New insights on the physical mechanisms sustaining the formation of free
alternate bars in rivers
Abstract
Free alternate bars are large-scale, downstream-migrating bedforms
characterized by an alternate sequence of three-dimensional scour and
deposition patches that frequently develop in rivers as the result of an
intrinsic instability of the erodible bed. Theoretical models based on
two-dimensional shallow water and Exner equations have been successfully
employed to capture the bar instability phenomenon, and to estimate bar
properties such as height, wavelength and migration rate. However, the
mathematical complexity of the problem hampered the understanding of the
key physical mechanisms that sustain the bar formation. To fill this
gap, we considered a simplified version of the equations, based on
neglecting the deformation of the free surface, which allows us to: (i)
provide the first complete explanation of the bar formation mechanism as
the result of a simple bond between variations of the water weight and
flow acceleration; (ii) derive a simplified, physically based formula
for predicting bar formation in a river reach, depending on channel
width-to-depth ratio, Shields number and relative submergence.
Comparison with an unprecedented large set of laboratory experiments
reveals that our simplified formula appropriately predicts alternate bar
formation in a wide range of conditions. Noteworthy, the hypothesis of
negligible free surface effect also implies that bars formation is fully
independent of the Froude number. We show that this intriguing property
is intimately related to the three-dimensional nature of river bars,
which allows for a gentle lateral deviation of the flow without
significant deformation of the water surface.