Generation of waves in running stream

• Autorzy: Basu U. , Ghosh P.
• Języki publikacji: EN

Abstrakty

EN

In this paper, a problem of the two-dimensional wave generation due to an initial disturbance at the free surface in an ocean of finite depth in the presence of surface tension and a uniform running stream is investigated. Using linear theory, the problem is formulated as an initial value problem for the velocity potential describing the ensuing motion in the fluid. In the mathematical analysis the Laplace and Hankel transform techniques have been utilized to obtain the elevation of the free surface in the form of an infinite integral. This is then evaluated asymptotically for large time and distance by applying the method of stationary phase. The form of the free surface is depicted graphically for two types of initial disturbances. The effect of the surface tension and the presence of the running stream on the wave motion are discussed.

Słowa kluczowe

EN

wave generation; surface tension; running stream; stationary phase; free surface elevation

PL

wytrzymałość materiałów; generowanie fal; napięcie powierzchniowe

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2003
• Tom: Vol. 8, no 1
• Strony: 17--26
• Opis fizyczny: Bibliogr. 7 poz., wykr.

Twórcy

autor

Basu U.

• Department of Applied Mathematics, Calcutta University 92 A.P.C. Road, Calcutta - 700 009, INDIA

autor

Ghosh P.

• Physics and Applied Mathematics Unit, Indian Statistical Institute 203, B.T. Road, Calcutta - 700 035, INDIA

Bibliografia

• [1] Debnath L. and Basu U. (1978): On generation and propagation of tsunamis in a shallow running stream. - Internal J. Math. and Math. Sci., vol.l, pp.373-390.
• [2] Debnath L. and Basu U. (1989): The Cauchy-Poisson problem in an inviscid stratified liauid. - Appl. Math. Letter, vol.2, pp.337-340.
• [3] Debnath L. and Rosenblant S. (1969): The ultimate approach to the steady State in the generation of waves on a running stream. - Quart. J. and Appl. Math., vol.22, pp.221-233.
• [4] Mandal B.N. and Basu U. (1996): Free surace flow over a smali geometrical disturbance at the bottom. - Buli. Cal. Math. Soc., vol.88, pp.409-425.
• [5] Miles J. (1962): Transient gravity wave response to an oscillatory pressure. - J. Fluid Mech., vol.l3, pp.145-150.
• [6] Stoker J.J. (1957): Water Waves. - New York: Interscience Publishers.
• [7] Tripathi U. and Basu U. (1987): The reflection of water waves by undulation on the sea-bed in a running stream. - Ind. J. Pure Appl. Math., vol.l8, pp.861-870.