A paradox of the Navier-Stokes turbulence
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918466955509760 |
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| author | Qin, Shijie Xu, Kun Liao, Shijun |
| author_facet | Qin, Shijie Xu, Kun Liao, Shijun |
| contents | The Navier-Stokes (NS) equations as a turbulence model have been widely applied in lots of fields. The NS equations contain such a fundamental assumption that all small physical/artificial disturbances could be neglected. Is this assumption correct? In this paper a two-dimensional Rayleigh-Bénard convection governed by the NS equations is predicted by traditional direct numerical simulation (DNS) using double precision arithmetic and a range of different time-steps. It is found that the final flow type tends either to vortical flow or zonal flow, whose statistics are completely different. Notably, these two flow types frequently alternate as the time-step is reduced to a very small value, suggesting that the time-step corresponding to each turbulent flow type should be densely distributed. Thus, stochastic numerical noise exerts a huge influence on the final flow type and statistics of numerically simulated NS turbulence because the time-step has a close relationship with numerical noise. This clearly indicates that small disturbances have significant influences on the NS turbulence, which therefore should not be neglected. This leads to a logical paradox for the NS turbulence, which is a great challenge for us, although a paradox often leads to some significant breakthroughs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11220 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A paradox of the Navier-Stokes turbulence Qin, Shijie Xu, Kun Liao, Shijun Fluid Dynamics Chaotic Dynamics Computational Physics The Navier-Stokes (NS) equations as a turbulence model have been widely applied in lots of fields. The NS equations contain such a fundamental assumption that all small physical/artificial disturbances could be neglected. Is this assumption correct? In this paper a two-dimensional Rayleigh-Bénard convection governed by the NS equations is predicted by traditional direct numerical simulation (DNS) using double precision arithmetic and a range of different time-steps. It is found that the final flow type tends either to vortical flow or zonal flow, whose statistics are completely different. Notably, these two flow types frequently alternate as the time-step is reduced to a very small value, suggesting that the time-step corresponding to each turbulent flow type should be densely distributed. Thus, stochastic numerical noise exerts a huge influence on the final flow type and statistics of numerically simulated NS turbulence because the time-step has a close relationship with numerical noise. This clearly indicates that small disturbances have significant influences on the NS turbulence, which therefore should not be neglected. This leads to a logical paradox for the NS turbulence, which is a great challenge for us, although a paradox often leads to some significant breakthroughs. |
| title | A paradox of the Navier-Stokes turbulence |
| topic | Fluid Dynamics Chaotic Dynamics Computational Physics |
| url | https://arxiv.org/abs/2510.11220 |