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.
Scott , R K & Dritschel , D G 2019 , ' Scale-invariant singularity of the surface quasigeostrophic patch ' Journal of Fluid Mechanics , vol. 863 , R2 . https://doi.org/10.1017/jfm.2019.7
Journal of Fluid Mechanics
© 2019, Cambridge University Press. This work has been made available online in accordance with the publisher's policies. This is the author created accepted version manuscript following peer review and as such may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1017/jfm.2019.7
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