Chaotic behavior in the flow along a wedge modeled by the Blasius equation
The Blasius equation describes the properties of steady-state two dimensional boundary layer forming over a semi-infinite plate parallel to a unidirectional flow field. The flow is governed by a modified Blasius equation when the surface is aligned along the flow. In this paper, we demonstrate using...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2011-03-01
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| Series: | Nonlinear Processes in Geophysics |
| Online Access: | http://www.nonlin-processes-geophys.net/18/171/2011/npg-18-171-2011.pdf |
| _version_ | 1811274856208007168 |
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| author | B. Basu E. Foufoula-Georgiou A. S. Sharma |
| author_facet | B. Basu E. Foufoula-Georgiou A. S. Sharma |
| author_sort | B. Basu |
| collection | DOAJ |
| description | The Blasius equation describes the properties of steady-state two dimensional boundary layer forming over a semi-infinite plate parallel to a unidirectional flow field. The flow is governed by a modified Blasius equation when the surface is aligned along the flow. In this paper, we demonstrate using numerical solution, that as the wedge angle increases, bifurcation occurs in the nonlinear Blasius equation and the dynamics becomes chaotic leading to non-convergence of the solution once the angle exceeds a critical value of 22°. This critical value is found to be in agreement with experimental results showing the development of shock waves in the medium and also with analytical results showing multiple solutions for wedge angles exceeding a critical value. Finally, we provide a derivation of the equation governing the boundary layer flow for wedge angles exceeding the critical angle at the onset of chaos. |
| first_indexed | 2024-04-12T23:27:41Z |
| format | Article |
| id | doaj.art-fa8fdf226c0344d7afe44d53617aeb73 |
| institution | Directory Open Access Journal |
| issn | 1023-5809 1607-7946 |
| language | English |
| last_indexed | 2024-04-12T23:27:41Z |
| publishDate | 2011-03-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Nonlinear Processes in Geophysics |
| spelling | doaj.art-fa8fdf226c0344d7afe44d53617aeb732022-12-22T03:12:23ZengCopernicus PublicationsNonlinear Processes in Geophysics1023-58091607-79462011-03-0118217117810.5194/npg-18-171-2011Chaotic behavior in the flow along a wedge modeled by the Blasius equationB. BasuE. Foufoula-GeorgiouA. S. SharmaThe Blasius equation describes the properties of steady-state two dimensional boundary layer forming over a semi-infinite plate parallel to a unidirectional flow field. The flow is governed by a modified Blasius equation when the surface is aligned along the flow. In this paper, we demonstrate using numerical solution, that as the wedge angle increases, bifurcation occurs in the nonlinear Blasius equation and the dynamics becomes chaotic leading to non-convergence of the solution once the angle exceeds a critical value of 22°. This critical value is found to be in agreement with experimental results showing the development of shock waves in the medium and also with analytical results showing multiple solutions for wedge angles exceeding a critical value. Finally, we provide a derivation of the equation governing the boundary layer flow for wedge angles exceeding the critical angle at the onset of chaos.http://www.nonlin-processes-geophys.net/18/171/2011/npg-18-171-2011.pdf |
| spellingShingle | B. Basu E. Foufoula-Georgiou A. S. Sharma Chaotic behavior in the flow along a wedge modeled by the Blasius equation Nonlinear Processes in Geophysics |
| title | Chaotic behavior in the flow along a wedge modeled by the Blasius equation |
| title_full | Chaotic behavior in the flow along a wedge modeled by the Blasius equation |
| title_fullStr | Chaotic behavior in the flow along a wedge modeled by the Blasius equation |
| title_full_unstemmed | Chaotic behavior in the flow along a wedge modeled by the Blasius equation |
| title_short | Chaotic behavior in the flow along a wedge modeled by the Blasius equation |
| title_sort | chaotic behavior in the flow along a wedge modeled by the blasius equation |
| url | http://www.nonlin-processes-geophys.net/18/171/2011/npg-18-171-2011.pdf |
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