Models for thin viscous sheets
Leading-order equations governing the dynamics of a two-dimensional thin viscous sheet are derived. The inclusion of inertia effects is found to result in an ill-posed model when the sheet is compressed, and the resulting paradox is resolved by rescaling the equations over new length- and timescales...
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| Format: | Journal article |
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1996
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| _version_ | 1797070673942675456 |
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| author | Howell, P |
| author_facet | Howell, P |
| author_sort | Howell, P |
| collection | OXFORD |
| description | Leading-order equations governing the dynamics of a two-dimensional thin viscous sheet are derived. The inclusion of inertia effects is found to result in an ill-posed model when the sheet is compressed, and the resulting paradox is resolved by rescaling the equations over new length- and timescales which depend on the Reynolds number of the flow and the aspect ratio of the sheet. Physically this implies a dominant lengthscale for transverse displacements during viscous buckling. The theory is generalised to give new models for fully three-dimensional sheets. |
| first_indexed | 2024-03-06T22:42:18Z |
| format | Journal article |
| id | oxford-uuid:5bfed38c-f279-4636-8af1-f0abc02cf9ff |
| institution | University of Oxford |
| last_indexed | 2024-03-06T22:42:18Z |
| publishDate | 1996 |
| record_format | dspace |
| spelling | oxford-uuid:5bfed38c-f279-4636-8af1-f0abc02cf9ff2022-03-26T17:25:28ZModels for thin viscous sheetsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:5bfed38c-f279-4636-8af1-f0abc02cf9ffMathematical Institute - ePrints1996Howell, PLeading-order equations governing the dynamics of a two-dimensional thin viscous sheet are derived. The inclusion of inertia effects is found to result in an ill-posed model when the sheet is compressed, and the resulting paradox is resolved by rescaling the equations over new length- and timescales which depend on the Reynolds number of the flow and the aspect ratio of the sheet. Physically this implies a dominant lengthscale for transverse displacements during viscous buckling. The theory is generalised to give new models for fully three-dimensional sheets. |
| spellingShingle | Howell, P Models for thin viscous sheets |
| title | Models for thin viscous sheets |
| title_full | Models for thin viscous sheets |
| title_fullStr | Models for thin viscous sheets |
| title_full_unstemmed | Models for thin viscous sheets |
| title_short | Models for thin viscous sheets |
| title_sort | models for thin viscous sheets |
| work_keys_str_mv | AT howellp modelsforthinviscoussheets |