Run-Up of Linear Long Waves on Uniform Slope in Lagrangian Description

• Autorzy: Chybicki W.
• Języki publikacji: EN

Abstrakty

EN

The case of linear, two-dimensional long waves on a uniform slope is considered. It is assumed that the fluid is nonviscous and incompressible. In the present paper the description of the long wave proposed by Wilde (Wilde, Chybicki 2004) is based on the fundamental assumption that the vertical material lines of fluid remain vertical during the entire motion. The equations of motion are derived with the help of a variational formulation of the problem. The Lagrangian is the difference between the kinetic and potential energy of the fluid. In the paper a correction followed from dispersion to the results obtained by Shuto is presented.

Słowa kluczowe

EN

wave run-up; Langrangian description; Hamilton principle; hypergeometric functions

• Wydawca: Institute of Hydro-Engineering of Polish Academy of Sciences
• Czasopismo: Archives of Hydro-Engineering and Environmental Mechanics
• Rocznik: 2006
• Tom: Vol. 53, nr 2
• Strony: 97--104
• Opis fizyczny: Bibliogr. 7 poz., il.

Twórcy

autor

Chybicki W.

• Institute of Hydro-Engineering of the Polish Academy of Sciences, ul. Kościerska 7, 80-328 Gdańsk, Poland,

Bibliografia

• 1. Carrier G. P., Greenspan H. P. (1958), Water waves of finite amplitude on a sloping beach, J. Of Fluid Mech., Vol. 4, 97–109.
• 2. Herivel J. W. (1955), The derivation of the equations of motion of an ideal fluid by Hamilton’s principle, Math. Proc. Cambridge Philos. Soc., 51, 344–349.
• 3. Morse P. M., Feshbach H. (1953), Method of Theoretical Physics, Part I, McGraw Hill Book Company, New York, Toronto, London.
• 4. Shuto N. (1967), Run–up of long waves on a sloping beach, Coastal Engineering in Japan, 10, 23–37.
• 5. Szmidt K. (1988), On the Hamilton principle for perfect fluids, Bulletin of the Polish Academy of Sciences, Vol. 46, No. 2, 199–207.
• 6. Voltzinger N. E., Klevanny K. A., Pelinovsky E. N. (1989), Long Waves Dynamics of the Coastal Zone, Gidrometeoizdat, Lenningrad (in Russian).
• 7. Wilde P., ChybickiW. (2004), LongWaterWaves as a Structure Fluid Interaction Problem, Archives of Hydro-Engineering and Environmental Mechanics, Vol. 51, No. 2, 95–118.