On the computation of the Benjamin-Feir Index

Recently it has been shown theoretically, numerically and experimentally that the statistical properties (probability density function of wave amplitude and wave height)of long crested surface gravity waves depend not only on steepness but also on the Benjamin-Feir Index (BFI), which is the ratio between wave steepness and spectral bandwidth. The computation of this index requires the estimation of a number of parameters such as the spectral bandwidth and the peak frequency. For a given time series or a wave spectrum those parameters can be calculated using different methods, thus leading to different numerical values of the BFI. We analyze different approaches for computing the BFI and, based on numerical experiments with simulated spectra, we outline a unique robust methodology for its computation.