Dynamics of channel incision in a granular bed driven by subsurface water flow

We propose a dynamical model for the erosive growth of a channel in a granular medium driven by subsurface water flow. The model is inferred from experimental data acquired with a laser-aided imaging technique. The evolution equation for transverse sections of a channel has the form of a non-locally driven Burgers equation. With fixed coefficients this equation admits an asymptotic similarity solution. Ratios of the granular transport coefficients can therefore be extracted from the shape of channels that have evolved in steady driving conditions.