Hydrodynamically locked morphogenesis in karst and ice flutings

Two of the most widespread and fascinating patterns observed on cave walls and icefalls - karst and ice flutings - are demonstrated to share the same morphogenesis, whose core is a water film-induced locking mechanism. Creeping flow-based parallel and non-parallel stability analyses are developed through a numerical and analytical approach. These instabilities are shown to develop at inverted overhung conditions. A sharp transition between fluting and ripple-like patterns is presented. The non-parallel problem is solved with the use of Papkovich-Neuber solutions in order to obtain a finite wavelength selection close to the critical conditions. The method and results can be extended to similar problems where the temporal evolution of the interface is linearly related to the film depth.