Gravity waves generated by an oscillatory surface pressure in a two-layer fluid with a porous bottom

Wave motion due to a prescribed time-harmonic surface pressure distribution in a two-layer fluid is studied in this paper. The lower fluid is assumed to have a porous bottom. Using linear theory, the physical problem is formulated as an initial boundary value problem. Employing Fourier transform technique, the forms of the free surface and the interface are obtained in terms of infinite integrals, which are evaluated asymptotically for large distance and time using the stationary phase method and Bleistein's method. Asymptotic forms of the free surface and interface are depicted graphically, illustrating their behaviors for large distance and time. Furthermore, the dispersion relation, as well as the phase and group velocities are also analyzed by depicting them in various figures.