Towards a theory for the formation of sea stacks

We provide a continuum model that has the capability to explain the dynamical processes which lead to the formation of sea stacks. The basic concept is that a uniformly retreating sea cliff face can be unstable to the formation of spatial undulations, initially as sine waves, but with increasing contortion as the sinuosity develops. The mechanism for instability is the positive feedback created by enhanced erosion rate caused by the shore debris created by cliff collapse. This mechanism is somewhat similar to the morphological effects of wave-induced sand transport in forming irregular beach-bounded coastlines. The key ingredient of the theory which can potentially enable cave formation and isolated stacks to occur is that the relevant spatial variable describing along-shore transport is the along-shore arc length. We formulate the model, show that it provides the sought-for instability, and give numerical solutions for the resulting shore-line. As yet, we have not found self-intersecting shore-lines, which would be the harbinger of sea stack formation.