Oblique sub- and super-harmonic Bragg resonance of surface waves by bottom ripples
We consider a class of higher order (quartet) Bragg resonance involving two incident wave components and a bottom ripple component (so called class III Bragg resonance). In this case, unlike class I/II Bragg resonance involving a single incident wave and one/two bottom ripple components, the frequen...
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| Format: | Article |
| Language: | en_US |
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Cambridge University Press
2013
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| Online Access: | http://hdl.handle.net/1721.1/82516 https://orcid.org/0000-0003-1273-9964 |
| _version_ | 1826192068071915520 |
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| author | Alam, Mohammad-Reza Liu, Yuming Yue, Dick K. P. |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Alam, Mohammad-Reza Liu, Yuming Yue, Dick K. P. |
| author_sort | Alam, Mohammad-Reza |
| collection | MIT |
| description | We consider a class of higher order (quartet) Bragg resonance involving two incident wave components and a bottom ripple component (so called class III Bragg resonance). In this case, unlike class I/II Bragg resonance involving a single incident wave and one/two bottom ripple components, the frequency of the resonant wave, which can be reflected or transmitted, is a sum or difference of the incident wave frequencies. In addition to transferring energy across the spectrum leading to potentially significant spectral transformation, such resonances may generate long (infragravity) waves of special importance to coastal processes and engineering applications. Of particular interest here is the case where the incident waves are oblique to the bottom undulations (or to each other) which leads to new and unexpected wave configurations. We elucidate the general conditions for such resonances, offering a simple geometric construction for obtaining these. Perturbation analysis results are obtained for these resonances predicting the evolutions of the resonant and incident wave amplitudes. We investigate special cases using numerical simulations (applying a high-order spectral method) and compare the results to perturbation theory: infragravity wave generation by co- and counter-propagating incident waves normal to bottom undulations; longshore long waves generated by (bottom) oblique incident waves; and propagating–standing resonant waves due to (bottom) parallel incident waves. Finally, we consider a case of multiple resonance due to oblique incident waves on bottom ripples which leads to complex wave creation and transformations not easily tractable with perturbation theory. These new wave resonance mechanisms can be of potential importance on continental shelves and in littoral zones, contributing to wave spectral evolution and bottom processes such as sandbar formation. |
| first_indexed | 2024-09-23T09:05:47Z |
| format | Article |
| id | mit-1721.1/82516 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:05:47Z |
| publishDate | 2013 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | mit-1721.1/825162022-09-30T13:22:25Z Oblique sub- and super-harmonic Bragg resonance of surface waves by bottom ripples Alam, Mohammad-Reza Liu, Yuming Yue, Dick K. P. Massachusetts Institute of Technology. Department of Mechanical Engineering Massachusetts Institute of Technology. School of Engineering Alam, Mohammad-Reza Liu, Yuming Yue, Dick K. P. We consider a class of higher order (quartet) Bragg resonance involving two incident wave components and a bottom ripple component (so called class III Bragg resonance). In this case, unlike class I/II Bragg resonance involving a single incident wave and one/two bottom ripple components, the frequency of the resonant wave, which can be reflected or transmitted, is a sum or difference of the incident wave frequencies. In addition to transferring energy across the spectrum leading to potentially significant spectral transformation, such resonances may generate long (infragravity) waves of special importance to coastal processes and engineering applications. Of particular interest here is the case where the incident waves are oblique to the bottom undulations (or to each other) which leads to new and unexpected wave configurations. We elucidate the general conditions for such resonances, offering a simple geometric construction for obtaining these. Perturbation analysis results are obtained for these resonances predicting the evolutions of the resonant and incident wave amplitudes. We investigate special cases using numerical simulations (applying a high-order spectral method) and compare the results to perturbation theory: infragravity wave generation by co- and counter-propagating incident waves normal to bottom undulations; longshore long waves generated by (bottom) oblique incident waves; and propagating–standing resonant waves due to (bottom) parallel incident waves. Finally, we consider a case of multiple resonance due to oblique incident waves on bottom ripples which leads to complex wave creation and transformations not easily tractable with perturbation theory. These new wave resonance mechanisms can be of potential importance on continental shelves and in littoral zones, contributing to wave spectral evolution and bottom processes such as sandbar formation. United States. Office of Naval Research 2013-11-19T21:27:13Z 2013-11-19T21:27:13Z 2010-01 2009-10 Article http://purl.org/eprint/type/JournalArticle 0022-1120 1469-7645 http://hdl.handle.net/1721.1/82516 ALAM, MOHAMMAD-REZA, YUMING LIU, and DICK K. P. YUE. Oblique Sub- and Super-harmonic Bragg Resonance of Surface Waves by Bottom Ripples. Journal of Fluid Mechanics 643 (January 15, 2010): 437. https://orcid.org/0000-0003-1273-9964 en_US http://dx.doi.org/10.1017/s0022112009992850 Journal of Fluid Mechanics Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Cambridge University Press MIT web domain |
| spellingShingle | Alam, Mohammad-Reza Liu, Yuming Yue, Dick K. P. Oblique sub- and super-harmonic Bragg resonance of surface waves by bottom ripples |
| title | Oblique sub- and super-harmonic Bragg resonance of surface waves by bottom ripples |
| title_full | Oblique sub- and super-harmonic Bragg resonance of surface waves by bottom ripples |
| title_fullStr | Oblique sub- and super-harmonic Bragg resonance of surface waves by bottom ripples |
| title_full_unstemmed | Oblique sub- and super-harmonic Bragg resonance of surface waves by bottom ripples |
| title_short | Oblique sub- and super-harmonic Bragg resonance of surface waves by bottom ripples |
| title_sort | oblique sub and super harmonic bragg resonance of surface waves by bottom ripples |
| url | http://hdl.handle.net/1721.1/82516 https://orcid.org/0000-0003-1273-9964 |
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