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

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, 111.36 (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.

17 pages. 13 figures

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• Hyperviscosity, Galerkin truncation and bottlenecks in turbulence
• Transition from dissipative to conservative dynamics in equations of hydrodynamics
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Cited by in corpus (4)

• On the thermalization of the three-dimensional, incompressible, Galerkin-truncated Euler equation
• Eye of the Tyger: early-time resonances and singularities in the inviscid Burgers equation
• Logarithmic lattice models for flows with boundaries
• Tracking complex singularities of fluids on log-lattices