Potential-flow instability theory and alluvial stream bed forms

The present work constitutes a reassessment of the role of potential-flow a nalyses in describing alluvial-bed instability. To facilitate the analyses, a new potential-flow description of unsteady alluvial flow is presented, w ith arbitrary phase lags between local flow conditions and sediment transpo rt permitted implicitly in the flow model Based on the present model, the e xplicit phase lag between local sediment transport rate and local flow cond itions adopted for previous potential-flow models is shown to be an artific ial measure that results in model predictions that are not consistent with observed flow system behaviour. Previous potential-flow models thus do not provide correct descriptions of alluvial flows, and the understanding of be d-wave mechanics inferred based upon these models needs to be reassessed. I n contrast to previous potential-flow models, the present one, without the use of an explicit phase lag, predicts instability of flow systems of rippl ed or dune-covered equilibrium beds. Instability is shown to occur at finit e growth rates for a range of wavelengths via a resonance mechanism occurri ng for surface waves and bed waves travelling at the same celerity. In addi tion, bed-wave speeds are predicted to decrease with increasing wavelength, and bed waves are predicted to grow and move at faster rates for flows of larger Froude numbers. All predictions of the present potential-flow model are consistent with observations of physical flow systems. Based on the pre dicted unstable wavelengths for a given alluvial flow, it is concluded that bed waves are not generated from plane bed conditions by any potential-flo w instability mechanism. The predictions of instability are nevertheless co nsistent with instances of accelerated wave growth occurring for flow syste ms of larger finite developing waves. Potential-flow description of alluvia l flows should, however, no longer form the basis of instability analyses d escribing bed-form (sand-wavelet) generation from flat bed conditions.