A normal form of thin fluid film equations solves the transient paradox
Article
Roberts, A. J.. 2006. "A normal form of thin fluid film equations solves the transient paradox." Physica D: Nonlinear Phenomena. 223 (1), pp. 69-81. https://doi.org/10.1016/j.physd.2006.08.018
| Article Title | A normal form of thin fluid film equations solves the transient paradox |
|---|---|
| ERA Journal ID | 352 |
| Article Category | Article |
| Authors | |
| Author | Roberts, A. J. |
| Journal Title | Physica D: Nonlinear Phenomena |
| Journal Citation | 223 (1), pp. 69-81 |
| Number of Pages | 12 |
| Year | 2006 |
| Place of Publication | Amsterdam, Netherlands |
| ISSN | 0167-2789 |
| 1872-8022 | |
| Digital Object Identifier (DOI) | https://doi.org/10.1016/j.physd.2006.08.018 |
| Abstract | Imagine two constant thickness, thin films of fluid colliding together: the transient flow forms a hump where they collide; thereafter they slowly relax. But, apparently reliable lubrication models expressed only in the thickness of the fluid forecast that precisely nothing happens. How can we resolve this paradox? Dynamical systems theory constructs a normal form of the Navier–Stokes equations for the flow of a thin layer of fluid upon a solid substrate. These normal form equations illuminate the fluid dynamics by decoupling the interesting long-term ‘lubrication’ flow from the rapid viscous decay of transient shear modes. The normal form clearly shows the slow manifold of the lubrication model and demonstrates that |
| Keywords | normal form; thin fluid film; lubrication model; nitial conditions; slow manifold |
| ANZSRC Field of Research 2020 | 401207. Fundamental and theoretical fluid dynamics |
| 401204. Computational methods in fluid flow, heat and mass transfer (incl. computational fluid dynamics) | |
| Public Notes | File reproduced in accordance with the copyright policy of the publisher/author. |
| Byline Affiliations | Department of Mathematics and Computing |
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