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  1. 紀要論文
  2. 琉球大学理工学部紀要 工学編
  3. 14号
  1. 部局別インデックス
  2. 工学部

浅海における進行波の砕波について(第2報) : 砕波モデルに対するCatastropheポテンシャル

http://hdl.handle.net/20.500.12000/26954
http://hdl.handle.net/20.500.12000/26954
f8ebcf3f-a485-4224-8116-46af82fa64b0
名前 / ファイル ライセンス アクション
No14P189.pdf No14P189.pdf
Item type デフォルトアイテムタイプ(フル)(1)
公開日 2013-07-22
タイトル
タイトル 浅海における進行波の砕波について(第2報) : 砕波モデルに対するCatastropheポテンシャル
言語 ja
作成者 筒井, 茂明

× 筒井, 茂明

ja 筒井, 茂明

Tsutsui, Shigeaki

× Tsutsui, Shigeaki

en Tsutsui, Shigeaki

アクセス権
アクセス権 open access
アクセス権URI http://purl.org/coar/access_right/c_abf2
内容記述
内容記述タイプ Other
内容記述 As a fundamental study on the elucidation of wave motions in the coast, one of analytical methods proposing the dynamical systems that represent the history of waves is presented as follows: The wave equation, expressed in the surface displacement only, and its Lagrangian function for the variational principle are obtained from the results of application of the perturbation method, where the method is applied to basic equations of hydrodynamics in the same way as the non-linear wave theory in shallow water. Motions of gravity waves are physical phenomena on the potential field. In this case, Hamiltonian function is identical to the integral surface (energy surface) of basic equations, when Euler-Lagrange's dynamical systems are transformed into Hamiltonian systems, and the independent variables do not appear explicitly. But quasi-linearised differential equations, based on the conventional perturbation method, are impossible to express the breaking of waves. Therefore, new concepts are necessary in order to have reasonable solutions analyzing the problem where proper dynamical systems are to be clarified the breaking. For the phenomena with discontinuities, R.Thom established the catastrophe theory, which deals with singular points of mappings and its structural stabilities, and has classified the singularities for certain classes of functions. This theory gives us clear understanding of the qualitative aspect of discontinuity in natural processes. The main theoretical significance of Thom's classification is to allow us to determine the stable equilibria of gradient systems subjected to small number of constraints, and to describe how these equilibria change as the constraints vary. On the other hand, since Hamiltonian function is the manifold constructed by two physical variables and basic equations are related to dynamical systems on this manifold, the topology of this differentiable manifold becomes important. Consequently, Hamiltonian function should be taken as Taylor's approximation to the exact energy surface at a local position near the stationary point of the variational principle, where topologically important properties are preserved. From the analytical studies on the catastrophe theory and the properties of Hamiltonian function mentioned above, it becomes clear that Hamiltonian function corresponds to the catastrophe potential for the breaking model. The numerical calculation using the first approximation to the breaking of the solitary waves is shown in which classical hydrodynamics and R.Thom's catastorophe theory are combined.
内容記述タイプ Other
内容記述 紀要論文
出版者
言語 ja
出版者 琉球大学理工学部
言語
言語 jpn
資源タイプ
資源タイプ departmental bulletin paper
資源タイプ識別子 http://purl.org/coar/resource_type/c_6501
出版タイプ
出版タイプ VoR
出版タイプResource http://purl.org/coar/version/c_970fb48d4fbd8a85
識別子
識別子 http://hdl.handle.net/20.500.12000/26954
識別子タイプ HDL
収録物識別子
収録物識別子タイプ ISSN
収録物識別子 0387-429X
収録物識別子タイプ NCID
収録物識別子 AN00250785
収録物名
言語 ja
収録物名 琉球大学理工学部紀要. 工学篇
書誌情報
号 14, p. 189-202
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