Formulation and solution of the problem of the stability of a cohesionless channel bottom

The problem of the stability of the sandy bottom of a rectangular channel with respect to spatially onedimensional perturbations is formulated. The channel stability problem is solved using the sediment discharge formula modified by taking into account the effect of free-surface perturbations on sediment transport. Analytic dependences of the propagation velocity of bottom perturbations on time are obtained for small Froude numbers. Wavelengths for the most rapidly growing bottom perturbations are obtained analytically, and the problem of the evolution of a single bottom perturbation is solved.