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 $\omega_{i}$, involve spatial branches of the dispersion relation which, for large positive values of $\omega_{i}$, lie in the same half $\lambda$-plane, $\lambda$ 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.

Despite the high accuracy of conventional acoustic hydrographic systems, measurement of the seabed along coastal belts is still a complex problem due to the limitations arising from shallow water. In addition to traditional echo sounders, airborne LiDAR also suffers from high application costs, low efficiency, and limited coverage. On the other hand, remote sensing offers a practical alternative for the extraction of depth information, providing fast, reproducible, low-cost mapping over large areas to optimize and minimize fieldwork. Satellite-derived bathymetry (SDB) techniques have proven to be a promising alternative to supply shallow-water bathymetry data. However, this methodology is still limited since it usually requires in situ observations as control points for multispectral imagery calibration and bathymetric validation. In this context, this paper illustrates the potential for bathymetric derivation conducted entirely from open satellite data, without relying on in situ data collected using traditional methods. The SDB was performed using multispectral images from Sentinel-2 and bathymetric data collected by NASA’s ICESat-2 on two areas of relevant interest. To assess outcomes’ reliability, bathymetries extracted from ICESat-2 and derived from Sentinel-2 were compared with the updated and reliable data from the BathyDataBase of the Italian Hydrographic Institute.