Modelling of non-linear long water waves on a sloping beach

• Autorzy: Schmidt K.
• Języki publikacji: EN

Abstrakty

EN

The paper deals with a non-linear problem of long water waves approaching a sloping beach. In order to describe the phenomenon we apply the Lagrange's system of material variables. With these variables it is much easier to solve boundary conditions, especially conditions on a shoreline. The formulation is based on the fundamental assumption for long waves propagating in shallow water of constant depth that vertical material lines of fluid particles remain vertical during entire motion of the fluid. The analysis is confined to one - dimensional case of unsteady water motion within a 'triangular' body of fluid. The partial differential equations of fluid motion, obtained by means of a variational pro-cedure, are then substituted by a system of equations resulting from a perturbation scheme with the second order expansion with respect to a small parameter. In this way the original problem bas been reduced to a system of linear partial differential equations with variable coefficients. The latter equations are, in turn, substituted by a system of dif-ference equations, which arf then integrated in a discrete time space by means of the Wilson-B method. The procedure developed in this paper may be a convenient tool in analysing non-breaking waves propagating in coastal zones of seas. Moreover, the model can also deliver useful results for cases when breaking of waves near a shoreline may be expected.

Słowa kluczowe

EN

shallow water; non-linear wave; unsteady motion; sloping beach

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2006
• Tom: Vol. 54, nr 4
• Strony: 381--389
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Schmidt K.

• Institute of Hydro-Engineering, Polish Academy of Sciences, 17 Waryńskiego St., 71-310 Szczecin, Poland,

Bibliografia

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