On the relationship between the energy dissipation rate of surface-breaking waves and oceanic whitecap coverage

Abstract

Wave 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 (Swcap) and the area of whitecap foam per unit area ocean surface (W) is expected, but there is a lack of consensus on what form this relationship should take. Here, mathematical representations of whitecap coverage (W), and growth phase whitecap coverage (Wgrowth) are derived, and an energy-balance approach is used to formulate W and Wgrowth in terms of Swcap. Both W and Wgrowth are found to be linearly proportional to Swcap, 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 Swcap and either W or Wgrowth 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 W measurements to compute Swcap. An estimate of the relative magnitude of Swcap to the rate of energy input from the wind to the waves, Sin, is made. Above wind speeds of about 12 m/s, Sin is largely balanced by Swcap. At lower wind speeds the ratio Swcap/Sin quickly drops below unity with decreasing wind speed. It is proposed that sea state driven variability in both Swcap/Sin and bubble plume penetration depth are significant causes of variation in whitecap coverage datasets and parameterizations.