Marco Colombini

Revisiting the linear theory of sand dune formation

A linear stability theory for dune and antidune formation is presented that implements a rotational two-dimensional flow model. As in previous linear theories, the phase-lag between sediment transport and bed elevation remains the main mechanism driving instability. However, it is shown that this phase-lag varies significantly in a neighbourhood of the bed. Moreover, since the layer in which sediments are moving has a finite (though small) thickness, it is assumed that the perturbations of the fluid stress driving bedload transport should be evaluated at the top of the layer itself. It is shown that such an apparently minor modification of the classical approach alters remarkably the balance between stabilizing and destabilizing effects that drives the instability process. This also allows a clarification of the debated role of bedslope on the formation of dunes and antidunes. Following the above ideas, antidunes are shown to form in the absence of suspended sediment load and without any effect associated with sediment inertia. The present analysis ultimately allows a successful unification of the theories of dune and antidune formation.

Finite-amplitude river dunes

The linear and weakly nonlinear stability of a uniform flow in an infinitely wide open channel with erodible bottom is studied. Under suitable conditions the flow is found to be unstable, leading to the formation of dunes and antidunes. At a linear level, the corresponding regions of existence are presented and compared with experimental data. A weakly nonlinear analysis is then performed in a neighbourhood of the critical conditions for dune and antidune formation. The analysis shows that, for values of the ratio of the shear velocity to the depth-averaged velocity of practical interest, dune bifurcation is supercritical, whereas antidune bifurcation is subcritical. The latter result suggests a possible interpretation of the plane-antidune transition, where plane bed and antidune configurations are observed to coexist for the same values of the flow and the sediment parameters. The supercritical behaviour of the dune bifurcation allows for the prediction of an equilibrium amplitude that successfully compares with the amplitudes measured in laboratory experiments.

Ripple and dune formation in rivers

A linear stability analysis for dune and ripple formation is presented that implements a rotational two-dimensional flow model valid in the smooth as well as in the transitional and rough flow regimes. Sediment is assumed to be transported as bedload, disregarding the role of suspension. Therefore, the main mechanism driving instability, for both ripples and dunes, is the phase lag between bed shear stress and bed elevation. Ripples are shown to be confined to relatively low values of the Shields parameter and of the particle Reynolds number. For higher values of the Shields parameter and of the particle Reynolds number (and thus of the Froude number and of the roughness Reynolds number), ripples are replaced by dunes. The present analysis ultimately allows for a successful unification of the theories of dune and ripple formation and for a clarification of the debated role of ripples on the formation of dunes. A good agreement between predicted and observed wavelengths for both ripples and dunes is found.

Coupling or decoupling bed and flow dynamics: Fast and slow sediment waves at high Froude numbers

The effect of coupling or decoupling bed and flow dynamics is analyzed in the framework of a linear analysis of the stability of a uniform, rotational, two-dimensional flow in an infinitely wide channel with a bed composed by incoherent sediments. It is shown that results obtained with the coupled analysis in term of instability of slow sediment waves of the dune/antidune kind are quite similar to the results obtained making use of the “quasisteady hypothesis,” which forms the basis of most of the existing linear stability analyses of bedforms and formally justifies the decoupling procedure. Small differences can be observed, for Froude numbers of O(1), in the surroundings of the marginal curves that bound the instability regions, mainly due to the removal of the artificial resonance that is introduced in the analysis when the quasisteady hypothesis is enforced. The decoupled approach, however, completely wipes out a mode of instability associated with fast-moving sediment waves, which appear at high Frou...

Case Study: Design of Flood Control Systems on the Vara River by Numerical and Physical Modeling

In the present paper, we investigate the effectiveness of a flood defense project based on storage reservoirs, presently under study for the Magra River and Vara River (Italy). We have focused the analysis on two detention reservoirs and studied their response to different hydrological scenarios mostly in terms of flood mitigation efficiency, leaving aside sediment transport issues. The analysis has been carried out with the aid of a physical model and one-dimensional numerical simulations. Experimental and numerical simulations have been performed spanning a wide range of hydrological conditions. Some of the results can be generalized for different applications where similar flood control systems are employed.

Axisymmetric flow within a torsionally oscillating sphere

The flow of an incompressible Newtonian fluid inside a torsionally oscillating spherical cavity is considered. The three-dimensional Navier-Stokes and continuity equations are solved by means of a Galerkin projection spectral method, based on a second-order incremental fractional-step approach. Legendre and Jacobi polynomial expansions are used in the zenithal and radial directions, respectively. Axisymmetric solutions are sought for a relatively wide set of the parameters controlling the flow, namely, the Rossby and the Womersley numbers. In particular, the behaviour of the flow for relatively large amplitudes of oscillation is studied, with emphasis on the generation of centrifugal instabilities. Numerical results are compared with experimental observations and semi-analytical solutions in the small-amplitude regime, showing good agreement.