Coupling or decoupling bed and flow dynamics: fast and slow sediment waves at high Froude numbers

The effect of coupling or decoupling bed and flow dynamics is analyzed in the framework of a linear analysis of the stability of a uniform, rotational, two-dimensional flow in an infinitely wide channel with a bed composed by incoherent sediments. It is shown that results obtained with the coupled analysis in term of instability of slow sediment waves of the dune/antidune kind are quite similar to the results obtained making use of the “quasisteady hypothesis,” which forms the basis of most of the existing linear stability analyses of bedforms and formally justifies the decoupling procedure. Small differences can be observed, for Froude numbers of O(1), in the surroundings of the marginal curves that bound the instability regions, mainly due to the removal of the artificial resonance that is introduced in the analysis when the quasisteady hypothesis is enforced. The decoupled approach, however, completely wipes out a mode of instability associated with fast-moving sediment waves, which appear at high Froude numbers in connection with the formation of roll waves on the free surface. This mode of instability, characterized by large wavelengths, is shown to coexist with the slower, shorter antidune mode.