The development of biofilm architecture.

We extend the one-dimensional polymer solution theory of bacterial biofilm growth described by Winstanley et al. (2011 Proc. R. Soc. A467, 1449-1467 (doi:10.1098/rspa.2010.0327)) to deal with the problem of the growth of a patch of biofilm in more than one lateral dimension. The extension is non-trivial, as it requires consideration of the rheology of the polymer phase. We use a novel asymptotic technique to reduce the model to a free-boundary problem governed by the equations of Stokes flow with non-standard boundary conditions. We then consider the stability of laterally uniform biofilm growth, and show that the model predicts spatial instability; this is confirmed by a direct numerical solution of the governing equations. The instability results in cusp formation at the biofilm surface and provides an explanation for the common observation of patterned biofilm architectures.

Subglacial swamps.

The existence of both water and sediment at the bed of ice streams is well documented, but there is a lack of fundamental understanding about the mechanisms of ice, water and sediment interaction. We pose a model to describe subglacial water flow below ice sheets, in the presence of a deformable sediment layer. Water flows in a rough-bedded film; the ice is supported by larger clasts, but there is a millimetric water layer submerging the smaller particles. Partial differential equations describing the water film are derived from a description of the dynamics of ice, water and mobile sediment. We assume that sediment transport is possible, either as fluvial bedload, but more significantly by ice-driven shearing and by internal squeezing. This provides an instability mechanism for rivulet formation; in the model, downstream sediment transport is compensated by lateral squeezing of till towards the incipient streams. We show that the model predicts the formation of shallow, swamp-like streams, with a typical depth of the order of centimetres. The swamps are stable features, typically with a width of the order of tens to hundreds of metres.

Subglacial hydrology and the formation of ice streams.

Antarctic ice streams are associated with pressurized subglacial meltwater but the role this water plays in the dynamics of the streams is not known. To address this, we present a model of subglacial water flow below ice sheets, and particularly below ice streams. The base-level flow is fed by subglacial melting and is presumed to take the form of a rough-bedded film, in which the ice is supported by larger clasts, but there is a millimetric water film which submerges the smaller particles. A model for the film is given by two coupled partial differential equations, representing mass conservation of water and ice closure. We assume that there is no sediment transport and solve for water film depth and effective pressure. This is coupled to a vertically integrated, higher order model for ice-sheet dynamics. If there is a sufficiently small amount of meltwater produced (e.g. if ice flux is low), the distributed film and ice sheet are stable, whereas for larger amounts of melt the ice-water system can become unstable, and ice streams form spontaneously as a consequence. We show that this can be explained in terms of a multi-valued sliding law, which arises from a simplified, one-dimensional analysis of the coupled model.