Breaking Probability for Dominant Waves on the Sea Surface

Abstract

The breaking probability is investigated for the dominant surface waves observed in three geographically diverse natural bodies of water: Lake Washington, the Black Sea, and the Southern Ocean. The breaking probability is taken as the average number of breaking waves passing a fixed point per wave period. The data covered a particularly wide range of dominant wavelengths (3?300 m) and wind speeds (5?20 m s?1). In all cases, the wave breaking events were detected visually. It was found that the traditional approach of relating breaking probability to the wind speed or wave age provided reasonable correlations within individual datasets, but when the diverse datasets are combined, these correlations are significantly degraded. Motivated by the results of recent computational studies of breaking onset in wave groups, the authors investigated the hypothesis that nonlinear hydrodynamic processes associated with wave groups are more fundamental to the process of breaking than previously advocated aerodynamic properties, such as the wind speed or wave age. Further, these computational studies suggest that the significant wave steepness is an appropriate parameter for characterizing the nonlinear group behavior. Based on this approach, analysis of the data revealed that the probability of dominant wave breaking is strongly correlated with the significant wave steepness for the broad range of wave conditions investigated. Of particular interest is a threshold of this parameter below which negligible dominant wave breaking occurs. Once this threshold is exceeded, a near-quadratic dependence of the breaking probability on the significant wave steepness was observed, with a correlation coefficient of 0.78. The inclusion of parameters representing the secondary influence of wind forcing and background current shear improved the correlation only marginally to 0.81. The applicability of the breaking probability dependence found for the dominant waves was investigated for higher-frequency bins up to twice the spectral peak frequency fp. The Black Sea data were used for this analysis, in which shorter breaking wave statistics were also measured. It was found that the maximum of the composite breaking frequency distribution gradually shifts from about 1.6fp for lower values of the peak steepness parameter to fp for higher values of this parameter. The breaking probability in a comparable higher frequency band has a similar dependence on significant steepness to that found for the dominant waves.