A Comparative Study on Generation and Propagation of Nonlinear Waves in Shallow Waters
This study is concerned with the generation and propagation of strongly nonlinear waves in shallow water. A numerical wave flume is developed where nonlinear waves of solitary and cnoidal types are generated by use of the Level I Green-Naghdi (GN) equations by a piston-type wavemaker. Waves generate...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Journal of Marine Science and Engineering |
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| Online Access: | https://www.mdpi.com/2077-1312/11/5/917 |
| _version_ | 1797599598277033984 |
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| author | Jiaqi Liu Masoud Hayatdavoodi R. Cengiz Ertekin |
| author_facet | Jiaqi Liu Masoud Hayatdavoodi R. Cengiz Ertekin |
| author_sort | Jiaqi Liu |
| collection | DOAJ |
| description | This study is concerned with the generation and propagation of strongly nonlinear waves in shallow water. A numerical wave flume is developed where nonlinear waves of solitary and cnoidal types are generated by use of the Level I Green-Naghdi (GN) equations by a piston-type wavemaker. Waves generated by the GN theory enter the domain where the fluid motion is governed by the Navier–Stokes equations to achieve the highest accuracy for wave propagation. The computations are performed in two dimensions, and by an open source computational fluid dynamics package, namely OpenFoam. Comparisons are made between the characteristics of the waves generated in this wave tank and by use of the GN equations and the waves generated by Boussinesq equations, Laitone’s 1st and 2nd order equations, and KdV equations. We also consider a numerical wave tank where waves generated by the GN equations enter a domain in which the fluid motion is governed by the GN equations. Discussion is provided on the limitations and applicability of the GN equations in generating accurate, nonlinear, shallow-water waves. The results, including surface elevation, velocity field, and wave celerity, are compared with laboratory experiments and other theories. It is found that the nonlinear waves generated by the GN equations are highly stable and in close agreement with laboratory measurements. |
| first_indexed | 2024-03-11T03:36:31Z |
| format | Article |
| id | doaj.art-7c36259afbc7408784adad52a7b87a67 |
| institution | Directory Open Access Journal |
| issn | 2077-1312 |
| language | English |
| last_indexed | 2024-03-11T03:36:31Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Journal of Marine Science and Engineering |
| spelling | doaj.art-7c36259afbc7408784adad52a7b87a672023-11-18T01:58:26ZengMDPI AGJournal of Marine Science and Engineering2077-13122023-04-0111591710.3390/jmse11050917A Comparative Study on Generation and Propagation of Nonlinear Waves in Shallow WatersJiaqi Liu0Masoud Hayatdavoodi1R. Cengiz Ertekin2College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, ChinaCollege of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, ChinaCollege of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, ChinaThis study is concerned with the generation and propagation of strongly nonlinear waves in shallow water. A numerical wave flume is developed where nonlinear waves of solitary and cnoidal types are generated by use of the Level I Green-Naghdi (GN) equations by a piston-type wavemaker. Waves generated by the GN theory enter the domain where the fluid motion is governed by the Navier–Stokes equations to achieve the highest accuracy for wave propagation. The computations are performed in two dimensions, and by an open source computational fluid dynamics package, namely OpenFoam. Comparisons are made between the characteristics of the waves generated in this wave tank and by use of the GN equations and the waves generated by Boussinesq equations, Laitone’s 1st and 2nd order equations, and KdV equations. We also consider a numerical wave tank where waves generated by the GN equations enter a domain in which the fluid motion is governed by the GN equations. Discussion is provided on the limitations and applicability of the GN equations in generating accurate, nonlinear, shallow-water waves. The results, including surface elevation, velocity field, and wave celerity, are compared with laboratory experiments and other theories. It is found that the nonlinear waves generated by the GN equations are highly stable and in close agreement with laboratory measurements.https://www.mdpi.com/2077-1312/11/5/917Green–Naghdi equationsNavier–Stokes equationsBoussinesq equationsKdV equationsolitary wavecnoidal wave |
| spellingShingle | Jiaqi Liu Masoud Hayatdavoodi R. Cengiz Ertekin A Comparative Study on Generation and Propagation of Nonlinear Waves in Shallow Waters Journal of Marine Science and Engineering Green–Naghdi equations Navier–Stokes equations Boussinesq equations KdV equation solitary wave cnoidal wave |
| title | A Comparative Study on Generation and Propagation of Nonlinear Waves in Shallow Waters |
| title_full | A Comparative Study on Generation and Propagation of Nonlinear Waves in Shallow Waters |
| title_fullStr | A Comparative Study on Generation and Propagation of Nonlinear Waves in Shallow Waters |
| title_full_unstemmed | A Comparative Study on Generation and Propagation of Nonlinear Waves in Shallow Waters |
| title_short | A Comparative Study on Generation and Propagation of Nonlinear Waves in Shallow Waters |
| title_sort | comparative study on generation and propagation of nonlinear waves in shallow waters |
| topic | Green–Naghdi equations Navier–Stokes equations Boussinesq equations KdV equation solitary wave cnoidal wave |
| url | https://www.mdpi.com/2077-1312/11/5/917 |
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