Stability, resonance and role of turbulent stresses in 1D alluvial flows

Abstract Linear stability analysis is used to investigate the behavior of small perturbations a uniform flow in straight channel with an erodible bed composed by unisize sediment. A shallow-water model employed and bedload sediment transport assumed. The mathematical structure linear problem, terms eigenvalues their associated eigenvectors explored detail information gathered on wavespeed growth rate as function wavelength relevant parameters. Several aspects solution are discussed, particular focus behaviour transcritical region where Froude number approaches unity. An approximate for roots eigenrelationship presented, which not uniformly valid region, leading appearance unphysical instability. regular perturbation expansion then introduced that allows elimination this singularity.