Waves due to an oscillating and translating disturbance in a two-layer density-stratified fluid

Wave generation due to the steady translational motion of an oscillatory disturbance in a two-layer density-stratified fluid is studied. In the context of linearized two- and three-dimensional potential flow, explicit expressions for the Green functions are derived and limiting cases discussed. Of special interest are the waves in the far field. The number and amplitudes of these waves depend on the characteristics of the disturbance (location, speed and oscillation frequency) and the ocean (stratified layer density and depth ratios). These dependencies are elucidated in concrete examples. An interesting finding, for example, is that, for constant frequency, there are critical speeds (as functions of density and depth ratios) at which the specific amplitudes attain maxima. For the more general problem and as an independent validation, an efficient numerical scheme for the problem based on a spectral method is developed. Direct simulation results compare well with analytical predictions in the near- and far-fields and offer a powerful tool for practical problems with general time-dependent motions of one or more bodies.