| Summary: | We develop a mathematical model for esker formation by the continuous deposition of sediments near the mouth of water-filled subglacial tunnels. We assume a retreating ice sheet margin and prescribe meltwater and sediment supply to a channelized subglacial drainage system. The hydrodynamic model for the subglacial channel has its cross section governed by wall melting, creep closure, and sediment deposition. Sediment-carrying capacity typically increases downstream, before decreasing rapidly near the margin, suggesting that most deposition occurs there. This can lead to “choking” near the margin, which is offset by enhanced melting to keep the channel open. The model shows that the deposition rate varies roughly quadratically with sediment supply and inversely with water flux. For given sediment supply, the model suggests esker formation is most prevalent in smaller channels. Larger ice sheet melt rates likely produce more closely spaced eskers, but with smaller cross sections.
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