ratio of the channel $\beta$. The threshold value $\beta_R$ separating the upstream from the downstream influence regimes coincides with the resonant value discovered by Blondeaux & Seminara (1985). Indeed it is observed that upstream influence may occur only in relatively wide channels, while narrower streams are dominated by downstream influence. A series of experiments has been carried out in order to check the above theoretical predictions and show, for the first time, evidence of the occurrence of upstream overdeepening. Two different sets of experiments have been designed where a discontinuity in channel geometry was present such that the channel morphodynamics was influenced in the upstream direction under super-resonant conditions ($\beta{>}\beta_R$) and in the downstream direction under sub-resonant conditions ($\beta{<}\beta_R$). Experimental results give qualitative and quantitative support to the theoretical predictions and allow us to clarify the limits of the linear analysis.