Alternate bar instability: 2D vs. 3D modeling of the flow field

The bed instability leading to the formation of alternate and multiple bars in river has been deeply investigated in the past, starting from the linear analyses of Callander (1969) and Blondeaux and Seminara (1985), through the weakly nonlinear analyses of Colombini et al. (1987) and Schielen et al. (1993), up to the fully nonlinear solution of Colombini and Tubino (1991). All these works were based on a 2D depth-averaged steady flow model coupled with a suitable implementation of the Exner equation. The rationale behind this choice is that the shallow-water assumption holds whenever the relevant processes occur over streamwise and spanwise distances many times greater than the flow depth. As a consequence, the formation of ‘longer’ bed forms, such as bars, can be studied by means of depth-averaged models, whereas ‘shorter’ bed forms, such as dunes and antidunes, require the implementation of more refined flow models, whereby the vertical structure of the flow is accounted for in the calculations. Quite recently, Colombini and Stocchino (2012) have presented a 3D flow model aiming at the investigation of the effects associated with three-dimensionality in the formation of dunes and antidunes. In the present contribution we focus on alternate bar linear stability and perform a comparison between the results obtained with the latter three-dimensional flow model and with a conventional two-dimensional depth-averaged formulation.