Dual Theory of Decaying Turbulence: 1: Fermionic Representation

Alexander Migdal

doi:10.20944/preprints202312.1012.v2

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preprints.org > physical sciences > fluids and plasmas physics > doi: 10.20944/preprints202312.1012.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Dual Theory of Decaying Turbulence: 1: Fermionic Representation

Alexander Migdal

Version 1 : Received: 13 December 2023 / Approved: 13 December 2023 / Online: 14 December 2023 (08:24:06 CET)
Version 2 : Received: 24 December 2023 / Approved: 26 December 2023 / Online: 26 December 2023 (09:54:09 CET)
Version 3 : Received: 7 March 2024 / Approved: 7 March 2024 / Online: 7 March 2024 (14:17:24 CET)
Version 4 : Received: 24 March 2024 / Approved: 25 March 2024 / Online: 26 March 2024 (08:24:14 CET)
Version 5 : Received: 26 March 2024 / Approved: 27 March 2024 / Online: 27 March 2024 (14:15:31 CET)
Version 6 : Received: 27 March 2024 / Approved: 28 March 2024 / Online: 28 March 2024 (13:31:01 CET)
Version 7 : Received: 2 April 2024 / Approved: 3 April 2024 / Online: 3 April 2024 (14:11:11 CEST)
Version 8 : Received: 7 April 2024 / Approved: 8 April 2024 / Online: 8 April 2024 (11:36:43 CEST)
Version 9 : Received: 11 April 2024 / Approved: 12 April 2024 / Online: 12 April 2024 (14:39:31 CEST)
Version 10 : Received: 13 April 2024 / Approved: 15 April 2024 / Online: 17 April 2024 (07:19:09 CEST)

How to cite: Migdal, A. Dual Theory of Decaying Turbulence: 1: Fermionic Representation. Preprints 2023, 2023121012. https://doi.org/10.20944/preprints202312.1012.v2 Migdal, A. Dual Theory of Decaying Turbulence: 1: Fermionic Representation. Preprints 2023, 2023121012. https://doi.org/10.20944/preprints202312.1012.v2

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MDPI and ACS Style

Migdal, A. Dual Theory of Decaying Turbulence: 1: Fermionic Representation. Preprints 2023, 2023121012. https://doi.org/10.20944/preprints202312.1012.v2

APA Style

Migdal, A. (2023). Dual Theory of Decaying Turbulence: 1: Fermionic Representation. Preprints. https://doi.org/10.20944/preprints202312.1012.v2

Chicago/Turabian Style

Migdal, A. 2023 "Dual Theory of Decaying Turbulence: 1: Fermionic Representation" Preprints. https://doi.org/10.20944/preprints202312.1012.v2

Abstract

This is the first paper in a cycle investigating the exact solution of the loop equation for decaying unforced turbulence in three dimensions, which we have found in the previous work. In this paper, we prove the exact equivalence of this solution (the Euler ensemble) to the theory of Fermi particles on a ring. The continuum limit of this theory will be studied in the next papers.

Keywords

Turbulence; fractal; anomalous dissipation; fixed point; velocity circulation; loop equations; Euler Phi; prime numbers

Subject

Physical Sciences, Fluids and Plasmas Physics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Comments (1)

Comment 1

Received: 26 December 2023
Commenter: Alexander Migdal
Commenter's Conflict of Interests: Author

Comment: Changed the physical introduction by adding a detailed comparison of our dual theory with available data on decaying turbulence. The main result (Quantum Trace Theorem) remains unchanged.

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