Arid alluvial channels on piedmonts and valley floors often exhibit an oscillating pattern of narrow, deeply incised reaches and wide, shallow reaches with a characteristic wavelength. How do these oscillations develop and what controls their wavelengths? To address these questions we developed a two-dimensional numerical model that couples erosion and deposition in a channel bed with cross-sectional widening and narrowing. This model is inherently unstable over a range of spatial scales dependent on the channel width, depth, and slope. In the initial phase of model evolution, wider-than-average channel reaches become zones of distributary flow that aggrade, lose stream power, and further widen in a positive feedback. Simultaneously, narrower-than-average reaches incise, gain stream power, and further narrow. In the second stage of model evolution, this instability is balanced by the diffusive nature of longitudinal profile evolution, and solitary topographic waves propagate in the upstream direction with a characteristic wavelength and amplitude. The model predicts a specific quantitative relationship between the oscillation wavelength and channel width, depth, and slope that is verified by a database of channel geometries in southern Arizona.