Effect of hyperviscosity on the Navier-Stokes turbulence
In this article, we modified the Navier-Stokes equations by adding a higher order artificial viscosity term to the conventional system. We first show that the solution of the regularized system converges strongly to the solution of the conventional system as the regularization parameter approach...
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| Format: | Article |
| Language: | English |
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Texas State University
2010-08-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2010/110/abstr.html |
| _version_ | 1819044033075347456 |
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| author | Abdelhafid Younsi |
| author_facet | Abdelhafid Younsi |
| author_sort | Abdelhafid Younsi |
| collection | DOAJ |
| description | In this article, we modified the Navier-Stokes equations by adding a higher order artificial viscosity term to the conventional system. We first show that the solution of the regularized system converges strongly to the solution of the conventional system as the regularization parameter approaches zero, for each dimension $dleq 4$. Then we show that the use of this artificial viscosity term leads to truncated the number of degrees of freedom in the long-time behavior of the solutions to these equations. This result suggests that the hyperviscous Navier-Stokes system is an interesting model for three-dimensional fluid turbulence. |
| first_indexed | 2024-12-21T10:06:14Z |
| format | Article |
| id | doaj.art-c230eb7007fe4f8099aef660ca7daab0 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-21T10:06:14Z |
| publishDate | 2010-08-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-c230eb7007fe4f8099aef660ca7daab02022-12-21T19:07:49ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912010-08-012010110,119Effect of hyperviscosity on the Navier-Stokes turbulenceAbdelhafid YounsiIn this article, we modified the Navier-Stokes equations by adding a higher order artificial viscosity term to the conventional system. We first show that the solution of the regularized system converges strongly to the solution of the conventional system as the regularization parameter approaches zero, for each dimension $dleq 4$. Then we show that the use of this artificial viscosity term leads to truncated the number of degrees of freedom in the long-time behavior of the solutions to these equations. This result suggests that the hyperviscous Navier-Stokes system is an interesting model for three-dimensional fluid turbulence.http://ejde.math.txstate.edu/Volumes/2010/110/abstr.htmlNavier-Stokes equationshyperviscosityweak solutionsattractor dimensionturbulence models |
| spellingShingle | Abdelhafid Younsi Effect of hyperviscosity on the Navier-Stokes turbulence Electronic Journal of Differential Equations Navier-Stokes equations hyperviscosity weak solutions attractor dimension turbulence models |
| title | Effect of hyperviscosity on the Navier-Stokes turbulence |
| title_full | Effect of hyperviscosity on the Navier-Stokes turbulence |
| title_fullStr | Effect of hyperviscosity on the Navier-Stokes turbulence |
| title_full_unstemmed | Effect of hyperviscosity on the Navier-Stokes turbulence |
| title_short | Effect of hyperviscosity on the Navier-Stokes turbulence |
| title_sort | effect of hyperviscosity on the navier stokes turbulence |
| topic | Navier-Stokes equations hyperviscosity weak solutions attractor dimension turbulence models |
| url | http://ejde.math.txstate.edu/Volumes/2010/110/abstr.html |
| work_keys_str_mv | AT abdelhafidyounsi effectofhyperviscosityonthenavierstokesturbulence |