A weakly nonlinear stability analysis of flows over erodible beds is c
onducted to investigate the formation of dunes. The flow is modeled wi
th the steady vorticity transport equation and the sediment transport
is described with Bagnold's bed load-transport rate formula that takes
into account the effect of the dune-surface local slope. From the ana
lysis, linear and nonlinear models are derived. Results of the models
indicate that although both are able to simulate the instabilities ass
ociated with dunes, the nonlinear model predicts more reasonable dune
length and development time and is less sensitive to variations of the
model parameters. The physical mechanisms controlling the development
and downstream migration of dunes also are examined. Predictions of t
he nonlinear model are in good agreement with selected experimental da
ta.