Use of a viscous model of till rheology to describe gravitational loading instabilities in glacial sediments

This paper models the operation of loading (Rayleigh-Taylor) instabilities in sediments using an effective-pressure-dependent viscosity such has been used to model the deformation of sediment beneath glaciers. A particular feature is a strong increase of viscosity with depth, resulting from the fact that the effective pressure increases with depth. Observations suggest that more than one wavelength is generally present (e.g. diapirism and loadcasting) which requires at least three layers with uniform properties to be present. Three layers permit wavelength growth maxima at two distinct wavelengths. We investigate whether an effective-pressure dependent rheology is consistent with RT instabilities, and whether the non-uniformity it produces is able to increase the number of growth-rate maxima. The investigation starts from the point where sediment in an underlying layer is less dense than the overlying sediment, and the Rayleigh-Taylor instability starts to operate. The mechanics of two layers of finite thickness but infinite extent are modelled by the Stokes equations. The equation set is linearized, and the Fourier transform taken in order to describe the periodic horizontal variation of flow fields at a specified wavelength. The influences of layer thickness and viscosity ratio on the flow fields are considered. It is found that, for a given wavelength, layer thickness has a far stronger influence on flow fields than does viscosity ratio. For all configurations inspected, the dependence of growth rate on wavenumber exhibited one maximum, meaning that a variable viscosity model does not produce multiple wavelengths. Maximum growth rates occur at wavelengths corresponding to the layer thicknesses. We infer that loading instabilities occurring at wavelengths around the layer thicknesses are consistent with the effective-pressure-dependent viscous model.

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