Ultra-chaotic property of Navier-Stokes turbulence
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915960174149632 |
|---|---|
| author | Qin, Shijie Xu, Kun Liao, Shijun |
| author_facet | Qin, Shijie Xu, Kun Liao, Shijun |
| contents | A chaotic system is called ultra-chaos when its statistics have sensitivity dependence on initial condition and/or other small disturbances. In this paper, using two-dimensional turbulent Kolmogorov flow as an example, we illustrate that tiny variation of initial condition of Navier-Stokes equations can lead to huge differences not only in spatiotemporal trajectory but also in flow symmetry and its statistics. Here, in order to avoid the influence of artificial numerical noise, we apply ``clean numerical simulation'' (CNS) which can guarantee that the numerical noise can be reduced to such a desired low level that they are negligible in a time interval long enough for calculating statistics. This discovery highly suggests that the Navier-Stokes turbulence (i.e. turbulence governed by the Navier-Stokes equations) might be an ultra-chaos, say, small disturbances must be considered even from viewpoint of statistics. This however leads to a paradox in logic, since small disturbances, which are unavoidable in practice, are unfortunately neglected by the Navier-Stokes turbulence. Some fundamental characteristics of turbulence model are discussed and suggested in general meanings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06620 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ultra-chaotic property of Navier-Stokes turbulence Qin, Shijie Xu, Kun Liao, Shijun Chaotic Dynamics Fluid Dynamics A chaotic system is called ultra-chaos when its statistics have sensitivity dependence on initial condition and/or other small disturbances. In this paper, using two-dimensional turbulent Kolmogorov flow as an example, we illustrate that tiny variation of initial condition of Navier-Stokes equations can lead to huge differences not only in spatiotemporal trajectory but also in flow symmetry and its statistics. Here, in order to avoid the influence of artificial numerical noise, we apply ``clean numerical simulation'' (CNS) which can guarantee that the numerical noise can be reduced to such a desired low level that they are negligible in a time interval long enough for calculating statistics. This discovery highly suggests that the Navier-Stokes turbulence (i.e. turbulence governed by the Navier-Stokes equations) might be an ultra-chaos, say, small disturbances must be considered even from viewpoint of statistics. This however leads to a paradox in logic, since small disturbances, which are unavoidable in practice, are unfortunately neglected by the Navier-Stokes turbulence. Some fundamental characteristics of turbulence model are discussed and suggested in general meanings. |
| title | Ultra-chaotic property of Navier-Stokes turbulence |
| topic | Chaotic Dynamics Fluid Dynamics |
| url | https://arxiv.org/abs/2510.06620 |