Two-diffusion description of hyperpycnal deltas

Alluvial deltas formed upstream of lakes and reservoirs often exhibit concave foresets with maximum inclinations smaller than the angle of repose. In the present work, we test whether this morphology could be attributed to bed load sediment transport by turbid underflows, acting along the foreset beds before their fine sediment load settles out of suspension. Under hyperpycnal conditions, both the topset and foreset of the delta would thus be subject to the geomorphic influence of the dense river inflow. To describe this joint geomorphic action by subaerial and subaqueous currents, we derive a two-diffusion theory and modify it to account for inclination thresholds. Different diffusion strengths apply to the topset and foreset, on either side of the moving shoreline. For a channel of uniform initial slope and a constant water level in the body of standing water, we show that the resulting moving boundary problem admits exact similarity solutions. To test the theory, the analytical solutions are compared with small-scale laboratory experiments in which turbid underflows are replaced by brine currents. The curved profiles predicted by the theory and measured in the experiments resemble those of surveyed deltaic deposits in lakes known to be prone to turbidity currents.