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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.

Generation of waves at an inertial interface

Ghosh P., Mandal B. N.

Applied Mechanics and Engineering

1999

Vol. 4, no 1

73-96

This paper is concerned with the generation of three-dimensional unsteady motion due to initial disturbances at the interface between two superposed fluids wherein the upper fluid extends infinitely upwards and the lower fluid is of uniform finite depth. The interface is composed of a thin but uniform distribution of a non-interacting material termed as an inertial surface. Assuming linear theory, the problem is formulated as a coupled initial value problem in the velocity potentials describing the motion in the two fluids. The Laplace transform in time and double Fourier transform in space have been utilised in the mathematical analysis to obtain the depression of the inertial interface in terms of a double integral, whose asymptotic form is obtained for large values of time and distance by the method of stationary phase. This is then depicted graphically for two types of initial disturbances in a number of figures to visualise the effect of the upper fluid and also the presence of the inertial surface at the interface on the wave motion. The time evolution of the interface depression is also shown graphically and the decaying phenomena are demonstrated by drawing the phase diagram.

Waves due to initial disturbances at the interface between two superposed fluids

Ghosh P., Basu S. K.

Applied Mechanics and Engineering

1998

Vol. 3, no 2

233-247

This paper is concerned with generation of interface waves due to an initial disturbance at the interface between two superposed homogeneous and inviscid fluids, the lower fluid being of finite depth and the upper fluid extending infinitely upwards. Assuming linear theory, the problem is formulated as a coupled boundary value problem in the velocity potentials describing the motion in the two fluids. The interface depression is obtained when the initial disturbance at the interface is in the form of a prescribed depression of the interface or an impulse concentrated at a point. In both the cases, the interface depression is obtained in terms of an infinite integral which is evaluated asymptotically for large time and distance. This is then displayed graphically in a number of figures to visualise the effect of the upper fluid and also the effect of the finite depth of the lower fluid on the wave motion at the interface.