Effect of an Uneven Bottom on Gravity Waves
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概要
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Effect of an uneven bottom on the long gravity waves is investigated by using a nonlinear perturbation method. The following simple nonlinear equation is obtained, to the lowest order of perturbation, for the free-surface elevation h^<(1)>: [numerical formula], where ξ and η are stretched space-time coordinates, and the coefficients c_1, c_2 and c_3 are all functions of the bottom surface B(η). If the bottom is flat (dB/dη=0), the equation reduces to the well-known Korteweg-de Vries equation. It is interesting to note that, due to the presence of the last term, damping or instability may occur depending upon the sign of the local slope, dB/dη, of the bottom. A comment is given on the relationship between he conventional shallow-water (or long-wave9 theory and the present analysis.
- 社団法人日本物理学会の論文
- 1971-01-05
著者
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Kakutani Tsunehiko
Department Of Engineering Mathematics University Of Newcastle Upon Tyne:(present Address) Department
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Kakutani Tsunehiko
Department Of Engineering Mathematics University Of Newcastle Upon Type
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