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Generation of waves in two superposed fluids covered by an elastic plate in the presence of running stream

Dolai P.

International Journal of Applied Mechanics and Engineering

2009

Vol. 14, no 1

139-156

This paper is concerned with the problem of two-dimensional wave generation due to an initial disturbance created at the upper surface of two superposed fluid layers in the presence of uniform running streams. The upper fluid of finite height is covered by a thin elastic plate. The lower fluid of finite depth is separated from the upper one by a common interface. Assuming linear theory, the problem is formulated as a coupled initial value problem of the velocity potentials describing the motion in the two fluids. In the mathematical analysis, the Laplace and Fourier transform techniques have been utilized to obtain the elevations at the upper fluid surface and the interface in the form of infinite integrals involving the initial elevation due to plate deflection. As a special case when the initial elevation concentrated at a point on the upper surface, these integrals are evaluated asymptotically by the method of stationary phase. The asymptotic forms of the upper surface elevation and the interface elevation are depicted graphically in a number of figures. The effects of the upper fluid covered by an elastic plate and the presence of running streams on the wave motion are discussed.

Interface wave generation in two fluid medium in the presence of running stream

Dolai P.

International Journal of Applied Mechanics and Engineering

2008

Vol. 13, no 3

669-679

In this paper, a problem of two-dimensional wave generation due to initial disturbance at the interface between two superposed fluids wherein the upper fluid of finite height above the interface with a horizontal rigid lid and the lower fluid of finite depth in the presence of a uniform running stream in both the fluids is investigated. Assuming linear theory, the problem is formulated as a coupled initial value problem of the velocity potentials describing the motion in the two fluids. In the mathematical analysis, the Laplace and Fourier transform techniques have been utilized to obtain the interface depression when the initial disturbance at the interface is in the form of a prescribed interface depression or an impulse concentrated at the origin. In both the cases, the interface depression is obtained in terms of an infinite integral which is evaluated asymptotically for large time and distance by the method of stationary phase. The asymptotic forms of the interface depression are depicted graphically in a number of figures. The effect of the upper fluid and the presence of the running stream in both the fluids on the wave motion are discussed.