A Nonlinear Model for Infragravity Waves Trapped Around Circular islands

Unusually-high infragravity runup events (2.5-m height) have been observed on Banneg Island, France, under a combination of favorable swell (2-m high) and high tide (7.5-m height). The analysis of observations (Sheremet et al., 2014, and references therein) suggests that the infragravity-wave component of the runup was not generated directly by the nonlinear shoaling of the swell, but could have been the result of internal nonlinear interactions within the infragravity wave band. This hypothesis, however, could not be verified, due to the lack of nonlinear models for wave propagation around circular islands. Here, we develop a theoretical framework for the nonlinear evolution of complex wavefields over circular bathymetry, that accounts for incoming swell and infragravity trapped-wave modes. We extend the linear approach due to Longuet-Higgins (1967) to include a mildly-varying cross-shore profile and second order nonlinearities (3-wave interactions), and examine the behavior of the system, to identify its instability characteristics. 

Sheremet, A., T. Staples, F. Ardhuin, S. Suanez, and B. Fichaut (2014), Observations of large infragravity wave runup at Banneg Island, France, Geophys. Res. Lett., 41, doi:10.1002/2013GL058880.

Longuet-Higgins, M.S. (1967), On the trapping of wave energy round islands, Fluid Mech. 29(4), 781-821.