A Newtonian fluid model of the onset of plane folding in a single rock layer with surface tension effects

Abstract

The prototype structural dynamics problem of the initiation of plane folding in a single more competent rock layer, where both that layer and its embedding medium are originally undergoing a uniform parallel-layer compression at a constant strain rate, is reexamined. The two-dimensional mathematical model employed represents this situation in terms of a layered quasistatic Newtonian fluid involving surface tension effects. The critical conditions for the onset of folding are developed by performing the relevant linear stability analysis of an appropriate planar interface solution to this governing system of equations using a modified normal mode technique. These results depend crucially upon a nondimensional stability parameter proportional to the ratio of strain rate to surface tension. Consistent with models ignoring these surface tension effects, the wave train of a fold occuring over an unbounded region is characterized by the dominant wavelength of that disturbance corresponding to the maximum perturbation growth rate. For finite territory size limited in lateral extent to the order of the dominant wavelength, however, this wave train can be characterized by the critical wavelength at which the growth rate vanishes. The latter result is used to explain why some folds have a wavelength to thickness ratio of less than six while minor folds seem to have a preference for that quantity between six and four. This approach is presented as an alternative to a non-Newtonian one.