Nonlinear Waves Passing over Rectangular Obstacles: Multimodal Method and Experimental Validation
We report a theoretical and experimental investigation of the propagation of nonlinear waves passing over a submerged rectangular step. A multimodal method allows calculating the first- and second-order reflected and transmitted waves. In particular, at the second order, the propagation of free and...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-04-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/7/5/145 |
| _version_ | 1797499991306010624 |
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| author | Eduardo Monsalve Agnès Maurel Vincent Pagneux Philippe Petitjeans |
| author_facet | Eduardo Monsalve Agnès Maurel Vincent Pagneux Philippe Petitjeans |
| author_sort | Eduardo Monsalve |
| collection | DOAJ |
| description | We report a theoretical and experimental investigation of the propagation of nonlinear waves passing over a submerged rectangular step. A multimodal method allows calculating the first- and second-order reflected and transmitted waves. In particular, at the second order, the propagation of free and bound waves is theoretically presented. A detailed analysis of the convergence of the second-order problem shows that a finite truncation of the series of evanescent bound waves is necessary to obtain a smooth and convergent solution. The computed coefficients of the first and second harmonics are experimentally validated via a complete space-time-resolved measurements of the wave propagation, which permits us to verify the relative amplitude, phase and spatial interference (beating) of the free and bound waves at the second order. This result can be useful in future multimodal models since it not only keeps the accuracy of the model with the inclusion of the first part of the evanescent bound terms (being also the dominants) but also ensures the convergence of the multimodal computation with an error that decreases as a function of the number of modes. |
| first_indexed | 2024-03-10T03:55:25Z |
| format | Article |
| id | doaj.art-b367204537384fdc81245298674666de |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-10T03:55:25Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-b367204537384fdc81245298674666de2023-11-23T10:57:41ZengMDPI AGFluids2311-55212022-04-017514510.3390/fluids7050145Nonlinear Waves Passing over Rectangular Obstacles: Multimodal Method and Experimental ValidationEduardo Monsalve0Agnès Maurel1Vincent Pagneux2Philippe Petitjeans3Laboratoire de Physique et Mécanique des Milieux Hétérogènes, UMR CNRS 7636, ESPCI-Paris, PSL Research University, Sorbonne Université, Paris Diderot University, CEDEX 5, 75231 Paris, FranceInstitut Langevin, UMR CNRS 7587, ESPCI-Paris, 75005 Paris, FranceLaboratoire d’Acoustique de l’Université du Maine, UMR CNRS 6613, CEDEX 9, 72085 Le Mans, FranceLaboratoire de Physique et Mécanique des Milieux Hétérogènes, UMR CNRS 7636, ESPCI-Paris, PSL Research University, Sorbonne Université, Paris Diderot University, CEDEX 5, 75231 Paris, FranceWe report a theoretical and experimental investigation of the propagation of nonlinear waves passing over a submerged rectangular step. A multimodal method allows calculating the first- and second-order reflected and transmitted waves. In particular, at the second order, the propagation of free and bound waves is theoretically presented. A detailed analysis of the convergence of the second-order problem shows that a finite truncation of the series of evanescent bound waves is necessary to obtain a smooth and convergent solution. The computed coefficients of the first and second harmonics are experimentally validated via a complete space-time-resolved measurements of the wave propagation, which permits us to verify the relative amplitude, phase and spatial interference (beating) of the free and bound waves at the second order. This result can be useful in future multimodal models since it not only keeps the accuracy of the model with the inclusion of the first part of the evanescent bound terms (being also the dominants) but also ensures the convergence of the multimodal computation with an error that decreases as a function of the number of modes.https://www.mdpi.com/2311-5521/7/5/145nonlinear waveswater wavesfree wavesbound wavessubmerged obstacle |
| spellingShingle | Eduardo Monsalve Agnès Maurel Vincent Pagneux Philippe Petitjeans Nonlinear Waves Passing over Rectangular Obstacles: Multimodal Method and Experimental Validation Fluids nonlinear waves water waves free waves bound waves submerged obstacle |
| title | Nonlinear Waves Passing over Rectangular Obstacles: Multimodal Method and Experimental Validation |
| title_full | Nonlinear Waves Passing over Rectangular Obstacles: Multimodal Method and Experimental Validation |
| title_fullStr | Nonlinear Waves Passing over Rectangular Obstacles: Multimodal Method and Experimental Validation |
| title_full_unstemmed | Nonlinear Waves Passing over Rectangular Obstacles: Multimodal Method and Experimental Validation |
| title_short | Nonlinear Waves Passing over Rectangular Obstacles: Multimodal Method and Experimental Validation |
| title_sort | nonlinear waves passing over rectangular obstacles multimodal method and experimental validation |
| topic | nonlinear waves water waves free waves bound waves submerged obstacle |
| url | https://www.mdpi.com/2311-5521/7/5/145 |
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