Surface wavepackets subject to an abrupt depth change. Part 1. Second-order theory
This paper develops second-order theory for narrow-banded surface gravity wavepackets experiencing a sudden depth transition based on a Stokes and multiple-scales expansion. As a wavepacket travels over a sudden depth transition, additional wavepackets are generated that propagate freely obeying the...
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| Veröffentlicht in: | Journal of fluid mechanics Jg. 915 |
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| Hauptverfasser: | , , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
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Cambridge, UK
Cambridge University Press
19.03.2021
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| ISSN: | 0022-1120, 1469-7645 |
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| Abstract | This paper develops second-order theory for narrow-banded surface gravity wavepackets experiencing a sudden depth transition based on a Stokes and multiple-scales expansion. As a wavepacket travels over a sudden depth transition, additional wavepackets are generated that propagate freely obeying the linear dispersion relation and arise at both first and second order in wave steepness in a Stokes expansion. In the region near the top of the depth transition, the resulting transient processes play a crucial role. At second order in wave steepness, free and bound waves coexist with different phases. Their different speeds of travel result in a local peak a certain distance after the depth transition. This distance depends on the water depth $h_s$ relative to the carrier wavelength on the shallower side $\lambda _{0s}$. We validate our theory through comparison with fully nonlinear numerical simulations. Experimental validation is provided in a companion paper (Li et al, J. Fluid Mech., 2021, 915, A72). We conjecture that the combination of the local transient peak at second order and the magnitude of the linear free waves provides the explanation for the rogue waves observed after a sudden depth transition reported in a significant number of papers and reviewed in Trulsen etal (J. Fluid Mech., vol. 882, 2020, R2). |
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| AbstractList | This paper develops second-order theory for narrow-banded surface gravity wavepackets experiencing a sudden depth transition based on a Stokes and multiple-scales expansion. As a wavepacket travels over a sudden depth transition, additional wavepackets are generated that propagate freely obeying the linear dispersion relation and arise at both first and second order in wave steepness in a Stokes expansion. In the region near the top of the depth transition, the resulting transient processes play a crucial role. At second order in wave steepness, free and bound waves coexist with different phases. Their different speeds of travel result in a local peak a certain distance after the depth transition. This distance depends on the water depth $h_s$ relative to the carrier wavelength on the shallower side $\lambda _{0s}$. We validate our theory through comparison with fully nonlinear numerical simulations. Experimental validation is provided in a companion paper (Li et al, J. Fluid Mech., 2021, 915, A72). We conjecture that the combination of the local transient peak at second order and the magnitude of the linear free waves provides the explanation for the rogue waves observed after a sudden depth transition reported in a significant number of papers and reviewed in Trulsen etal (J. Fluid Mech., vol. 882, 2020, R2). This paper develops second-order theory for narrow-banded surface gravity wavepackets experiencing a sudden depth transition based on a Stokes and multiple-scales expansion. As a wavepacket travels over a sudden depth transition, additional wavepackets are generated that propagate freely obeying the linear dispersion relation and arise at both first and second order in wave steepness in a Stokes expansion. In the region near the top of the depth transition, the resulting transient processes play a crucial role. At second order in wave steepness, free and bound waves coexist with different phases. Their different speeds of travel result in a local peak a certain distance after the depth transition. This distance depends on the water depth $h_s$ relative to the carrier wavelength on the shallower side $\lambda _{0s}$ . We validate our theory through comparison with fully nonlinear numerical simulations. Experimental validation is provided in a companion paper (Li et al , J. Fluid Mech. , 2021, 915, A72). We conjecture that the combination of the local transient peak at second order and the magnitude of the linear free waves provides the explanation for the rogue waves observed after a sudden depth transition reported in a significant number of papers and reviewed in Trulsen etal ( J. Fluid Mech. , vol. 882, 2020, R2). |
| ArticleNumber | A71 |
| Author | Lin, Zhiliang Zheng, Yaokun Adcock, Thomas A.A. van den Bremer, Ton S. Li, Yan |
| Author_xml | – sequence: 1 givenname: Yan orcidid: 0000-0001-8925-3749 surname: Li fullname: Li, Yan email: yan.li@ntnu.no organization: 1Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK – sequence: 2 givenname: Yaokun surname: Zheng fullname: Zheng, Yaokun organization: 3State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China – sequence: 3 givenname: Zhiliang surname: Lin fullname: Lin, Zhiliang organization: 3State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China – sequence: 4 givenname: Thomas A.A. orcidid: 0000-0001-7556-1193 surname: Adcock fullname: Adcock, Thomas A.A. organization: 1Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK – sequence: 5 givenname: Ton S. orcidid: 0000-0001-6154-3357 surname: van den Bremer fullname: van den Bremer, Ton S. organization: 1Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK |
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| Keywords | coastal engineering surface gravity waves |
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| Title | Surface wavepackets subject to an abrupt depth change. Part 1. Second-order theory |
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