Highly nonlinear short-crested water waves

Abstract

The properties of a fully three-dimensional surface gravity wave, the short-crested wave, are examined. Linearly, a short-crested wave is formed by two wavetrains of equal amplitudes and wavelengths propagating at an angle to each other. Resonant interactions between the fundamental and its harmonics are a major feature of short-crested waves and a major complication to the use at finite wave steepness of the derived perturbation expansion. Nonetheless, estimates are made of the maximum steepnesses, and wave properties are calculated over the range of steepnesses. Although results for values of the parameter θ near 20° remain uncertain, we find that short-crested waves can be up to 60% steeper than the two-dimensional progressive wave. At limits of the parameter range the results compare well with those for known two-dimensional progressive and standing water waves.