Longitudinal profile of channels cut by springs

We propose a simple theory for the longitudinal profile of channels incised by groundwater flow. The aquifer surrounding the stream is represented in two dimensions through Darcy’s law and the Dupuit approximation. The model is based on the assumption that, everywhere in the stream, the shear stress exerted on the sediment by the flow is close to the minimal intensity required to displace a sand grain. Due to the coupling of the stream discharge with the water table elevation in the neighbourhood of the channel head, the stream elevation decreases as the distance from the stream’s tip with an exponent of 2/3. Field measurements of steephead ravines in the Florida panhandle conform well to this prediction.