Distinction of turbulence from chaos - rough dependence on initial data
This article presents a new theory on the nature of turbulence: when the Reynolds number is large, violent fully developed turbulence is due to "rough dependence on initial data" rather than chaos which is caused by "sensitive dependence on initial data"; when the Reynolds num...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2014-04-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2014/104/abstr.html |
| _version_ | 1819205087797444608 |
|---|---|
| author | Y. Charles Li |
| author_facet | Y. Charles Li |
| author_sort | Y. Charles Li |
| collection | DOAJ |
| description | This article presents a new theory on the nature of turbulence:
when the Reynolds number is large, violent fully developed turbulence is due
to "rough dependence on initial data" rather than chaos which is caused by
"sensitive dependence on initial data"; when the Reynolds number is moderate,
(often transient) turbulence is due to chaos. The key in the validation
of the theory is estimating the temporal growth of the initial perturbations
with the Reynolds number as a parameter. Analytically, this amounts
to estimating the temporal growth of the norm of the derivative of the solution |
| first_indexed | 2024-12-23T04:46:08Z |
| format | Article |
| id | doaj.art-a0bf6c76b9944851aa7296670285e755 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-23T04:46:08Z |
| publishDate | 2014-04-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-a0bf6c76b9944851aa7296670285e7552022-12-21T17:59:38ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912014-04-012014104,18Distinction of turbulence from chaos - rough dependence on initial dataY. Charles Li0 Univ. of Missouri, Columbia, MO, USA This article presents a new theory on the nature of turbulence: when the Reynolds number is large, violent fully developed turbulence is due to "rough dependence on initial data" rather than chaos which is caused by "sensitive dependence on initial data"; when the Reynolds number is moderate, (often transient) turbulence is due to chaos. The key in the validation of the theory is estimating the temporal growth of the initial perturbations with the Reynolds number as a parameter. Analytically, this amounts to estimating the temporal growth of the norm of the derivative of the solutionhttp://ejde.math.txstate.edu/Volumes/2014/104/abstr.htmlRough dependence on initial datachaosturbulencedependence on initial data |
| spellingShingle | Y. Charles Li Distinction of turbulence from chaos - rough dependence on initial data Electronic Journal of Differential Equations Rough dependence on initial data chaos turbulence dependence on initial data |
| title | Distinction of turbulence from chaos - rough dependence on initial data |
| title_full | Distinction of turbulence from chaos - rough dependence on initial data |
| title_fullStr | Distinction of turbulence from chaos - rough dependence on initial data |
| title_full_unstemmed | Distinction of turbulence from chaos - rough dependence on initial data |
| title_short | Distinction of turbulence from chaos - rough dependence on initial data |
| title_sort | distinction of turbulence from chaos rough dependence on initial data |
| topic | Rough dependence on initial data chaos turbulence dependence on initial data |
| url | http://ejde.math.txstate.edu/Volumes/2014/104/abstr.html |
| work_keys_str_mv | AT ycharlesli distinctionofturbulencefromchaosroughdependenceoninitialdata |