Experimental investigation of the impact of directional distribution on the geometric characteristics of focused waves in finite water depth

In actual wave fields, short-crested behavior is typically observed due to the superposition of wave components with varying wave frequencies and directional distributions. However, most of previous studies have simplified these as two-dimensional waves, neglecting the impact of directional distribution and leading to an incomplete understanding of its influence on nonlinear characteristics. This study investigates multi-directional focused waves with a single frequency in a laboratory setting. The comparison reveals that, unlike wave frequency, the vertical asymmetry factor influenced by directional distribution is linked to the variation in the period from zero-upcrossing to the crest. In multi-directional waves, the wave steepness defined for unidirectional waves is inadequate for measuring nonlinearity. There can be instances where the ratio of the subsequent envelope height at half the characteristic period to the preceding one exceeds 1, indicating a configuration highly prone to extreme events, especially with wider directional distributions. Furthermore, the deviation of the higher-order energy ratio from the theoretical solution increases with wave steepness (defined for the corresponding unidirectional waves) when the directional distribution is relatively concentrated, but no clear conclusion is reached at the directional distribution with θmax = 60°. This suggests that multi-directional waves, particularly with θmax greater than 45°, warrant more attention as a critical inflection point. These findings provide a reference for future research on multi-directional, multi-frequency wave components.