The Computation of the Benjamin-Fair Index Based on Wave Measurements at Sea

Modulation instability is the main physical mechanism that leads to the appearance of abnormally high waves on the sea surface, as well as to the formation of a group structure. The parameter characterizing modulation instability is the Benjamin-Fair index (BFI). The paper presents a comparative analysis of two methods for calculating BFI, which is determined by the ratio of wave steepness and spectral bandwidth. The analysis was based on wave measurements carried out in the Black Sea from a stationary oceanographic platform. The first method uses spectral moments to determine the characteristic frequency and spatial scales of waves (BFIm), while the second method uses the peak frequency of the wave spectrum (BFIp). Based on field measurement data, the ranges in which the values of BFIm and BFIp change are determined. Values BFIm vary in the range 0.03–0.28, and values BFIp vary in the range 0.05–1.00. At the same time, changes in the BFI values calculated by the two methods are statistically interconnected; the correlation coefficient is 0.54. The influence of the ratio of the spectral peak frequency and the sampling frequency of wave measurements on the accuracy of calculating the wave steepness and the spectral bandwidth using the spectral moment method is investigated. It is shown that in a situation where the wave peak frequency is 11 times less than the sampling frequency, the error in calculating the spectral bandwidth, caused by the limitation of the upper integration limit when calculating the spectral moments, does not exceed 10%. At the same time, the error in determining the wave steepness is less than 1%.