Backward Integration of Nonlinear Shallow Water Model: Part I: Solitary Rossby Waves
The inviscid, nonlinear shallow water model developed by Sun was applied to study the inverse of equatorial Rossby solitons, which can be represented by the Korteweg–De Vries equation (KdV equation). The model was integrated forward in time, then the results were used as initial conditions for backw...
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2024-09-01
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| author | Wen-Yih Sun |
| author_facet | Wen-Yih Sun |
| author_sort | Wen-Yih Sun |
| collection | DOAJ |
| description | The inviscid, nonlinear shallow water model developed by Sun was applied to study the inverse of equatorial Rossby solitons, which can be represented by the Korteweg–De Vries equation (KdV equation). The model was integrated forward in time, then the results were used as initial conditions for backward integration by just changing time step from positive to negative. The detailed structure, secondary circulation, and propagating speed of waves from both integrations are in good agreement with analytic solutions. The total mass, energy, and enstrophy are also well conserved. The procedure is much simpler and the results are more accurate than other backward integrations of 2D nonlinear models, which require significant modification of the model and can be contaminated by unwanted diffusion in forward–backward integrations or time-consuming iterative methods. This paper is also different from the numerical method for solving the inverse of the KdV equation. |
| format | Article |
| id | doaj-art-04b840ef94ec46ea820d2db0b64305ab |
| institution | OA Journals |
| issn | 2073-4433 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | MDPI AG |
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| series | Atmosphere |
| spelling | doaj-art-04b840ef94ec46ea820d2db0b64305ab2025-08-20T02:11:09ZengMDPI AGAtmosphere2073-44332024-09-011510116110.3390/atmos15101161Backward Integration of Nonlinear Shallow Water Model: Part I: Solitary Rossby WavesWen-Yih Sun0Department of Earth, Atmospheric and Planetary Sciences, Purdue University, West Lafayette, IN 47907, USAThe inviscid, nonlinear shallow water model developed by Sun was applied to study the inverse of equatorial Rossby solitons, which can be represented by the Korteweg–De Vries equation (KdV equation). The model was integrated forward in time, then the results were used as initial conditions for backward integration by just changing time step from positive to negative. The detailed structure, secondary circulation, and propagating speed of waves from both integrations are in good agreement with analytic solutions. The total mass, energy, and enstrophy are also well conserved. The procedure is much simpler and the results are more accurate than other backward integrations of 2D nonlinear models, which require significant modification of the model and can be contaminated by unwanted diffusion in forward–backward integrations or time-consuming iterative methods. This paper is also different from the numerical method for solving the inverse of the KdV equation.https://www.mdpi.com/2073-4433/15/10/1161nonlinear shallow water modelRossby solitonKdVforward and backward integrationsinverseNavier–Stokes equations |
| spellingShingle | Wen-Yih Sun Backward Integration of Nonlinear Shallow Water Model: Part I: Solitary Rossby Waves Atmosphere nonlinear shallow water model Rossby soliton KdV forward and backward integrations inverse Navier–Stokes equations |
| title | Backward Integration of Nonlinear Shallow Water Model: Part I: Solitary Rossby Waves |
| title_full | Backward Integration of Nonlinear Shallow Water Model: Part I: Solitary Rossby Waves |
| title_fullStr | Backward Integration of Nonlinear Shallow Water Model: Part I: Solitary Rossby Waves |
| title_full_unstemmed | Backward Integration of Nonlinear Shallow Water Model: Part I: Solitary Rossby Waves |
| title_short | Backward Integration of Nonlinear Shallow Water Model: Part I: Solitary Rossby Waves |
| title_sort | backward integration of nonlinear shallow water model part i solitary rossby waves |
| topic | nonlinear shallow water model Rossby soliton KdV forward and backward integrations inverse Navier–Stokes equations |
| url | https://www.mdpi.com/2073-4433/15/10/1161 |
| work_keys_str_mv | AT wenyihsun backwardintegrationofnonlinearshallowwatermodelpartisolitaryrossbywaves |