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Geomorphic patterns are abundant in nature, however the mechanisms that drive the formation and the evolution of these structures are not well understood. In this thesis, we focus on one such pattern. On the surface of stalactites, we find centimetre scale ripples, called crenulations. Stalactites grow as a result of a thin film flowing down the outside, which deposits calcium on the surface. This deposition changes the shape of the wall, which will in turn affect the flow. As the stalactite grows at a much slower rate than the fluid flows, we can model these separately. In this thesis, we will first look at modelling the thin film flow in the appropriate geometries. For this problem, we will consider the radius and the wavelength to be of similar sizes. These will be much larger than the fluid thickness. For this model, we consider the crenulation amplitude to be a similar size to the fluid thickness. We will then look to see how the crenulation wavelength and amplitude affects the flow. Using these flows, we then look at modelling the evolution of the stalactite wall. We examine under what conditions we would expect the crenulations to form and how they evolve once they do.