Long water waves as a structure fluid interaction problem

• Autorzy: Wilde P. , Chybicki W.
• Języki publikacji: EN

Abstrakty

EN

The paper describes a new formulation of the theory of long shallow water waves, which is based on the fundamental assumption that vertical material lines of fluid remain vertical during the entire motion. To make the problem consistent from the point of view of physics the case of waves in a flume due to the motion of a piston type generator is considered. At the piston the material line of water particles remains vertical during the entire motion and thus the generation follows the assumption in the description of the motion of water in the flume. Wave equations are derived with the help of a variational formulation of the problem in a material description. The Lagrangian is the difference between the kinetic and potential energies of the fluid and the mechanical system that describes a very simplified wave generator. The basic assumption simplifies the geometry of the displacement field. The definitions of generalized forces follow from variational calculus. The procedure ensures that the energy is preserved. A simple discrete formulation of the problem is based on the finite element method and the corresponding approximate expressions for energies.

Słowa kluczowe

EN

long waves; Lagrangian description; Hamilton principle

• Wydawca: Institute of Hydro-Engineering of Polish Academy of Sciences
• Czasopismo: Archives of Hydro-Engineering and Environmental Mechanics
• Rocznik: 2004
• Tom: Vol. 51, nr 2
• Strony: 95--118
• Opis fizyczny: Bibliogr. 8 poz., il.

Twórcy

autor

Wilde P.

• Institute of Hydro-Engineering of the Polish Academy of Sciences ul. Kościerska 7, 80-953 Gdańsk, Poland

autor

Chybicki W.

• Institute of Hydro-Engineering of the Polish Academy of Sciences ul. Kościerska 7, 80-953 Gdańsk, Poland

Bibliografia

• Abbot M. B. (1979), Computational Hydraulics – Elements of the Theory of Free Surface Flows, Pitman Publishing Limited, London.
• Madsen P. A., Murray R., Sorensen O. R. (1991), A New Form of the Boussinesq Equation with Improved Linear Dispersion Characteristics, Coastal Engineering, 15(4), 371–388.
• Mei C. C. (1983), The Applied Dynamics of Ocean Surface Waves, J. Wiley & Sons, New York.
• Stoker J. J. (1957), Water Waves, Inter Science Publishers, New York.
• Ursell F. (1953), The Long Wave Paradox in the Theory of Gravity Waves, Proc. Cambridge Philos. Soc., 49, 685–694.
• Wilde P., Sobierajski E., Sobczak Ł. (2001), Non-linear Water Waves – Experiments and Theory, Archives of Hydro-Engineering and Environmental Mechanics, Vol. 48, No. 2, 107–128.
• Wilde P., Sobierajski E. & Sobczak Ł. (2000), Laboratory Studies of the Influence of Generation on long-Waves Properties (in Polish), internal report available at the library of the Institute.
• Whitham G. B. (1974), Linear and Non-Linear Waves, J. Wiley & Sons, New York.