| DAI Dejun,WANG Wei,ZHANG Qinghua,QIAO Fangli,YUAN Yeli. 2011. Eigen solutions of internal waves over subcritical topography. Acta Oceanologica Sinica, (2):1－8 |
| Eigen solutions of internal waves over subcritical topography |
| Eigen solutions of internal waves over subcritical topography |
| Received:June 13, 2010 Revised:December 02, 2010 |
| DOI：10.1007/s13131-011-0099-2 |
| Key words:internal waves transform method eigen solutions subcritical curved topography |
| 中文关键词: internal waves transform method eigen solutions subcritical curved topography |
| 基金项目:the National Nature Science Foundation of China under contract No. 40876015 and the National High Technology Research and Development Program of China (863 Program) under contract No. 2008AA09A402. |
| Author Name | Affiliation | E-mail | | DAI Dejun | The First Institute of Oceanography, State Oceanic Administration, Qingdao 266061, China
Key Laboratory of Marine Science and Numerical Modeling, State Oceanic Administration, Qingdao 266061, China | djdai@fio.org.cn | | WANG Wei | Physical Oceanography Laboratory, Ocean University of China, Qingdao 266003, China | | | ZHANG Qinghua | The First Institute of Oceanography, State Oceanic Administration, Qingdao 266061, China
Key Laboratory of Marine Science and Numerical Modeling, State Oceanic Administration, Qingdao 266061, China | | | QIAO Fangli | The First Institute of Oceanography, State Oceanic Administration, Qingdao 266061, China
Key Laboratory of Marine Science and Numerical Modeling, State Oceanic Administration, Qingdao 266061, China | | | YUAN Yeli | The First Institute of Oceanography, State Oceanic Administration, Qingdao 266061, China
Key Laboratory of Marine Science and Numerical Modeling, State Oceanic Administration, Qingdao 266061, China | |
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| Abstract: |
| Diapycnal mixing plays an important role in the ocean circulation. Internal waves are a kind of bridge relating the diapycnal mixing to external sources of mechanical energy. Difficulty in obtaining eigen solutions of internal waves over curved topography is a limitation for further theoretical study on the generation problem and scattering process. In this study, a kind of transform method is put forward to derive the eigen solutions of internal waves over subcritical topography in twodimensional and linear framework. The transform converts the curved topography in physical space to flat bottom in transform space while the governing equation of internal waves is still hyperbolic if proper transform function is selected. Thus, one can obtain eigen solutions of internal waves in the transform space. Several examples of transform functions, which convert the linear slope, the convex slope, and the concave slope to flat bottom, and the corresponding eigen solutions are illustrated. A method, using a polynomial to approximate the transform function and least squares method to estimate the undetermined coefficients in the polynomial, is introduced to calculate the approximate expression of the transform function for the given subcritical topography. |
| 中文摘要: |
| Diapycnal mixing plays an important role in the ocean circulation. Internal waves are a kind of bridge relating the diapycnal mixing to external sources of mechanical energy. Difficulty in obtaining eigen solutions of internal waves over curved topography is a limitation for further theoretical study on the generation problem and scattering process. In this study, a kind of transform method is put forward to derive the eigen solutions of internal waves over subcritical topography in twodimensional and linear framework. The transform converts the curved topography in physical space to flat bottom in transform space while the governing equation of internal waves is still hyperbolic if proper transform function is selected. Thus, one can obtain eigen solutions of internal waves in the transform space. Several examples of transform functions, which convert the linear slope, the convex slope, and the concave slope to flat bottom, and the corresponding eigen solutions are illustrated. A method, using a polynomial to approximate the transform function and least squares method to estimate the undetermined coefficients in the polynomial, is introduced to calculate the approximate expression of the transform function for the given subcritical topography. |
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