Cyclic steps on ice

M. Yokokawa, N. Izumi, K. Naito, G. Parker, T. Yamada, R. Greve

Research output: Contribution to journalArticlepeer-review


Boundary waves often form at the interface between ice and fluid flowing adjacent to it, such as ripples under river ice covers, and steps on the bed of supraglacial meltwater channels. They may also be formed by wind, such as the megadunes on the Antarctic ice sheet. Spiral troughs on the polar ice caps of Mars have been interpreted to be cyclic steps formed by katabatic wind blowing over ice. Cyclic steps are relatives of upstream-migrating antidunes. Cyclic step formation on ice is not only a mechanical but also a thermodynamic process. There have been very few studies on the formation of either cyclic steps or upstream-migrating antidunes on ice. In this study, we performed flume experiments to reproduce cyclic steps on ice by flowing water, and found that trains of steps form when the Froude number is larger than unity. The features of those steps allow them to be identified as ice-bed analogs of cyclic steps in alluvial and bedrock rivers. We performed a linear stability analysis and obtained a physical explanation of the formation of upstream-migrating antidunes, i.e., precursors of cyclic steps. We compared the results of experiments with the predictions of the analysis and found the observed steps fall in the range where the analysis predicts interfacial instability. We also found that short antidune-like undulations formed as a precursor to the appearance of well-defined steps. This fact suggests that such antidune-like undulations correspond to the instability predicted by the analysis and are precursors of cyclic steps.

Original languageEnglish (US)
Pages (from-to)1023-1048
Number of pages26
JournalJournal of Geophysical Research: Earth Surface
Issue number5
StatePublished - May 1 2016


  • antidunes
  • cyclic steps
  • flume experiments
  • ice
  • linear stability analysis

ASJC Scopus subject areas

  • Earth-Surface Processes
  • Geophysics


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