Scale-invariant singularity of the surface quasigeostrophic patch

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Numerical simulations of the surface quasigeostrophic patch indicate the development of a scale-invariant singularity of the boundary curvature in finite time, with some evidence of universality across a variety of initial conditions. At the time of singularity, boundary segments are shown to possess an exact and simple analytic form, described by branches of a logarithmic spiral centred on the point of singularity. The angles between the branches depend non-trivially on the shape of the smooth connecting boundary as the singularity is approached, but are independent of the global boundary.
Original languageEnglish
Article numberR2
Number of pages12
JournalJournal of Fluid Mechanics
Early online date28 Jan 2019
Publication statusPublished - 25 Mar 2019


  • Contour dynamics
  • Quasi-geostrophic flows


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