On the Development of Transverse Ridges on Rock Glaciers

The stability of a low Reynolds number flow on an inclined plane is investigated with respect to modelling the initiation of transverse wave-like ridges which commonly occur on the surfaces of rock-glacier forms. In accordance with field observations indicating the presence of stratification in rock glaciers, two models of rock-glacier structure are considered, each stratified and possessing a lower layer which is treated as a Newtonian fluid. An upper, less compliant layer is treated, alternatively, as a Newtonian fluid of viscosity greater than that of the lower layer, or as an elastic solid under longitudinal compression induced by a decrease in the slope of the underlying incline. A linear stability analysis is used to examine the behaviour of each of the proposed models, and both are found to generate instabilities at wavelengths comparable to those associated with transverse surficial ridges on rock glaciers. The growth rates of a flow disturbance predicted by the viscous-stratified model appear to be too slow to account fully for the development of wave forms of finite amplitude, suggesting that other mechanisms are involved in the amplification of an initial disturbance. The results of the stability analysis of the elastic lamina model indicate that finite surficial ridges may develop on rock glaciers as a product of a buckling instability in the surface region if there is a decrease in the slope of the underlying incline. Both of the analyses illustrate that transverse ridges can occur on the surface of a rock glacier in the absence of any variations in debris supply to the system. The results further imply that the use of these features in the paleoreconstruction of Holocene climatic conditions must entail an assessment of the relative roles of external climatically driven forcing versus internal Theologically derived instability.