Interpretation of soliton energy ratios in directional wave fields

Highly nonlinear soliton-dominated sea states in deep water have been explored in previous studies through nonlinear theory and physical experiments. Deep water solitons are known to retain their characteristic properties during evolution within one-dimensional wave fields that are described by the nonlinear Schrödinger (NLS) equation, which is the most important model for their study. However, realistic ocean wave fields are typically multidirectional, a condition that can destabilize solitons and challenge the direct application of NLS-based interpretations. To address this gap, we generate directional JONSWAP wave fields with different directional spreadings that can be directly compared to field measurements to discuss the directional effects on soliton-dominated seas. The soliton energy ratio derived from the nonlinear Fourier spectrum is used as an indicator to assess dominant components of directional sea states. We investigate the relation between the soliton energy ratio obtained from the original time series, where the full directionality is present, to that obtained from the time series with reduced directionality using a directional filtering approach. For small directional spreading without filtering, the soliton energy ratio in the main direction is only slightly lower compared to initial wave fields, as expected. With increasing directional spreading, the soliton energy ratio decreases more significantly in most cases. However, in highly nonlinear soliton-dominated directional sea states, soliton energy is found to be concentrated in the main propagation direction, as the soliton ratio remains large after the directional interference has been removed.