Simple physics-based predictor for the number of river bars and the transition between meandering and braiding

The number of bars that form in an alluvial channel cross section can be determined from a physics-based linear model for alluvial bed topography. The classical approach defines separators between ranges in which river planform styles with certain numbers of bars are linearly stable and linearly unstable. We propose an alternative method that is easier to apply. Instead of defining separators between stable and unstable conditions for certain river planform styles, the method directly estimates the most likely number of bars. It is based on a demonstration that conditions of zero spatial damping in a linear model for steady bars are representative for the bar mode that develops inside a river channel. We argue that a method based on steady bars is more appropriate for real rivers than a method based on free migrating bars. We verified the method by applying it to several existing rivers at bankfull conditions. The results are good for width-to-depth ratios up to 100 but deteriorate for higher width-to-depth ratios. We explain the deficiencies for large width-to-depth ratios from the linearity of the model. The results show that our method can be used as a reliable predictor for whether reducing or enlarging the width of a river will lead to a meandering, transition, or braided planform.