On the Relationship between the Energy Dissipation Rate of Surface-Breaking Waves and Oceanic Whitecap Coverage

Abstract

AbstractWave breaking is the most important mechanism that leads to the dissipation of oceanic surface wave energy. A relationship between the energy dissipation rate associated with breaking wave whitecaps and the area of whitecap foam per unit area ocean surface is expected, but there is a lack of consensus on what form this relationship should take. Here, mathematical representations of whitecap coverage and growth-phase whitecap coverage are derived, and an energy-balance approach is used to formulate and in terms of . Both and are found to be linearly proportional to but also inversely proportional to the bubble plume penetration depth during active breaking. Since this depth can vary for breaking waves of different scales and slopes, there is likely no unique relationship between and either or as bubble plume penetration depth must also be specified. Whitecap observations from the North Atlantic are used to estimate bubble plume penetration depth as a function of wind speed and then used with measurements to compute . An estimate of the relative magnitude of to the rate of energy input from the wind to the waves is made. Above wind speeds of about 12 m s−1, is largely balanced by . At lower wind speeds the ratio quickly drops below unity with decreasing wind speed. It is proposed that sea-state-driven variability in both and bubble plume penetration depth are significant causes of variation in whitecap coverage datasets and parameterizations.