Spatial width oscillations in meandering rivers at equilibrium

In canaliform rivers channel width at bankfull stage is fairly uniform though, at bend apexes, it is typically smaller than at crossings. Conversely, in sinuous point bar rivers bankfull width peaks at bend apexes. Why? Is there any mechanistic constraint that forces this different behavior? We provide an answer to these questions investigating how bankfull width must vary in a sequence of sine-generated meanders in order for the constraints of equilibrium (constant flow discharge and sediment flux) to be satisfied. With the help of a 3-D fully nonlinear analytical model of flow and bed topography in meandering rivers with variable width, we show that, in a meandering channel characterized by a constant longitudinal free-surface slope, the equilibrium width thus obtained oscillates with a frequency twice the frequency of channel curvature and experiences the maximum width close to inflection points. This pattern is typically observed in canaliform rivers. We then show that a similar pattern is observed in sinuous point bar rivers, provided the hydrodynamic width (width of the free surface) is replaced by the active width, namely the width of the portion of the cross section where transport occurs at formative conditions. Theoretical results are substantiated by a satisfactory comparison with field observations referring to the Mississippi River (United States) and to the Bollin River (United Kingdom).