Eigen solutions of internal waves over subcritical topography |
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| Authors: | DAI Dejun WANG Wei ZHANG Qinghu QIAO Fangli and YUAN Yeli |
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| Institution: | 1.The First Institute of Oceanography, State Oceanic Administration, Qingdao 266061, China;Key Laboratory of Marine Science and Numerical Modeling, State Oceanic Administration, Qingdao 266061, China2.Physical Oceanography Laboratory, Ocean University of China, Qingdao 266003, 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 two-
dimensional 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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| Keywords: | internal waves transform method eigen solutions subcritical curved topography |
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