Flexural gravity wave generation by initial disturbances in the presence of current |
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Authors: | Joydip Bhattacharjee Trilochan Sahoo |
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Institution: | (1) Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology, Kharagpur, 721302, India |
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Abstract: | The effect of uniform current on the generation of flexural gravity waves resulting from initial disturbances at a point was
analyzed in two dimensions. The problem was formulated as an initial boundary value problem under the assumptions of the linearized
theory of water waves. By direct application of the Laplace transform and then the Fourier transform, explicit expressions
for the velocity potential and free surface elevation were obtained in integral forms; these were evaluated asymptotically
for large distances and times by the application of the method of the stationary phase to obtain the far field behavior of
the surface elevations in specific cases. Simple numerical computations were performed to illustrate the effect of uniform
current on the surface elevation, wavelength, phase velocity, and group velocity of the flexural gravity waves and on the
far field behavior of the progressive waves in two different cases, namely, when there is an initial depression concentrated
at the origin and an initial impulse concentrated at the origin. |
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Keywords: | Flexural gravity waves Uniform current Initial disturbance Asymptotic behavior Method of stationary phase |
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