Solution of Geomorphic Stefan Problems

Although, in a strict sense, the classic Stefan problem involves tracking the movement of the water/ice interface during melting, its mathematical formalization can be generalized to a wide number of systems. One emerging application is in the study of the growth of geomorphic landscape features, e.g., deltas formed by the deposition of sediments at the mouths of rivers entering standing bodies of water.

This presentation will show how a simple treatment of the growth of a sedimentary delta can be posed in the form of a generalized Stefan problem. Key features this system, not usually seen in the standard Stefan problem, are the appearance of spatially dependent diffusivities and latent heats. These features can be exploited to arrive at interesting and novel closed form solutions and interface stability criterion.