We study the steady three-dimensional flow field and bed topography in a channel with
sinusoidally varying width, under the assumptions of small-amplitude width variations
and sufficiently wide channel to neglect nonlinear effects and sidewall effects. The aim
of the work is to investigate the role of width variations in producing channel
bifurcation in braided rivers. We infer incipient bifurcation in cases where the growth
of a central bar leads to planimetric instability of the channel, i.e. when the given
infinitesimal width perturbation is enhanced. Results of the three-dimensional model
suggest that the equilibrium bottom profile mainly consists of a purely longitudinal
component, uniformly distributed over the cross-section, which induces deposition at
the wide section and scour at the constriction, and of a transverse component in
the form of a central bar (wide sections) and scour (constrictions), with longitudinal
wavelength equal to that of width variations. A comparison between the results of
the three-dimensional model and those obtained by means of a two-dimensional
depth-averaged approach shows that the transverse component is mainly related to
three-dimensional effects. Theoretical findings display a satisfactory agreement with
results of flume experiments. Transverse variations are responsible for the planimetric
instability of the channel; we find that in the range of values of Shields stress typical
of braided rivers, the incipient bifurcation is enhanced as the width ratio of the
channel increases.