We propose an exploratory model to describe the morphodynamics of distributary channel network growth on river deltas. The interface between deep channels and the shallow, unchannelized delta front deposits is modeled as a moving boundary. Steady flow over the unchannelized delta front is friction dominated and modeled by Laplace's equation. Shear stress along the network boundary produces nonlinear erosion rates at the interface, causing the boundary to move and network elements (channels and branches) to form. The model was run for boundary conditions resembling the Wax Lake Delta in coastal Louisiana, 20 parameterizations of sediment transport, and 3 parameterizations of discharge. In each case, the model produced a complex channel network with channel number, width, bifurcation angle, and channel shape depending on the sediment transport formula. For reasonable sediment transport parameters and gradually increasing water discharge, the model produced network characteristics and progradation rates similar to the Wax Lake Delta. This suggests that the model contains the processes responsible for network growth, despite its abstract formulation. Key Points:• Prograding distributary channel networks of varying morphology can be modeled as a simple moving boundary • Nonlinearities in the sediment transport formula dictate channel width, number of branches, bifurcation angle, and channel shape • Evolution is dictated by network morphology, sediment transport, and water discharge Supporting Information:• Supporting Information S1

When Gilbert‐type deltas respond to uneven sediment supply or advance over irregular basin bathymetry, they develop curved, creased fronts prograding at speeds that vary with location along the shoreline. Relations governing the progradation rate, however, have so far been proposed only for simple special cases. In this paper, we exploit the special properties of solutions to the eikonal equation to derive a general progradation relation, applicable to delta fronts of finite angle of repose and arbitrary shoreline planform. In these circumstances, the theory explicitly relates the progradation rate to the local shoreline curvature. We illustrate the resulting morphodynamics with numerical and analytical solutions for a sinuous delta front. The proposed relation can be used to model deltaic evolution or deduce spanwise distributions of sediment supply rates from observations of foreset evolution.

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