Principal Investigator Michael Triantafyllou
Co-investigator Dick Yue
Resonant interactions between Kelvin ship waves and ambient ocean waves. The influences of nonlinearity in a ship's wake is of theoretical and practical interest, especially in the cases with wave-wave resonances. Such resonances, however, do not occur among Kelvin ship waves themselves in third order (the lowest possible order for wave-wave resonances among gravity waves in deep water).
In this study, it is found that with the presence of an ambient ocean wave, a new propagating wave can be generated by the third-order resonant interactions between this wave and the Kelvin waves. This wave exists along a certain ray behind the ship. The wavenumber and propagating direction of the resonance-generated wave as well as the location of the resonance ray, which depend on ship speed and ambient-wave wavenumber, are determined by the resonant conditions.
Evolution equations of the interaction wave components are derived through multiple-scale analysis. By solving these equations, it is found that the new wave has a solitary envelope in the lateral direction and its amplitude grows with the distance from the ship in the near wake while slowly oscillates in the far wake. The initial growth rates of this wave are confirmed in the near field by direct numerical experiments obtained with high-order spectral method. The comparison with field experiments about the soliton-like features behind a ship shows that this mechanism is a possible explanation for the solitary features observed in field experiments.