Nonlinear loading of a two-dimensional heaving box

•The excitation, radiation and floating problem of a heaving box are considered.•Comparisons to a fully nonlinear potential flow method are provided.•Key sources of nonlinear forcing are identified and explained.•Significant harmonic motion content is observed in more than one wave regime.•The importance of both nonlinear forcing and dynamic response is considered.

A numerical investigation is presented addressing the nonlinear heave response of a rectangular box. The work specifically concerns the importance of the relative body dimensions, expressed through the product of the half-beam b and the wavenumber k  . When subjected to moderately steep incident waves, the second-harmonic content of the heave motion is found to be as large as 25% of the first-harmonic content. In considering the extent of this second-harmonic motion, three regimes may be defined: (i) the long wave regime, where kb≤0.4kb≤0.4, (ii) the intermediate regime, where 0.4