Potential singularity mechanism for the Euler equations
Abstract
Singular solutions to the Euler equations could provide essential insight into the formation of very small scales in highly turbulent flows. Previous attempts to find singular flow structures have proven inconclusive. We reconsider the problem of interacting vortex tubes, for which it has long been observed that the flattening of the vortices inhibits sustained self-amplification of velocity gradients. Here we consider an iterative mechanism, based on the transformation of vortex filaments into sheets and their subsequent instability back into filaments. Elementary fluid mechanical arguments are provided to support the formation of a singular structure via this iterated mechanism, which we analyze based on a simplified model of filament interactions.
Additional Information
© 2016 American Physical Society. (Received 22 June 2016; published 28 December 2016) We are greatly indebted to Leo Kadanoff for past support and encouragement and in particular for sparking the interest of M.P.B. in this problem by giving him a paper of A. Pumir [42] to read. This research was funded by the National Science Foundation through the Harvard Materials Research Science and Engineering Center Grant No. DMR1420570 and the Division of Mathematical Sciences Grant No. DMS-1411694. M.P.B. is grateful to the Simons foundation, and A.P. to the Humboldt foundation.Attached Files
Published - PhysRevFluids.1.084503.pdf
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Additional details
- Eprint ID
- 73223
- Resolver ID
- CaltechAUTHORS:20170104-144343934
- DMR-1420570
- NSF
- DMS-1411694
- NSF
- Simons Foundation
- Alexander von Humboldt Foundation
- Created
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2017-01-04Created from EPrint's datestamp field
- Updated
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2021-11-11Created from EPrint's last_modified field