Many gravel bed streams have a typical bed morphology consisting of pool-riffle sequences, which provides important habitat diversity both in terms of flow and substrate. A complete explanation of pool-riffle genesis and self-maintenance remains elusive and, despite advances in understanding the effects of flow spatial and temporal variability, the key sediment processes have been only marginally explored. Here we use a 1D unsteady multi-fraction morphodynamic model to explain the formation and degradation of pool-riffle sequences. Using a 1-year time series of measured flows below bankfull on a stream in which we have removed initial bedforms and sediment sorting our model spontaneously generates pools with finer substrate at narrow sections and riffles with coarser sediment at wider sections, closely resembling the natural bed morphology. Additional experiments show that under our modelling assumptions a variable flow regime is fundamental for development and self-maintenance of the longitudinal grain sorting characteristic of pool-riffle sequences, which could not be obtained or maintained with discharges held constant over relatively long periods.