Giovanni Seminara

A unified bar–bend theory of river meanders

A two-dimensional model of flow and bed topography in sinuous channels with erodible boundaries is developed and applied in order to investigate the mechanism of meander initiation. By reexamining the problem recently tackled by Ikeda, Parker & Sawai (1981), a previously undiscovered ‘resonance’ phenomenon is detected which occurs when the values of the relevant parameters fall within a neighbourhood of certain critical values. It is suggested that the above resonance controls the bend growth, and it is shown that it is connected in some sense with bar instability. In fact, by performing a linear stability analysis of flow in straight erodible channels, resonant flow in sinuous channels is shown to occur when curvature ‘forces’ a ‘natural’ solution represented by approximately steady perturbations of the alternate bar type. A comparison with experimental observations appears to support the idea that resonance is associated with meander formation.

Finite-amplitude alternate bars

Following ideas developed in the field of hydrodynamic stability of laminar flows (Stuart 1971) a predictive theory is proposed to determine the development of finite-amplitude alternate bars in straight channels with erodible bottoms. It is shown that an ‘equilibrium amplitude’ of bedforms is reached as t → ∞ within a wide range of values of the parameter (β − β c )/β c , where t is the time, β is the width ratio of the channel and β c is its ‘critical’ value below which bars would not form. The theory leads to relationships for the maximum height and the maximum scour of bars which compare satisfactorily with the experimental data of various authors. Moreover the experimentally detected tendency of the bed perturbation to form diagonal fronts is qualitatively reproduced.

On tide propagation in convergent estuaries

We revisit the problem of one-dimensional tide propagation in convergent estuaries considering four limiting cases defined by the relative intensity of dissipation versus local inertia in the momentum equation and by the role of channel convergence in the mass balance. In weakly dissipative estuaries, tide propagation is essentially a weakly nonlinear phenomenon where overtides are generated in a cascade process such that higher harmonics have increasingly smaller amplitudes. Furthermore, nonlinearity gives rise to a seaward directed residual current. As channel convergence increases, the distortion of the tidal wave is enhanced and both tidal wave speed and wave lenght increase. The solution loses its wavy character when the estuary reaches its “critical convergence”; above such convergence the weakly dissipative limit becomes meaningless. Finally, when channel convergence is strong or moderate, weakly dissipative estuaries turn out to be ebb dominated. In strongly dissipative estuaries, tide propagation becomes a strongly nonlinear phenomenon that displays peaking and sharp distortion of the current profile, and that invariably leads to flood dominance. As the role of channel convergence is increasingly counteracted by the diffusive effect of spatial variations of the current velocity on flow continuity, tidal amplitude experiences a progressively decreasing amplification while tidal wave speed increases. We develop a nonlinear parabolic approximation of the full de Saint Venant equations able to describe this behaviour. Finally, strongly convergent and moderately dissipative estuaries enhance wave peaking as the effect of local inertia is increased. The full de Saint Venant equations are the appropriate model to treat this case.

FREE-FORCED INTERACTIONS IN DEVELOPING MEANDERS AND SUPPRESSION OF FREE BARS

The coexistence of migrating alternate (free) bars, spontaneously developing in erodible channels as a result of an instability process, with steady point bars, forced by curvature in meandering reaches of rivers is investigated theoretically. A perturbation expansion is set up in terms of two dimensionless small parameters, describing free and forced perturbations. The effect of mixed interactions is found to be responsible for the damping and slowing down of free bars as channel curvature increases. The theory allows the determination of the threshold value of channel curvature above which free bars are suppressed as a function of meander wavenumber for given flow and sediment characteristics. The minimum channel sinuosity for free bar suppression is found to be associated with the resonant wavenumber range of Blondeaux & Seminara (1985). Theoretical predictions compare satisfactorily with experimental observations by Kinoshita & Miwa (1974). The theory also suggests that free bars may appear again in a more advanced stage of meander development in accordance with field observations by Kinoshita (1961).

Stability and Morphodynamics

Linear and nonlinear aspects of the development of morphodynamical features of fluvial and coastal environments are reviewed. It is emphasized that, in spite of the as yet incomplete understanding of the mechanics of sediment transport, some essential mechanisms operating in morphodynamics have been recently clarified by employing classical tools of linear and weakly nonlinear stability theory.

Weakly nonlinear theory of regular meanders

Flow and bed topography in a regular sequence of meanders is shown to be strongly influenced by nonlinear effects within a fairly wide range of aspect ratios of the channel and meander wavenumbers. This finding is associated with the behaviour of meanders as nonlinear resonators in a neighbourhood of the resonance conditions discovered by Blondeaux & Seminara (1985). A weakly nonlinear approach valid for relatively small measures of channel curvature and within a neighbourhood of the resonant conditions displays all the typical features of nonlinear resonators, including non-uniqueness of the channel response

On the convective nature of bar instability

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

River, coastal and estuarine morphodynamics

\omega_{i}

Sand bars in tidal channels. Part 1. Free bars

, involve spatial branches of the dispersion relation which, for large positive values of

Nearly pure sorting waves and formation of bedload sheets

\omega_{i}