The set-down and set-up of directionally spread and crossing surface gravity wave groups
For sufficiently directionally spread surface gravity wave groups, the set-down of the wave-averaged free surface, first described by Longuet-Higgins and Stewart (J. Fluid Mech. vol. 13, 1962, pp. 481–504), can turn into a set-up. Using a multiple-scale expansion for two crossing wave groups, we ex...
| मुख्य लेखकों: | , , , |
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| स्वरूप: | Journal article |
| प्रकाशित: |
Cambridge University
2017
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| _version_ | 1826304908078350336 |
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| author | McAllister, ML Adcock, TAA Taylor, PH van den Bremer, TS |
| author_facet | McAllister, ML Adcock, TAA Taylor, PH van den Bremer, TS |
| author_sort | McAllister, ML |
| collection | OXFORD |
| description | For sufficiently directionally spread surface gravity wave groups, the set-down of the wave-averaged free surface, first described by Longuet-Higgins and Stewart (J. Fluid Mech. vol. 13, 1962, pp. 481–504), can turn into a set-up. Using a multiple-scale expansion for two crossing wave groups, we examine the structure and magnitude of this wave-averaged set-up, which is part of a crossing wave pattern that behaves as a modulated partial standing wave: in space, it consists of a rapidly varying standing-wave pattern slowly modulated by the product of the envelopes of the two groups; in time, it grows and decays on the slow time scale associated with the translation of the groups. Whether this crossing wave pattern actually enhances the surface elevation at the point of focus depends on the phases of the linear wave groups, unlike the set-down, which is always negative and inherits the spatial structure of the underlying envelope(s). We present detailed laboratory measurements of the wave-averaged free surface, examining both single wave groups, varying the degree of spreading from small to very large, and the interaction between two wave groups, varying both the degree of spreading and the crossing angle between the groups. In both cases, we find good agreement between the experiments, our simple expressions for the set-down and set-up, and existing second-order theory based on the component-by-component interaction of individual waves with different frequencies and directions. We predict and observe a set-up for wave groups with a Gaussian angular amplitude distribution with standard deviations of above (Formula presented.) ((Formula presented.) for energy spectra), which is relatively large for realistic sea states, and for crossing sea states with angles of separation of (Formula presented.) and above, which are known to occur in the ocean. |
| first_indexed | 2024-03-07T06:24:50Z |
| format | Journal article |
| id | oxford-uuid:f3edb5af-9e07-4b27-8159-c66d2ab6f3f9 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:24:50Z |
| publishDate | 2017 |
| publisher | Cambridge University |
| record_format | dspace |
| spelling | oxford-uuid:f3edb5af-9e07-4b27-8159-c66d2ab6f3f92022-03-27T12:15:55ZThe set-down and set-up of directionally spread and crossing surface gravity wave groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f3edb5af-9e07-4b27-8159-c66d2ab6f3f9Symplectic Elements at OxfordCambridge University2017McAllister, MLAdcock, TAATaylor, PHvan den Bremer, TS For sufficiently directionally spread surface gravity wave groups, the set-down of the wave-averaged free surface, first described by Longuet-Higgins and Stewart (J. Fluid Mech. vol. 13, 1962, pp. 481–504), can turn into a set-up. Using a multiple-scale expansion for two crossing wave groups, we examine the structure and magnitude of this wave-averaged set-up, which is part of a crossing wave pattern that behaves as a modulated partial standing wave: in space, it consists of a rapidly varying standing-wave pattern slowly modulated by the product of the envelopes of the two groups; in time, it grows and decays on the slow time scale associated with the translation of the groups. Whether this crossing wave pattern actually enhances the surface elevation at the point of focus depends on the phases of the linear wave groups, unlike the set-down, which is always negative and inherits the spatial structure of the underlying envelope(s). We present detailed laboratory measurements of the wave-averaged free surface, examining both single wave groups, varying the degree of spreading from small to very large, and the interaction between two wave groups, varying both the degree of spreading and the crossing angle between the groups. In both cases, we find good agreement between the experiments, our simple expressions for the set-down and set-up, and existing second-order theory based on the component-by-component interaction of individual waves with different frequencies and directions. We predict and observe a set-up for wave groups with a Gaussian angular amplitude distribution with standard deviations of above (Formula presented.) ((Formula presented.) for energy spectra), which is relatively large for realistic sea states, and for crossing sea states with angles of separation of (Formula presented.) and above, which are known to occur in the ocean. |
| spellingShingle | McAllister, ML Adcock, TAA Taylor, PH van den Bremer, TS The set-down and set-up of directionally spread and crossing surface gravity wave groups |
| title | The set-down and set-up of directionally spread and crossing surface gravity wave groups |
| title_full | The set-down and set-up of directionally spread and crossing surface gravity wave groups |
| title_fullStr | The set-down and set-up of directionally spread and crossing surface gravity wave groups |
| title_full_unstemmed | The set-down and set-up of directionally spread and crossing surface gravity wave groups |
| title_short | The set-down and set-up of directionally spread and crossing surface gravity wave groups |
| title_sort | set down and set up of directionally spread and crossing surface gravity wave groups |
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