Version 1
: Received: 30 August 2019 / Approved: 4 September 2019 / Online: 4 September 2019 (03:23:01 CEST)
Version 2
: Received: 23 October 2019 / Approved: 25 October 2019 / Online: 25 October 2019 (04:38:16 CEST)
Version 3
: Received: 11 October 2022 / Approved: 12 October 2022 / Online: 12 October 2022 (12:23:21 CEST)
How to cite:
Merz, T. Application of Local Gauge Theories to Fluid Mechanics Part 1 - Fluid Mechanics as a Local Gauge Theory and Relation to Navier-Stokes Equations. Preprints2019, 2019090038. https://doi.org/10.20944/preprints201909.0038.v3
Merz, T. Application of Local Gauge Theories to Fluid Mechanics Part 1 - Fluid Mechanics as a Local Gauge Theory and Relation to Navier-Stokes Equations. Preprints 2019, 2019090038. https://doi.org/10.20944/preprints201909.0038.v3
Merz, T. Application of Local Gauge Theories to Fluid Mechanics Part 1 - Fluid Mechanics as a Local Gauge Theory and Relation to Navier-Stokes Equations. Preprints2019, 2019090038. https://doi.org/10.20944/preprints201909.0038.v3
APA Style
Merz, T. (2022). Application of Local Gauge Theories to Fluid Mechanics Part 1 - Fluid Mechanics as a Local Gauge Theory and Relation to Navier-Stokes Equations. Preprints. https://doi.org/10.20944/preprints201909.0038.v3
Chicago/Turabian Style
Merz, T. 2022 "Application of Local Gauge Theories to Fluid Mechanics Part 1 - Fluid Mechanics as a Local Gauge Theory and Relation to Navier-Stokes Equations" Preprints. https://doi.org/10.20944/preprints201909.0038.v3
Abstract
The problem of fluid dynamics can be greatly simplified if, for every point in space, the strain-rate tensor is diagonalized. This tensor is introduced into the Navier-Stokes equations via material law and divergence of the stress tensor. This article shows that local SO(3)xU(1) gauge fields can be used to locally diagonalize the diffusion components of the strain-rate tensor. The gauge fields resulting from the connection can be interpreted as convection components of the flow, they show properties of quasiparticles and can be interpreted as elementary vortices. Thus, the proposed approach not only offers new insights for the solution and situative simplification of the Navier-Stokes equations, it also uncovers hidden symmetries within the flow convection, allowing - depending on boundary conditions - further interpretation.
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.
Received:
12 October 2022
Commenter:
Thomas Merz
Commenter's Conflict of Interests:
Author
Comment:
An introduction and texts for reader guidance at the beginning of the sections were added. Two arguments concerning the contiunation to complex numbers and the comparison with the Navier-Stokes equations have been clarified. The title has been expanded to distinguish between the first and second parts.
Commenter: Thomas Merz
Commenter's Conflict of Interests: Author
Two arguments concerning the contiunation to complex numbers and the comparison with the Navier-Stokes equations have been clarified.
The title has been expanded to distinguish between the first and second parts.