Heaps in the fluid film induced by slip/non-slip switching boundary condition

How can localized, steady deformed structures be formed in the free surface of a fluid layer? For example, in vertically vibrated dense suspensions, heaping and stable holes are stable structures that are sustained against large gravitational pressure. Here we propose a new model of heaping induced by a boundary condition on a solid wall. We found that a flat fluid layer becomes unstable and forms heaps when we impose a boundary condition that shows slip/non-slip switching in synchronization with vertical vibration. The obtained onset acceleration, bifurcation type and flow of the heaps are consistent with those observed experimentally. Furthermore, we found that heaps can drift and climb a slope when the bottom is slightly inclined. This result indicates that our model can be applied to the migration of localized structures.