Nonlinear wave resonance due to oscillations of twin cylinders in a uniform current

A higher order finite element method with 8-node element is adopted to analyse the nonlinear wave resonance generated by oscillations of twin cylinders in a uniform current. The velocity potential in the fluid domain at each time step is obtained based on the finite element method through an iteration procedure. Numerical results are provided for twin rectangular cylinders undergoing specified oscillations in a uniform current at resonant frequencies. The effects of current on the wave and hydrodynamic force at the resonant frequencies are studied in detail and it is found that the resonance happens at all first-order resonant frequencies for both symmetric and antisymmetric motions of the cylinders. In particular, in addition to the first-order resonant frequency, the maximum wave elevation and horizontal force at resonance always regularly increase or decrease as the increase of the absolute value of Froude number or the spacing between two cylinders within the range of larger spacings. A similar trend can be also observed in the oscillational frequency of cylinders at resonance. Some results are also compared with those by linear solution and its superposition with the second-order, their difference at different Froude numbers are also discussed.