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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.18667 |
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| _version_ | 1866912084410761216 |
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| author | Wu, Jianfeng Ding, Lurong Lin, Hongtao Gao, Qi |
| author_facet | Wu, Jianfeng Ding, Lurong Lin, Hongtao Gao, Qi |
| contents | This study develops an effective theoretical framework that couples two vector fields: the velocity field $\mathbf{u}$ and an auxiliary vorticity field $\boldsymbolξ$. Together, these fields form a larger conserved dynamical system. Within this framework, the incompressible Navier-Stokes (NS) equation and a complementary vorticity equation with negative viscosity are derived. By introducing the concept of light-cone vorticity $\boldsymbolη_\pm = \mathbf{w} \pm \boldsymbolξ$, the paper constructs a unified framework for coupled dynamics. Furthermore, it explores the mechanism of spontaneous symmetry breaking from $SU(2)$ gauge theory to $U(1) \times U(1)$, which leads to the emergence of the coupled vector field theory in the non-relativistic limit. This approach uncovers a connection between fluid dynamics and fundamental gauge theories, suggesting that the NS equations describe a subsystem where dissipation results from energy transfer between the velocity and auxiliary fields. The study concludes by linking the complete dynamical framework to the Abrikosov-Nielsen-Olesen-Zumino (ANOZ) theory, a non-Abelian generalization of Bardeen-Cooper-Schrieffer (BCS) theory, offering new insights into fluid dynamics and quantum fluid theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18667 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Field Theory Framework of Incompressible Fluid Dynamics Wu, Jianfeng Ding, Lurong Lin, Hongtao Gao, Qi Fluid Dynamics High Energy Physics - Theory Mathematical Physics 76D05, 81T13 This study develops an effective theoretical framework that couples two vector fields: the velocity field $\mathbf{u}$ and an auxiliary vorticity field $\boldsymbolξ$. Together, these fields form a larger conserved dynamical system. Within this framework, the incompressible Navier-Stokes (NS) equation and a complementary vorticity equation with negative viscosity are derived. By introducing the concept of light-cone vorticity $\boldsymbolη_\pm = \mathbf{w} \pm \boldsymbolξ$, the paper constructs a unified framework for coupled dynamics. Furthermore, it explores the mechanism of spontaneous symmetry breaking from $SU(2)$ gauge theory to $U(1) \times U(1)$, which leads to the emergence of the coupled vector field theory in the non-relativistic limit. This approach uncovers a connection between fluid dynamics and fundamental gauge theories, suggesting that the NS equations describe a subsystem where dissipation results from energy transfer between the velocity and auxiliary fields. The study concludes by linking the complete dynamical framework to the Abrikosov-Nielsen-Olesen-Zumino (ANOZ) theory, a non-Abelian generalization of Bardeen-Cooper-Schrieffer (BCS) theory, offering new insights into fluid dynamics and quantum fluid theory. |
| title | A Field Theory Framework of Incompressible Fluid Dynamics |
| topic | Fluid Dynamics High Energy Physics - Theory Mathematical Physics 76D05, 81T13 |
| url | https://arxiv.org/abs/2410.18667 |