Kolluru, SSV and Sharma, P and Pandit, R (2022) Insights from a pseudospectral study of a potentially singular solution of the three-dimensional axisymmetric incompressible Euler equation. In: Physical Review E, 105 (6).
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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)0027-842410.1073/pnas.1405238111]. 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.
| Item Type: | Journal Article |
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| Publication: | Physical Review E |
| Publisher: | American Physical Society |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | Axisymmetric; Chebyshev; Direct-numerical-simulation; Euler's equation; Fourier; Incompressible Euler equations; Oscillatory structure; Pseudospectral; Pseudospectral direct numerical simulation; Singular solutions |
| Department/Centre: | Division of Physical & Mathematical Sciences > Physics |
| Date Deposited: | 18 Jul 2022 10:11 |
| Last Modified: | 18 Jul 2022 10:11 |
| URI: | https://eprints.iisc.ac.in/id/eprint/74948 |
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