Are the enigmatic "rolls" on the Ellesmere Ice Shelf initiated as viscous buckling from sea-ice pressure?

The Ellesmere Ice Shelf is currently represented by only a few remnants of its former presence in fjords and bays along the Ellesmere Island coast. It represents a thick ($>50$ m) form of Arctic sea ice that behaves much like an ice shelf that originates from glacial flow across a grounding line. An enigmatic and pervasive set of parallel waves in the surface topography "rolls" on the ice shelf have baffled scientists since they were first seen in 1876. How these rolls were first created, and what maintains them, are questions that have inspired a handful of competing hypotheses (Jeffries, 2017), ranging from those that appeal to surface glacio-hydrologic processes to one which appeals to viscous buckling from either thermal contraction or imposed sea-ice pressure from the Arctic Ocean north of the ice shelf. In this study, we examine the viscous-buckling hypothesis associated with compressive sea-ice pressure at the ice front. We use a variational approach to develop the underlying dynamics of viscous buckling and associated creep responses to compressive back-pressure. Our analysis suggests that viscous buckling can indeed be a plausible mechanism for initiating the rolls during periods when the ice shelf was still growing in thickness from its origin as land-fast sea ice. What is still problematic is that the topography induced by buckling subsequently relaxes back to flat in the absence of sea-ice pressure, hence viscous buckling alone cannot explain the persistence of the enigmatic rolls. Paleoceanographic evidence suggests that a large Arctic ice shelf, similar to the Ellesmere Ice Shelf, may have formed and collapsed repeatedly in the past with icebergs discharging enough fresh water flux into the North Atlantic to influence oceanographic currents and regional climate (Condron et al., 2020). A more thorough understanding the Ellesmere Ice Shelf and the physical causes of its surface rolls may potentially shed light on how ice shelves like the Ellesmere may have formed and broken up in the past.