Insights from a pseudospectral study of a potentially singular solution of the three-dimensional axisymmetric incompressible Euler equation

Sai Swetha Venkata Kolluru, Puneet Sharma, and Rahul Pandit
Phys. Rev. E 105, 065107 – Published 17 June 2022
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Abstract

We develop a Fourier-Chebyshev pseudospectral direct numerical simulation (DNS) to examine a potentially singular solution of the radially bounded, three-dimensional (3D), axisymmetric Euler equations [G. Luo and T.Y. Hou, Proc. Natl. Acad. Sci. USA 111, 12968 (2014)]. We demonstrate that (a) the time of singularity is preceded, in any spectrally truncated DNS, by the formation of oscillatory structures called tygers, first investigated in the one-dimensional (1D) Burgers and two-dimensional (2D) Euler equations; (b) the analyticity-strip method can be generalized to obtain an estimate for the (potential) singularity time.

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  • Received 15 February 2021
  • Revised 17 August 2021
  • Accepted 26 May 2022

DOI:https://doi.org/10.1103/PhysRevE.105.065107

©2022 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
  1. Physical Systems
Nonlinear DynamicsStatistical Physics & ThermodynamicsFluid Dynamics

Authors & Affiliations

Sai Swetha Venkata Kolluru1,*, Puneet Sharma2,†, and Rahul Pandit1,‡

  • 1Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
  • 2Dynamics of Complex Fluids (DCF), Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany

  • *saik@iisc.ac.in
  • puneet.sharma@ds.mpg.de
  • rahul@iisc.ac.in

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Issue

Vol. 105, Iss. 6 — June 2022

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