On variational formulation in water wave mechanics

• Autorzy: Wilde P. , Szmidt J. K.
• Języki publikacji: EN

Abstrakty

EN

In this paper variational formulations for surface gravitational waves in inviscid incompressible fluids are investigated. The formulations are introduced with the help of the principle of virtual work. The starting point are equations of motion multiplied by a field of virtual displacements and integrated over the region occupied by the fluid. In derivations of the virtual work equation careful attention is paid to mutual relations between Eulerian and Lagrangian descriptions. The integration of the equation with respect to time leads to the expression for the Lagrangian function and then the Hamilton's principle. The case of a potential flow and spatial description provides a generalisation of the Lagrangian given by Luke (1967).

Słowa kluczowe

EN

water wave; variational formulation; spatial and material description

• Wydawca: Institute of Hydro-Engineering of Polish Academy of Sciences
• Czasopismo: Archives of Hydro-Engineering and Environmental Mechanics
• Rocznik: 2004
• Tom: Vol. 51, nr 1
• Strony: 55--74
• Opis fizyczny: Bibliogr. 9 poz., il.

Twórcy

autor

Wilde P.

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

autor

Szmidt J. K.

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

Bibliografia

• Bateman H. (1929), Notes on a Differential Equation which Occurs in the Two Dimensional Motion of a Compressible Fluid and the Associated Variational Problems, Proceedings Roy. Soc., A, 125, 598–618.
• Van Groesen E. W. C., de Jager E. M. (1995), Mathematical Structures in Continuous Dynamical Systems, North-Holland.
• Herivel J. W. (1955), The Derivation of the Equations of Motion of an Ideal Fluid by Hamilton’s Principle, Proceedings Cambridge Phil. Soc. 51, 344–349.
• Luke J. C. (1967), A Variational Principle for a Fluid with Free Surface, J. Fluid Mech., Vol. 27, part 2, 395–397.
• Salmon R. (1988), Hamiltonian Fluid Mechanics, Ann. Rev. Fluid Mech., 20, 225–256.
• Serrin J. (1959), Mathematical Principles of Classical Fluid Mechanics, [in:] Encyclopaedia of Physics, Vol. VIII, ‘Fluid Dynamics I’, Springer Verlag, 125–263.
• Spencer A. J. M. (1980), Continuum Mechanics, Longman, London and New York.
• Truesdell C., Toupin R. (1960), The Classical Field Theories, [in:] Handbuch der Physik III-1, Springer Verlag, 226–790.
• Weinstock R. (1952), Calculus of Variations, McGraw-Hill Book Company, Inc. New York.