Infragravity (IG) waves (0.005-0.04 Hz) are surface waves that can dominate the nearshore hydrodynamics and can impact various coastal processes (e.g., run-up, overwash). A proper offshore description of incident IG waves is required for storm impact models, which generally assume a local equilibrium between sea-swell (SS) waves (0.04-0.33 Hz) and the resultant nonlinearly excited bound IG waves. The contribution of free incident IG waves and the directional properties
of the IG wave field are neglected, though they play a critical role in IG wave variations. Various research focuses on IG wave dynamics in shallow waters, but a detailed understanding of IG wave variability in intermediate water depth is lacking. Furthermore, the directional spectra of bound and free IG waves in the field are usually unavailable since bound IG waves do not follow linear dispersion relations, which is assumed by commonly applied directional spectra reconstruction methods.

In-situ observation data (surface elevation, pressure, and velocity) of IG waves from November 2021 to April 2022 at three cross-shore locations in intermediate water depth (∼ 6 − 14 m) off the Dutch coast are analyzed to study generation, propagation, and directional properties of IG waves. The bispectral technique is applied to quantify the contribution of bound IG waves to the total IG wave field. A newly developed method is validated and used on the offshore (∼ 14 m) data to reconstruct directional spectra of bound and free IG waves separately during storms.

The results show that IG wave heights are best predicted (correlation coefficient R² up to 0.94) with an offshore forcing parameter that includes peak period H_ssT_p² , which indicates SS wave energy flux. The growth rate of IG waves is in between the shallow water equilibrium solution (for bound waves) and Green’s Law (for free waves), indicating the total IG wave field consists of bound and free components. The relative contribution of bound IG energy (up to 76%) is correlated to SS wave energy, whereas it decreases dramatically during intense storms when SS waves break. The bound IG waves that are assumed to follow the weakly nonlinear wave theory, have a similar peak direction and broader directional spreading to SS waves. In contrast, the directional spectra of free IG waves are nearly isotropic during calm conditions, but may have diverse peaks during storms, which incident IG waves from remote sources and edge waves can
influence. A better understanding of the complex pattern of free IG waves requires more detailed observations and/ or modeling.