A simple morphological model is considered which describes the interac
tion between a unidirectional flow and an erodible bed in a straight c
hannel. For sufficiently large values of the width-depth ratio of the
channel the basic state, i.e. a uniform current over a flat bottom, is
unstable. At near-critical conditions growing perturbations are confi
ned to a narrow spectrum and the bed profile has an alternate bar stru
cture propagating in the downstream direction. The timescale associate
d with the amplitude growth is large compared to the characteristic pe
riod of the bars. Based on these observations a weakly nonlinear analy
sis is presented which results in a Ginzburg-Landau equation. It descr
ibes the nonlinear evolution of the envelope amplitude of the group of
marginally unstable alternate bars. Asymptotic results of its coeffic
ients are presented as perturbation series in the small drag coefficie
nt of the channel. In contrast to the Landau equation, described by Co
lombini et al. (1987), this amplitude equation also allows for spatial
modulations due to the dispersive properties of the wave packet. It i
s demonstrated rigorously that the periodic bar pattern can become uns
table through this effect, provided the bed is dune covered, and for r
ealistic values of the other physical parameters. Otherwise, it is fou
nd that the periodic bar pattern found by Colombini et al. (1987) is s
table. Assuming periodic behaviour of the envelope wave in a frame mov
ing with the group velocity, simulations of the dynamics of the Ginzbu
rg-Landau equation using spectral models are carried out, and it is sh
own that quasi-periodic behaviour of the bar pattern appears.