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A potential two-scale traveling wave singularity for 3D incompressible Euler equations

Hou, Thomas Y. and Huang, De (2022) A potential two-scale traveling wave singularity for 3D incompressible Euler equations. Physica D, 435 . Art. No. 133257. ISSN 0167-2789. doi:10.1016/j.physd.2022.133257.

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In this paper, we investigate a potential two-scale traveling wave singularity of the 3D incompressible axisymmetric Euler equations with smooth initial data of finite energy. The two-scale feature is characterized by the property that the center of the traveling wave approaches to the origin at a slower rate than the rate of the collapse of the singularity. The driving mechanism for this potential singularity is due to two antisymmetric vortex dipoles that generate a strong shearing layer in both the radial and axial velocity fields. Without any viscous regularization, the 3D Euler equations develop an additional small scale characterizing the thickness of the sharp front. In order to stabilize the rapidly decreasing thickness of the sharp front, we apply a vanishing first order numerical viscosity to the Euler equations. We present numerical evidence that the 3D Euler equations with this first order numerical viscosity develop a locally self-similar blowup at the origin.

Item Type:Article
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URLURL TypeDescription
Hou, Thomas Y.0000-0001-6287-1133
Huang, De0000-0003-4023-9895
Additional Information:© 2022 Elsevier. Received 15 October 2021, Revised 21 February 2022, Accepted 10 March 2022, Available online 11 April 2022, Version of Record 25 April 2022. The research was in part supported by NSF, USA Grants DMS-1907977 and DMS-1912654. DH gratefully acknowledges the supports from the Choi Family Postdoc Gift Fund and the Start-up funding from Peking University, China. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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Peking UniversityUNSPECIFIED
Subject Keywords:Impressible Euler equations; Impressible Navier–Stokes equations; Singularity; Numerical viscosity
Record Number:CaltechAUTHORS:20220607-425321000
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Official Citation:Thomas Y. Hou, De Huang, A potential two-scale traveling wave singularity for 3D incompressible Euler equations, Physica D: Nonlinear Phenomena, Volume 435, 2022, 133257, ISSN 0167-2789, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:115058
Deposited By: George Porter
Deposited On:07 Jun 2022 22:24
Last Modified:07 Jun 2022 22:24

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