ABSTRACT
Two multi-layer fluid models are investigated by employing linear stability theory. First, the onset of convection is reexamined for the Bénard problem, using a nondimensional model which includes both buoyancy and surface-tension driven mechanisms, as well as explicit consideration of the dynamics of the upper phase and the deviation of the fluid-fluid interface from its mean planar position. The critical conditions for the onset of convection, assumed to occur for a stationary state, and the critical wavelength of the resulting flow are determined numerically after a normal-mode linear stability analysis. These theoretical results differ from existing numerical calculations from water-benzene layers, but are in close quantitative agreement with relevant experimental findings for silicone oil-air layers. Second, the prototype structural geology 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 rate of strain, is examined. The two-dimensional mathematical model employed represents this situation in terms of a layered quasistatic heterogeneous Newtonian fluid, including the effects of gravity and surface tension, which were ignored during previous investigations of small scale folds. The critical conditions for the onset of such 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 approach. These stability results, which depend on both the imposed rate of strain and the layer thickness, are then used to explain the formation of short wavelength minor folds with particular emphasis on the Castile multilayer of Southern New Mexico, wherein thin planar layers are often found interspersed among thicker folded ones on length scales of 1 mm to 1 cm. The folding-type instability produced is termed Kelvin-Helmholtz because of its similarity in origin to those waves generated by the action of wind over water.
