Effect of current on flexural gravity waves

The effect of uniform current on the propagation of flexural gravity waves due to a floating ice sheet is analyzed in two dimensions. The problem is formulated as an initial boundary value problem in the linearized theory of water waves, By using Laplace transform technique, the initial boundary value problem is reduced to a boundary value problem, which is solved by the application of Fourier transform to obtain the surface elevation in terms of an integral, which is evaluated asymptotically for large distance and time by the application of method of stationary phase to obtain the far field behavior of the progressive waves. The effect of current on the wavelength, phase velocity and group velocity of the flexural gravity waves propagating below the floating ice sheet is analyzed theoretically to obtain certain critical values on the speed of current which are of significant importance. Simple numerical computations are performed to observe the effect of uniform current on the surface elevation, wavelength, phase velocity and group velocity of flexural gravity waves and on the far field behavior of the progressive waves.