Non-classical shallow water flows
This paper deals with violent discontinuities in shallow water flows with large Froude number F. On a horizontal base, the paradigm problem is that of the impact of two fluid layers in situations where the flow can be modelled as two smooth regions joined by a singularity in the flow field. Within t...
| Prif Awduron: | , , , |
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| Fformat: | Journal article |
| Iaith: | English |
| Cyhoeddwyd: |
2008
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| _version_ | 1826280166809141248 |
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| author | Edwards, C Howison, S Ockendon, H Ockendon, J |
| author_facet | Edwards, C Howison, S Ockendon, H Ockendon, J |
| author_sort | Edwards, C |
| collection | OXFORD |
| description | This paper deals with violent discontinuities in shallow water flows with large Froude number F. On a horizontal base, the paradigm problem is that of the impact of two fluid layers in situations where the flow can be modelled as two smooth regions joined by a singularity in the flow field. Within the framework of shallow water theory, we show that, over a certain time-scale, this discontinuity may be described by a delta shock, which is a weak solution of the underlying conservation laws in which the depth and mass and momentum fluxes have both delta function and step function components. We also make some conjectures about how this model evolves from the traditional model for jet impacts in which a spout is emitted. For flows on a sloping base, we show that for flow with an aspect ratio of O( F -2) on a base with an O(1) or larger slope, the governing equations admit a new type of discontinuous solution that is also modelled as a delta shock. The physical manifestation of this discontinuity is a small 'tube' of fluid bounding the flow. The delta-shock conditions for this flow are derived and solved for a point source on an inclined plane. This latter delta-shock framework also sheds light on the evolution of the layer impact on a horizontal base. © The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. |
| first_indexed | 2024-03-07T00:09:38Z |
| format | Journal article |
| id | oxford-uuid:78c734ac-f489-4c8d-9ec9-1451d913b9cb |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:09:38Z |
| publishDate | 2008 |
| record_format | dspace |
| spelling | oxford-uuid:78c734ac-f489-4c8d-9ec9-1451d913b9cb2022-03-26T20:32:55ZNon-classical shallow water flowsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:78c734ac-f489-4c8d-9ec9-1451d913b9cbEnglishSymplectic Elements at Oxford2008Edwards, CHowison, SOckendon, HOckendon, JThis paper deals with violent discontinuities in shallow water flows with large Froude number F. On a horizontal base, the paradigm problem is that of the impact of two fluid layers in situations where the flow can be modelled as two smooth regions joined by a singularity in the flow field. Within the framework of shallow water theory, we show that, over a certain time-scale, this discontinuity may be described by a delta shock, which is a weak solution of the underlying conservation laws in which the depth and mass and momentum fluxes have both delta function and step function components. We also make some conjectures about how this model evolves from the traditional model for jet impacts in which a spout is emitted. For flows on a sloping base, we show that for flow with an aspect ratio of O( F -2) on a base with an O(1) or larger slope, the governing equations admit a new type of discontinuous solution that is also modelled as a delta shock. The physical manifestation of this discontinuity is a small 'tube' of fluid bounding the flow. The delta-shock conditions for this flow are derived and solved for a point source on an inclined plane. This latter delta-shock framework also sheds light on the evolution of the layer impact on a horizontal base. © The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. |
| spellingShingle | Edwards, C Howison, S Ockendon, H Ockendon, J Non-classical shallow water flows |
| title | Non-classical shallow water flows |
| title_full | Non-classical shallow water flows |
| title_fullStr | Non-classical shallow water flows |
| title_full_unstemmed | Non-classical shallow water flows |
| title_short | Non-classical shallow water flows |
| title_sort | non classical shallow water flows |
| work_keys_str_mv | AT edwardsc nonclassicalshallowwaterflows AT howisons nonclassicalshallowwaterflows AT ockendonh nonclassicalshallowwaterflows AT ockendonj nonclassicalshallowwaterflows |