Rare wave groups

•A new mathematical definition of wave groups is developed from classic Fourier transform theory.•This new formulation is compared with Monte Carlo simulations and physical time series data.•This new definition is independent of spectral type and shape.

A theoretical basis for the occurrence of rare wave groups is developed. The work is not limited to a successive threshold crossing criteria, only that a derived Gaussian process, based on the wave elevation, has a maximum value in a given exposure time. The theory is compared with numerical Monte Carlo simulations in addition to physical oceanographic data. The wave groups, in run length, shape, and amplitude, are shown to be dependent on the wave spectrum and its spectral moments, a prescribed exposure time, and a pre-selected mean wavegroup period.