Showing papers by "Giovanni Seminara published in 1996"

Nearly pure sorting waves and formation of bedload sheets

Abstract: 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.

Waves of Finite Amplitude Trapped by Oscillating Gates

Abstract: Arrays of oscillating gates located at the inlet channels of Venice Lagoon have been recently proposed as a means to protect Venice from the phenomenon of high water associated with the propagation of high tides. It has sometimes been observed in laboratory investigations that the gates subjected to the action of incident monochromatic waves propagating along the inlet channel respond with oscillations which are out of phase among each other and not synchronous with the incident wave. The latter observations have been recently explained by Blondeaux et al. (Rend. Matem. Acc. Lincei 59 (1993), 291-298; 299-305) as a Mathieu type phenomenon whereby the incident wave excites free transverse modes of oscillation of the gate system. In the present investigation the above instability process is followed in the weakly nonlinear regime in the interesting case when the response is subharmonic. A bifurcation is shown to occur which may be either supercritical or subcritical in different regions of the parameter space. The equilibrium configurations are shown to correspond to attractive foci of the cubic amplitude equation describing the bifurcation process. This result bears some analogy with those found in a different context by Hall & Seminara (J. Fluid Mech. 101 (1980), 423-444) though differences originate from the `dissipative' effect exhibited by the gate system which is able to radiate energy through the generation of travelling waves.